Shingo Yonezawa

Claire A Marrache-Kikuchi

Klaus Bechgaard

Denis Jérome

Crossover from impurity-controlled to granular superconductivity in (TMTSF) 2 ClO 4

Using a proper cooling procedure, a controllable amount of nonmagnetic structural disorder can be introduced at low temperature in (TMTSF) 2 ClO 4 . Here we performed simultaneous measurements of transport and magnetic properties of (TMTSF) 2 ClO 4 in its normal and superconducting states, while finely covering three orders of magnitude of the cooling rate around the anion ordering temperature. Our result reveals, with increasing density of disorder, the existence of a crossover between homogeneous defect-controlled d-wave superconductivity and granular superconductivity. At slow cooling rates, with small amount of disorder, the evolution of superconducting properties is well described with the Abrikosov-Gorkov theory, providing further confirmation of non-s-wave pairing in this compound. In contrast, at fast cooling rates, zero resistance and diamagnetic shielding are achieved through a randomly distributed network of superconducting puddles embedded in a normal conducting background and interconnected by proximity effect coupling. The temperature dependence of the ac complex susceptibility reveals features typical for a network of granular superconductors. This makes (TMTSF) 2 ClO 4 a model system for granular superconductivity where the grain size and their concentration are tunable within the same sample.

I. INTRODUCTION

Most of the recently discovered so-called "unconventional superconductors," such as the quasi-one-dimensional (Q1D) organic superconductors [START_REF] Jerome | Superconductivity in a synthetic organic conductor (TMTSF) 2 PF 6[END_REF][START_REF] Bechgaard | Zero-Pressure Organic Superconductor: Di-(Tetramethyltetraselenafulvalenium)-Perchlorate [(TMTSF) 2 ClO 4[END_REF], copper oxides [START_REF] Bednorz | Possible high T c superconductivity in the Ba-La-Cu-O system[END_REF], two-dimensional organic superconductors based on bisethylenedithio-tetrathiafulvalene (BEDT-TTF) or related molecules [START_REF] Mckenzie | Similarities between organic and cuprate superconductors[END_REF][START_REF] Kanoda | Electron correlation, metal-insulator transition and superconductivity in quasi-2D organic systems, (ET) 2 X[END_REF][START_REF] Lefebvre | Mott Transition, Antiferromagnetism, and Unconventional Superconductivity in Layered Organic Superconductors[END_REF], and the layered iron pnictides [START_REF] Kamihara | Ironbased layered superconductor La[O 1-x F x ]FeAs (x = 0.05 -0.12with T c = 26 K[END_REF], share a unifying property: they exhibit a general phase diagram where superconductivity has a common border with a magnetically ordered phase. For such superconductors, the stability of superconductivity against nonmagnetic defects provides important information toward understanding of superconducting (SC) properties such as the pairing symmetry. As a particular example, in the ruthenate superconductor Sr 2 RuO 4 [START_REF] Maeno | Superconductivity in a layered perovskite without copper[END_REF], a strong reduction of T c by a small amount of nonmagnetic impurity lends support for triplet p-wave pairing [START_REF] Mackenzie | Extremely Strong Dependence of Superconductivity on Disorder in Sr 2 RuO 4[END_REF]. Since the nonmagnetic impurity effect is still actively debated for systems such as multiband superconductors [START_REF] Hirschfeld | Using gap symmetry and structure to reveal the pairing mechanism in Fe-based superconductors[END_REF] and topological superconductors [START_REF] Michaeli | Spin-Orbit Locking as a Protection Mechanism of the Odd-Parity Superconducting State against Disorder[END_REF][START_REF] Nagai | Robust superconductivity with nodes in the superconducting topological insulator Cu x Bi 2 Se 3 : Zeeman orbital field and nonmagnetic impurities[END_REF], a detailed and controlled investigation of the impurity effect is an important subject.

Q1D organic superconductors are textbook examples of unconventional superconductivity, with the competition between density wave (insulating) and pairing (superconducting) orderings, namely the Peierls and Cooper divergences [START_REF] Bychkov | Possibility of superconductivity type phenomena in a one-dimensional system[END_REF][START_REF] Emery | Theory of the one-dimensional electron gas[END_REF][START_REF] Sólyom | The Fermi gas model of one-dimensional conductors[END_REF]. Reviews can be found in Refs. [16][START_REF] Ishiguro | Organic Superconductors[END_REF][START_REF] Giamarchi | Quantum Physics in One-Dimension[END_REF]. In the case of (TMTSF) 2 PF 6 , a prototype of the (TMTSF) 2 X family, where TMTSF is the tetramethyl-tetrafulvalene electron-donor molecule and X is a monovalent anion, the balance between * yonezawa@scphys.kyoto-u.ac.jp the two possible ground states is controlled by the magnitude of the kinetic coupling between molecular stacks [START_REF] Yamaji | First-order phase transition boundary between superconducting and SDW phases in the bechgaard salts[END_REF][START_REF] Montambaux | Metal-spin-density-wave transition in a quasi-one-dimensional conductor: Pressure and magnetic field effects[END_REF]. Hence, the interplay between Peierls and Cooper channels can be controlled by an applied hydrostatic pressure: Under low pressures, a SDW ground state is stable [START_REF] Jerome | Superconductivity in a synthetic organic conductor (TMTSF) 2 PF 6[END_REF]16] due to the good nesting of the warped Fermi surfaces, whereas superconductivity is stable above ≈9 kbar when antinesting terms become dominant in their dispersion relation.

The only ambient-pressure superconductor in the (TMTSF) 2 X family, namely (TMTSF) 2 ClO 4 , was found shortly after the discovery of (TMTSF) 2 PF 6 [START_REF] Bechgaard | Zero-Pressure Organic Superconductor: Di-(Tetramethyltetraselenafulvalenium)-Perchlorate [(TMTSF) 2 ClO 4[END_REF]. The SC order parameter of the (TMTSF) 2 X family has been thoroughly investigated mainly on (TMTSF) 2 ClO 4 [START_REF] Takigawa | Proton spin relaxation in the superconducting state of (TMTSF) 2 ClO 4[END_REF][START_REF] Belin | Thermal Conductivity of Superconducting (TMTSF) 2 ClO 4 : Evidence for a Nodeless Gap[END_REF][START_REF] Joo | Suppression of superconductivity by non-magnetic disorder in the organic superconductor (TMTSF) 2 (ClO 4 ) (1-x) (ReO 4 ) x[END_REF][START_REF] Joo | Impurity-controlled superconductivity/spin density wave interplay in the organic superconductor: (TMTSF) 2 ClO 4[END_REF][START_REF] Shinagawa | Superconducting State of the Organic Conductor (TMTSF) 2 ClO 4[END_REF][START_REF] Yonezawa | Nodal superconducting order parameter and thermodynamic phase diagram of (TMTSF) 2 ClO 4[END_REF][START_REF] Pratt | Low-Field Superconducting Phase of (TMTSF) 2 ClO 4[END_REF]. Although the debate is not fully settled yet, one of the most plausible scenarios is the magnetic-fluctuation driven nodal d-wave-like pairing, as strongly demonstrated by the field-angle-dependent heat-capacity measurements [START_REF] Yonezawa | Nodal superconducting order parameter and thermodynamic phase diagram of (TMTSF) 2 ClO 4[END_REF][START_REF] Jerome | Novel superconducting phenomena in quasi-one-dimensional Bechgaard salts[END_REF]. Such a possibility has been indeed theoretically proposed even from early days [START_REF] Emery | The mechanisms of organic superconductivity[END_REF][START_REF] Hasegawa | A theory of phase transitions in quasi-one-dimensional electrons[END_REF][START_REF] Bourbonnais | The role of kinetic interchain coupling in Quasi-1D conductors[END_REF][START_REF] Hasegawa | NMR Relaxation Time of the anisotropic superconducting state in quasi-one-dimensional systems[END_REF][START_REF] Bourbonnais | Mechanisms for antiferromagnetism and superconductivity in the bechgaard salts[END_REF]. We note that, within this scenario, the gap nodes are accompanied by nontrivial topological features, as in the case of the nodes in d-wave superconductors [START_REF] Schnyder | Topological surface states in nodal superconductors[END_REF]. Thus (TMTSF) 2 X is a candidate for topological nodal superconductors [START_REF] Yonezawa | Bulk topological superconductors[END_REF], which are of interest in the context of recently developing topological materials science.

The impurity effect on the (TMTSF) 2 X family has been investigated for a long time. The remarkable sensitivity of superconductivity to irradiation [START_REF] Bouffard | Low-temperature metallic state and superconductivity in quasi-one-dimensional organic conductors: pressure and irradiation investigations[END_REF][START_REF] Choi | Effect of radiation damage on the metal-insulator transition and low-temperature transport in the tetramethyltetraselenofulvalinium PF 6 salt [(TMTSF) 2 PF 6[END_REF] has first been considered as a signature for triplet pairing [START_REF] Abrikosov | Superconductivity in a quasi-onedimensional metal with impurities[END_REF]. However, defects introduced by irradiation in a controlled way [START_REF] Zuppirolli | Low Dimensional Conductors and Superconductors[END_REF] can often be magnetic [START_REF] Sanquer | ESR properties of irradiated (TMTSF) 2 ClO 4[END_REF]. Hence, the suppression of superconductivity by irradiation-induced defects must be taken with care since local magnetic impurities can act as strong pair breakers even on s-wave superconductors. A softer way to introduce nonmagnetic impurities in the (TMTSF) 2 X series is to produce a solid solution of isoelectronic anions. The solid solution procedure of (TMTSF) 2 ClO 4 , replacing with the tetrahedral anion ClO 4 with ReO 4 , leads to a suppression of T c due to genuine nonmagnetic impurities [START_REF] Joo | Suppression of superconductivity by non-magnetic disorder in the organic superconductor (TMTSF) 2 (ClO 4 ) (1-x) (ReO 4 ) x[END_REF][START_REF] Tomić | Influence of the disorder potential of the anions on the ground state of the organic alloy (TMTSF) 2 (ClO 4 ) 1-x (ReO 4 ) x[END_REF]. These results provided strong evidence for the realization of a non-s-wave pairing state in (TMTSF) 2 X.

The ambient-pressure superconductor (TMTSF) 2 ClO 4 provides another unique means to control its unconventional superconductivity by disorder. This material exhibits superconductivity below T c ∼ 1.3 K if the sample is cooled slowly [START_REF] Bechgaard | Zero-Pressure Organic Superconductor: Di-(Tetramethyltetraselenafulvalenium)-Perchlorate [(TMTSF) 2 ClO 4[END_REF][START_REF] Garoche | Specific heat measurements of organic superconductivity in (TMTSF) 2 ClO 4[END_REF][START_REF] Schwenk | Meissner anisotropy in deuterated (TMTSF) 2 ClO 4[END_REF]. However, if the sample is cooled fast enough in the vicinity of 25 K, (TMTSF) 2 ClO 4 undergoes a spin-densitywave (SDW) transition towards an insulating ground state below 4-5 K [START_REF] Tomić | EPR and electrical conductivity of the organic superconductor di-tetramethyltetraselenafulvalenium-perchlorate, (TMTSF) 2 ClO 4 and a metastable magnetic state obtained by fast cooling[END_REF][START_REF] Ishiguro | Superconductivity and metal-nonmetal transitions in (TMTSF) 2 ClO 4[END_REF][START_REF] Takahashi | Observation of a magnetic state in the organic superconductor (TMTSF) 2 ClO 4 : influence of the cooling rate[END_REF]. This significant feature of (TMTSF) 2 ClO 4 is actually related to the noncentrosymmetric nature of the tetrahedral ClO 4 anion located on the inversion centers of the full structure. At high temperature, the thermal motion of the ClO 4 orientation makes it possible to preserve inversion symmetry on average since ClO 4 occupies randomly one or the other inversion-symmetry-related orientations. The structural disorder between two possible orientations no longer persists at low temperatures below T AO = 24 K, because an entropy gain due to the reduction of degrees of freedom triggers the anion ordering below this temperature.

The ordering transition has been studied by several techniques. In particular, diffuse x-ray work has shown that, while ClO 4 anions adopt a uniform orientation along a and c axes, they alternate along b [START_REF] Pouget | X-ray evidence of a structural phase transition in di-tetramethyltetraselenafulvalenium perchlorate [(TMTSF) 2 ClO 4 ], pristine and slightly doped[END_REF] when the crystal is cooled very slowly through T AO , to reach the so-called relaxed state [START_REF] Tomić | EPR and electrical conductivity of the organic superconductor di-tetramethyltetraselenafulvalenium-perchlorate, (TMTSF) 2 ClO 4 and a metastable magnetic state obtained by fast cooling[END_REF][START_REF] Gubser | Resistive and magnetic susceptibility transitions in superconducting (TMTSF) 2 ClO 4[END_REF]. Since the dynamics of the anion orientation was shown to be slow [START_REF] Tomić | EPR and electrical conductivity of the organic superconductor di-tetramethyltetraselenafulvalenium-perchlorate, (TMTSF) 2 ClO 4 and a metastable magnetic state obtained by fast cooling[END_REF][START_REF] Pouget | Structural aspects of the bechgaard and fabre salts: An update[END_REF][START_REF] Schwenk | Resistivity of the organic superconductor ditetramethyltetraselenafulvalenium perchlorate, (TMTSF) 2 ClO 4 , in its relaxed, quenched, and intermediate state[END_REF], fast cooling (i.e., cooling much faster than 17 K/min by quenching) enables us to retain anion disorder even below T AO in a metastable state with a single pair of Fermi-surface sheets resembling closely that of (TMTSF) 2 PF 6 . Consequently, the good nesting of the single-pair Fermi surfaces at ±k F for the quenched material stabilizes the insulating SDW state. In contrast, with the slow enough cooling rate, the alternating order of the anions along the b axis leads to a folding of the Fermi surface, opening a gap at ±b * /4 and resulting in doubling of the Fermi-surface sheets. This folding suppresses the SDW state by disturbing the Fermi-surface nesting, instead allowing superconductivity to appear below 1.2-1.3 K.

Although the two extreme situations, namely the relaxed and quenched states, with SC and SDW ground states respectively, have been fairly extensively studied from the early days, only limited studies have been published for the intermediate cooling-rate regime, where superconductivity is moderately suppressed [START_REF] Joo | Suppression of superconductivity by non-magnetic disorder in the organic superconductor (TMTSF) 2 (ClO 4 ) (1-x) (ReO 4 ) x[END_REF][START_REF] Garoche | Influence of the Cooling Rate on the Superconducting Properties of the Organic Solid Di-Tetramethyltetraselenafulvalenium-Perchlorate, (TMTSF) 2 ClO 4[END_REF][START_REF] Matsunaga | Anion disorder and two-dimensionality in the superconducting and SDW states of (TMTSF) 2 ClO 4[END_REF]. High-resolution x-ray investigations [START_REF] Kagoshima | Quenching effect of the anion ordering in the organic superconductor (TMTSF) 2 ClO 4 : An X-ray study[END_REF][START_REF] Moret | X-ray study of the anion ordering transition in di(tetramethyltetraselenafulvalen)-ium perchlorate (TMTSF) 2 ClO 4 : quenching and irradiation effects[END_REF][START_REF] Pouget | High resolution x-ray scattering study of the anion ordering phase transition of (TMTSF) 2 ClO 4[END_REF] have shown that samples in the intermediate coolingrate regime exhibit a peculiar anion ordering, in which domains with ordered anions of finite size are embedded in a disordered background. In the regime up to 5 K/min, high-resolution x-ray-diffraction measurements have determined both the volume fraction of ordered anions and the average size of ordered domains [START_REF] Pouget | High resolution x-ray scattering study of the anion ordering phase transition of (TMTSF) 2 ClO 4[END_REF].

Here, we report on the resistivity ρ c * along the least conducting c * axis [START_REF]investigation: Measurements of transport along the a or b axes are often perturbed by sample cracks occurring during cooling[END_REF] simultaneously measured with the ac susceptibility χ ac under carefully controlled cooling across T AO , in order to address the changes of properties of the normal and SC phases by the increase of disorder. With the experimental settings especially designed for the present investigation, we explored the cooling rate around T AO from 0.02 to 18 K/min with fine steps, nearly covering three orders of magnitude. We believe that the present study is one of the most careful impurity-effect studies in any unconventional superconductor, because we control the amount of the defects in identical samples, in a reversible way, and with very fine intervals. From our transport and magnetic measurements, we reveal that the intermediate cooling-rate regime of (TMTSF) 2 ClO 4 cannot be considered as a state exhibiting an average anion order/disorder evolving according to the cooling rate, but instead as a state comprising a cooling-rate-dependent volume fraction of well-ordered domains with the rest of the volume occupied by disordered anions. We also study the evolution of the onset T c of χ ac (T ) and that of ρ c * (T ). We note that T c under fast cooling has been studied using a time-dependent Ginzburg-Landau theory [START_REF] Haddad | Inhomogeneous superconductivity in organic conductors: the role of disorder and magnetic field[END_REF]. However, this earlier study was only based on transport properties.

II. EXPERIMENT

For the present study, two single crystals of (TMTSF) 2 ClO 4 from the same batch grown with an electrocrystallization method have been used. Simultaneous transport and susceptibility measurements have been performed on one sample (no. 1; with the size of ≈2.4 × 0.7 × 0.1 mm 3 ). The results thus obtained will constitute the core of the paper. With a slightly different setup with an additional thermometer directly attached beneath the sample, the ac susceptibility was measured for another sample (no. 2; with the size of ≈1.5 × 0.4 × 0.1 mm 3 ). Results for sample no. 2 and details of the measurement setup will be given in the Supplemental Material [58].

For both experiments, the samples were cooled down with a commercial cryostat (Quantum Design; Physical Property Measurement System (PPMS)) with an adiabatic demagnetization refrigerator (ADR) option. In order to control the disorder in the ClO 4 orientation within a sample, we first raised the temperature to 50 K and kept it for more than 1 h to fully randomize the anion orientations. The sample was first cooled in a controlled way down to 10 K using the temperature controller of the PPMS. After further cooling down to 1.8 K, the temperature was kept at 1.8 K and the dc magnetic field of 2.5 T applied. The sample chamber was then evacuated with a turbomolecular pump to achieve high-vacuum adiabatic condition. Then the magnetic field was turned off to reach ∼0.1 K, and the transport or magnetic data were collected during warming. See Fig. S2 of the Supplemental Material [58] as well as Fig. 8 of Ref. [START_REF] Yonezawa | Compact AC susceptometer for fast sample characterization down to 0.1 K[END_REF] for details of the cooling sequence of the ADR option. We should comment here that the sample was always in the field-cooled condition although all measurements were performed in zero dc field.

The resistivity of the sample was measured with the resistivity option of the PPMS. The current of 10 μA (1 mA for measurements at high temperatures) along the c * -axis direction was reversed to cancel the thermoelectric voltage. The ac susceptibility was measured with an ac field of ∼0.17-Oe rms at 3011 Hz (sample no. 1) or 887 Hz (sample no. 2) parallel to the c * axis, using a conventional mutual inductance method with a miniature susceptometer [START_REF] Yonezawa | Compact AC susceptometer for fast sample characterization down to 0.1 K[END_REF] fitting into the ADR option of the PPMS. The output signal of the susceptometer was measured using a lock-in amplifier (Stanford Research Systems, SR830). To correct a small mixing of the real and imaginary parts in the lock-in amplifier signal, an additional phase factor θ is adopted: χ ac ∝ V y cos(θ ) + V x sin(θ ) and χ ac ∝ V x cos(θ ) -V y sin(θ ), where V x and V y are changes in the reading of the lock-in amplifier. The value of θ is chosen as θ = 1.5 • and 8.5 • for samples no. 1 and no. 2, respectively, so that χ ac = 0 for T > T c and T → 0 for the 0.020-K/min data.

III. EXPERIMENTAL DATA

Figure 1(a) displays the temperature dependence of ρ c * up to 50 K upon cooling at 0.02 K/min. A clear anomaly at T AO = 24.5 K is observed. By comparing the fittings using polynomial functions to the ρ c * (T ) data above 25 K and below 12 K, we can notice that ρ c * (T ) jumps by ρ c * ≈ 0.23 cm, as indicated with the red arrow. This resistance drop reflects the decrease of the elastic scattering due to anion ordering.

Figures 1(b)-1(d) show the evolutions of the imaginary and real parts of the ac susceptibility [ χ ac (T ) and χ ac (T ) respectively] and of ρ c * with the cooling rate. All three quantities show that the sample cooled down at 0.02 K/min exhibits superconductivity below T c (0.02 K/min) ∼ 1.3 K. The superconducting features were progressively weakened upon increasing the cooling rate. We comment that the small upturn in χ ac (T ) and χ ac (T ) below 0.3 K is probably extrinsic, since such behavior was not observed in another sample (sample no. 2; see the Supplemental Material [58]). Perhaps the upturn could be attributed to the small background signal originating from the attached electrical leads and silver paint used for the resistivity measurements.

Based on these raw data, the cooling-rate dependence of various superconducting properties can be examined: T cχ is defined from the onset of χ ac (T ) and T cρ by the peak in the second derivative of ρ c * (T ). The zero-resistivity temperature T c,ρ=0 is the temperature where a linear extrapolation of the steep transition in ρ c * (T ) reaches zero. We found that T c,ρ=0 is approximately equal to T cχ . The evolutions of the different T c 's with the cooling rate are given in Fig. 2(a). The small difference in T cχ for samples no. 1 and no. 2 can be attributed to different ordering configurations which can exist even in samples of the same batch. As noticed in previous x-ray studies [START_REF] Pouget | Structural aspects of the bechgaard and fabre salts: An update[END_REF], no perfect long-range order of anions exists even in the slowest cooled samples. Let us moreover note that T cχ is not a thermodynamic quantity and, as we will later see, derives from a specific phase distribution within the sample.

Next, we focus on the change in the shielded volume fraction. Since the samples cooled at rates smaller than 0.02 K/min are fully in the relaxed-state regime and are expected to display perfect diamagnetism at low temperatures, we will consider this cooling rate as a reference. Figure 2(b) displays the cooling-rate dependence of the relative SC shielded volume fraction v shield , which is obtained from the zero-temperature extrapolation of χ ac (T ) divided by its value for 0.02 K/min: (c). The inset presents ρ c * (T ) on a broader temperature range for 0.020, 0.52, 2.5, 7.6, and 18 K/min. For the 0.020-and 18-K/min data, the results of the fitting, performed using the procedure explained in the text, are presented with the broken curves.

v shield ≡ | χ ac (T → 0)|/| χ ac (T → 0, 0.02 K/min)|.
The zero-temperature extrapolation of χ ac averaged on the 0.1-0.3-K range is also given in Fig. 2(d). We will discuss the meaning of this quantity in Sec. IV C.

The normal-state residual resistivity ρ c * 0 presented in Fig. 2(c) is obtained by fitting the relation ρ c * (T ) = ρ c * 0 + AT + BT 2 to the data between 6 and 12 K [see the inset of Fig. 1(d), as well as Fig. 1(a)]. We chose this fitting range to avoid the influence of the downturn of ρ c * (T ), quite prominent below 5 K especially in fast cooled samples. We note that the low-temperature downturn in ρ c * (T ) is ascribed to the sliding of SDW fluctuations [START_REF] Auban-Senzier | Fluctuating spin density wave conduction in (TMTSF) 2 X organic superconductors[END_REF] and will be examined in detail in a forthcoming publication. Such a fitting procedure is justified by previous extensive investigations ascribing scattering against spin fluctuations as the source of the dominant linear temperature dependence of the resistivity [START_REF] Doiron-Leyraud | Correlation between linear resistivity and Tc in the Bechgaard salts and the pnictide superconductor Ba(Fe 1-x Co x ) 2 As 2[END_REF][START_REF] Doiron-Leyraud | Linear-T scattering and pairing from antiferromagnetic fluctuations in the (TMTSF) 2 X organic superconductors[END_REF][START_REF] Sedeki | Extended quantum criticality of low-dimensional superconductors near a spindensity-wave instability[END_REF].

Systematic decreases of all characteristic temperatures are observed with increasing cooling rates, as expected when disorder is increased. However, although the decrease of T cρ levels off at a value of ≈1.25-1.30 K above 1 K/min, T cχ reveals a faster decrease above the same cooling rate. The shielded volume fraction for T → 0 steadily decreases with increasing cooling rate. Concomitantly, we notice an acceleration in the decrease of v shield above 1 K/min. No more than 50% of the sample volume is shielded at 18 K/min.

Explaining the difference in behavior between T cρ and T cχ is the major issue of the present work and will underline the interpretation proposed in Sec. IV C.

IV. DISCUSSION

A. Determination of the anion-ordered volume

So far, quantities such as T c , ρ c * 0 , or v shield were plotted against the cooling rate in Fig. 2. Since the amount of impurities introduced by the cooling may depend on samples, as well as on the details of the cooling procedure, the physical picture is better conveyed when representing T c and v shield as functions of the residual resistivity, as shown in Figs. 3(a) and 3(b). These figures reveal two regimes: below around ρ c 0 ≈ 0.05 cm (corresponding to the cooling rate of ≈1 K/min), T c , by all definitions, exhibits a steady decrease with increasing cooling rate whereas v shield stays ∼100%. However, above this threshold, T cρ becomes nearly independent of the cooling rate, whereas v shield clearly decreases. This fact suggests a possible change in the sample behavior. Particularly, the substantial decrease in v shield indicates that rapid cooling is no longer equivalent to creating local defects, and instead promotes the formation of clusters of disordered regions.

Expecting the picture of local defects to be no longer adequate at large cooling rates, it is important to derive the actual volume fraction in which bulk superconductivity develops since, in an inhomogeneous superconductor, it could be smaller than the shielded volume.

This volume fraction can be reached viewing the normalstate sample as a two-component composite conductor with resistivities ρ Min and ρ Max for ordered and disordered regions respectively. Such a problem of the mixture between two conductors of different conductivities is formally identical [START_REF] Creyssels | Pressure dependence of the electrical transport in granular materials[END_REF] FIG. 4. Volume fraction of the anion-ordered domain derived from resistivity (p, obtained from the effective-medium theory in this work, purple circles) and from high-resolution x rays (v XRD , from Ref. [START_REF] Pouget | High resolution x-ray scattering study of the anion ordering phase transition of (TMTSF) 2 ClO 4[END_REF], blue crosses), compared with the shielded fraction evaluated from the ac susceptibility (v shield , black squares). The broken arrow shows the estimate for the ordered volume from x-ray measurements at 100 K/min [START_REF] Kagoshima | Quenching effect of the anion ordering in the organic superconductor (TMTSF) 2 ClO 4 : An X-ray study[END_REF].

to the effective dielectric permeability of a two-component dielectric medium treated by Landau and Lifshitz [START_REF] Landau | Electrodynamical of Continous Media[END_REF]. The mixed conductor can thus be described at the lowest order by a three-dimensional (3D) effective-medium theory with an effective conductivity σ eff = 1/ρ eff , which can be derived as

1/ρ eff = [p(1/ρ Min ) 1/3 + (1 -p)(1/ρ Max ) 1/3 ] 3 , ( 1
)
where p is the volume fraction of the anion-ordered domain.

The resistivity in the ordered region ρ Min is given by ρ c * 0 for 0.02 K/min, based on the assumption that the system at the lowest cooling rate provides ρ Min . The data in Fig. 1 lead to ρ Min = 0.030 cm. For the disordered resistivity ρ Max , the change in the elastic contribution ρ c * across T AO , coming from the frozen anion disorder, must be added to ρ Min , i.e., ρ Max = ρ Min + ρ c * = 0.26 cm [66]. Figure 4 compares the ordered volume fraction p obtained from Eq. ( 1) with the shielded volume v shield and with the ordered volume fraction v XRD derived from x-ray measurements (Ref. [START_REF] Pouget | High resolution x-ray scattering study of the anion ordering phase transition of (TMTSF) 2 ClO 4[END_REF]). Considering the uncertainties in the x-ray determination, there is a fair agreement between v XRD and p, particularly in the fast-cooling regime. p obtained at high cooling rates is also of the same order as v XRD at even higher disorder (broken arrow on Fig. 4). Both p and v XRD reflect the size of the ordered domains, which can reasonably be assumed to be SC. In contrast, v shield measures the shielded volume fraction. Obviously, p and v XRD are always smaller than v shield : in particular, at the highest cooling rate achieved in this study, v shield is of about 50%, whereas p is reduced down to 36%. This fact can be seen as the signature of persistent shielding currents penetrating non-SC regions. The derivation of the relation between the ordered volume fraction and the cooling rate (Fig. 4) enables us to show how T cρ and the residual resistivity evolve against the disordered volume fraction; see Fig. 5. This figure reveals the occurrence of a regime change for both T cρ and ρ c * 0 around 30% disordered volume fraction. This feature will be studied more extensively in the following sections.

B. Local defect regime

Let us call the low cooling rate regime ( 1 K/min) "regime I," where both T cρ and T cχ decrease linearly with ρ c * 0 [i.e., in the range ρ c * 0 0.05 cm; see Fig. 3(a)]. In this regime, ρ c * 0 then is a good measure of disorder. Hence the usual analysis for the dependence of T c on nonmagnetic disorder in d-wave superconductors [START_REF] Sun | Impurity effects in d-wave superconductors[END_REF][START_REF] Suzumura | Thermodynamic properties of impure anisotropic quasi-one-dimensional superconductors[END_REF] can be undertaken.

The Abrikosov-Gorkov theory [START_REF] Abrikosov | Contribution to the theory of superconducting alloys with paramagnetic impurities[END_REF] (AG) extended to nonmagnetic impurities in the case of non-s-wave superconductivity gives ln

T c0 T c = 1 2 + αT c0 2πT c - 1 2 , ( 2
)
where (x) is the digamma function, α = h/2τ k B T c0 is the depairing parameter, τ is the elastic scattering time, and T c0 is the limit of T c in the absence of any scattering (i.e., the limit of ρ c * 0 → 0). The fit of T c derived from Eq. ( 2) to the data is presented in Fig. 3(a). Clearly, T cρ is well fitted in the slowcooling (small ρ c * 0 ) regime. This fact provides firm evidence that the superconductivity of (TMTSF) 2 ClO 4 is of non-s-wave nature, and is consistent with previous works [START_REF] Joo | Suppression of superconductivity by non-magnetic disorder in the organic superconductor (TMTSF) 2 (ClO 4 ) (1-x) (ReO 4 ) x[END_REF][START_REF] Joo | Impurity-controlled superconductivity/spin density wave interplay in the organic superconductor: (TMTSF) 2 ClO 4[END_REF]. If driven by local defects only, the critical value of the residual resistivity for the suppression of superconductivity would read ρ c * 0c = 0.24 cm from the fit to T cρ shown in the inset of Fig. 3(a). This value is practically identical to the critical resistivity ρ c * 0c = 0.23 cm obtained for the suppression of superconductivity on the ClO 4 -side of the (TMTSF) 2 (ClO 4 ) (1-x) (ReO 4 ) x solid solution due to the presence of nonmagnetic ReO 4 anions [START_REF] Jerome | Novel superconducting phenomena in quasi-one-dimensional Bechgaard salts[END_REF]. This gives additional confidence in the fact that, in regime I, the destruction of superconductivity can be explained by the effect of local defects.

The nature of disorder in the present situation of an anion misorientation is quite different from the disorder in a solid solution [START_REF] Joo | Impurity-controlled superconductivity/spin density wave interplay in the organic superconductor: (TMTSF) 2 ClO 4[END_REF]. The anion misorientation leads to disorder of the local electronic structures. Hence, anions, to be active scattering centers, must form large enough clusters exhibiting a local electronic structure (the single sheet Fermi surface at ±k F ) differing appreciably from the double-sheet Fermisurface structure in the ordered regions [START_REF] Alemany | Electronic structure and anion ordering in (TMTSF) 2 ClO 4 and (TMTSF) 2 NO 3 : A first-principles study[END_REF]. Such a condition requires the broadening of the Fermi surface due to a finite size of clusters to be kept at minimum, leading in turn to be at least 50 unit cells along the a axis [71].

The next task at hand is the derivation of the elastic mean free path for the best ordered sample. According to magnetotransport data, we have 9 × 10 -12 sec as the value for τ at the liquid-helium temperature in the best-ordered situation [START_REF]According to the transport data displaying T c vs ρ c * 0 , the critical scattering rate, τ -1 c =[END_REF], leading in turn to a corresponding mean free path l 0 along the a axis [73] of 1620 nm, taking the a-axis Fermi velocity of v Fa = 1.8 × 10 7 cm s -1 . Such an estimate for the mean free path is also in fair agreement with previous transport results, namely l 0 = 1400 nm [START_REF] Tomić | Non-Ohmic Electrical Transport in the Spin-Density-Wave State of Tetramethyltetraselenafulvalinium Nitrate[END_REF]. From the fitting of the AG theory to T cρ in regime I, the average mean free path at the border of regime I is obtained as l = 972 nm at 1p ∼ 0.3. Since T cρ is nearly constant beyond this regime, l is reasonably assumed to be invariant, on average, for 1p > 0.3.

Furthermore, as already explained, the extrapolation of the AG formalism [inset of Fig 3(a)] leads to the critical value ρ c * 0c = 0.24 cm, which is eight times larger than ρ Min . Thus, the critical mean free path l c corresponding to ρ c * 0c is given by l c = l 0 /8 = 202 nm. This is in good agreement with the critical mean free path l c,d-wave = πξ 0 ∼ 220 nm expected for the suppression of d-wave superconductivity [START_REF] Sun | Impurity effects in d-wave superconductors[END_REF], given the measured SC coherence length along the a axis, ξ 0a = 70 nm [START_REF] Murata | Upper critical field of the anisotropic organic superconductors, (TMTSF) 2 CIO 4[END_REF].

We comment here on the width of the superconducting transition. We claim that a broad distribution of the scattering length provides in turn a distribution of T c . Indeed, it has been reported that, even in the ordered phase achieved by very slow cooling, in which ClO 4 anions are ordered in one of their two possible ordering patterns, the domain size is largely distributed [START_REF] Pouget | Structural aspects of the bechgaard and fabre salts: An update[END_REF]. This is also supported by the fact that (TMTSF) 2 ClO 4 ordinarily exhibits a broader superconducting transition than the pressure-induced superconductor (TMTSF) 2 PF 6 , which does not have any anion disorder because the PF 6 anion is a centrosymmetric anion. Moreover, as analyzed above using the AG model, scattering centers in regime I are small-sized disordered clusters. It is reasonable to assume that these clusters nucleate on the walls between ordered domains, because disorder ordinarily tends to develop in the vicinity of preexisting disorder, namely the domain walls in our case. Then, the somewhat broad transition and the double-transition-like feature for our slowly cooled data (e.g., 0.02 K/min) can be attributed to such anion disorder remaining even under slow cooling. In addition, the sample can contain microcracks, which are often formed in organic crystals during cooling due to thermal-contraction strain, and such microcracks can also contribute to the broadness of the transition, by modulating T c and/or by introducing additional weak-links within the sample. In sample no. 1, we indeed observed a few small jumps in the temperature dependence of resistivity from room temperature to the lowest temperature. Such jumps indicate formation of a small number of microcracks.

C. Evidences for a granular behavior

Let us now call the higher cooling-rate regime "regime II," for which ρ c * 0 > 0.05 cm and 1p 0.3. In this regime, T cρ is nearly constant (T cρ = 1.27 ± 0.03 K), whereas the width of the resistive transition, measured by T cρ -T c,ρ=0 , increases as the cooling rate increases and the system becomes more and more disordered. In this regime, the macroscopic SC coherence is weaker than what would be expected if superconductivity was controlled by local defects only.

In this section, we will demonstrate that this behavior can be interpreted as a consequence of granular superconductivity: SC puddles, consisting of an assembly of grains where ClO 4 anions are ordered along one of the ordering patterns (updown-up-down ... or down-up-down-up ...; labeled as A or B, respectively) [START_REF] Pouget | Structural aspects of the bechgaard and fabre salts: An update[END_REF], are distributed within a metallic background consisting of anion-disordered regions.

The progressive establishment of superconductivity in regime II resembles in several respects the situations observed in the studies of superconductivity in 3D granular compounds [START_REF] Oda | The Meissner effect of polysulfur nitride, (SN) x[END_REF] and in 2D hybrid superconductor-normalmetal-superconductor arrays [START_REF] Deutscher | Percolation description of granular superconductors[END_REF][START_REF] Lobb | Theoretical interpretation of resistive transition data from arrays of superconducting weak links[END_REF][START_REF] Eley | Approaching zero-temperature metallic states in mesoscopic superconductor-normal-superconductor arrays[END_REF]: superconductivity first appears in disconnected grains which couple via the proximity (or Josephson) effect at lower temperatures.

The system considered in this work differs from other granular materials [START_REF] Oda | The Meissner effect of polysulfur nitride, (SN) x[END_REF] insofar as, as we will see, the averaged puddle size is larger than the SC coherence length (the averaged coherence length within the ab plane is ξ 0 = 45 nm; from the upper critical field measurements [START_REF] Murata | Upper critical field of the anisotropic organic superconductors, (TMTSF) 2 CIO 4[END_REF], ξ were evaluated to be 70, 30, and 2 nm along the a, b, and c axes, respectively; and the averaged ξ 0 mentioned here is evaluated using the geometrical mean √ ξ a ξ b ), but is smaller than the penetration depth. Thus, bulk superconductivity is first established within each puddle while cooling. Moreover, there is a strong coupling between neighboring puddles since the interpuddle background (disordered regions) is metallic, albeit with a resistivity (ρ Max = 0.26 cm) about ten times larger than the puddle normal resistivity (ρ Min = 0.030 cm) (see Sec. IV A). Let us emphasize that, in the present system, the grain size is tunable and solely governed by the cooling rate using a single sample.

Thus, T cρ corresponds to the temperature at which superconductivity begins to appear within each puddle. It is governed by the puddle size L. Although the puddles probably have a broad distribution in size, an estimate of the upper limit of L can be derived from the AG approach. Assuming that the electronic mean free path l is limited by L, one then obtains l L = 970 nm. Such a large puddle size implies that they are composed of an equal weight of domains A and B, whose individual dimensions are of the order of 39 nm at 5 K/min, according to direct x-ray measurements [START_REF] Pouget | High resolution x-ray scattering study of the anion ordering phase transition of (TMTSF) 2 ClO 4[END_REF]. However, let us keep in mind that this estimated L reflects the size of the largest puddles, which have the highest T cρ .

A close look at the shape of the resistive transition shown in Fig. 1(d) reveals that it takes place in two stages (particularly visible on the run at 18 K/min). First, the resistance drops by a factor of about 2 before leveling off and giving rise to a second drop whose long tail ends at around T cχ . The temperature width of the first transition T 1 is analogous to the one measured in regime I [ T 1 (T cρ -T cχ )| regime I 0.2 K]. It seems natural to ascribe the first drop to the onset of superconductivity in individual puddles, T 1 reflecting the distribution in the puddles size. The second resistive drop can then be attributed to the progressive establishment of SC coherence over the whole sample: the SC puddles progressively couple through proximity effect to form SC clusters. Let us also note that the value 1p = 0.3, at which regime II begins, is actually quite close to the percolation threshold for site percolation in a 3D cubic lattice [START_REF] Kirkpatrick | Percolation and conduction[END_REF][START_REF] Stauffer | Introduction to Percolation Theory[END_REF].

Given the current structural knowledge on this system [START_REF] Pouget | Structural aspects of the bechgaard and fabre salts: An update[END_REF][START_REF] Pouget | High resolution x-ray scattering study of the anion ordering phase transition of (TMTSF) 2 ClO 4[END_REF], it is difficult to assess the shape and individual size of the SC puddles. However, the nearly constant value of T 1 signifies that there is little change in the puddles' size distribution in regime II, at least before the interpuddle coupling sets in. This assumption is also supported by x-ray data [START_REF] Pouget | Structural aspects of the bechgaard and fabre salts: An update[END_REF]. The decrease of the ordered volume fraction p with the cooling rate therefore must be related to an increase of the average interpuddle distance d. The typical value of d can be crudely approximated assuming spherical puddles forming a simple cubic lattice: p = [(4π/3)(L/2) 3 ]/(L + d) 3 . For example, spheres of diameter L = 970 nm lead to d = 130 nm at p = 0.36.

We here would like to comment on the distribution of the interpuddle distance d. Although we assumed in the above analysis that d is the same for all puddles, we do not think that the actual distribution of d is so sharp. Indeed, when this is the case, the final resistance drop would be much sharper, as observed in, e.g., Ref. [START_REF] Eley | Approaching zero-temperature metallic states in mesoscopic superconductor-normal-superconductor arrays[END_REF]. In the other limit, when there is a wide distribution in d, the final drop would be much broader and illdefined [START_REF] Allain | Electrical control of the superconducting-to-insulating transition in graphene-metal hybrids[END_REF]. Thus, the actual d distribution in (TMTSF) 2 ClO 4 is in a somewhat intermediate situation between the two limits. Nevertheless, we continue to use the constant-d assumption, which is the simplest model to capture the physics behind, in the model calculation and analysis below.

Once superconductivity of individual puddles is established, further cooling enables interpuddle phase coherence via proximity effect through the normal metallic region in between, in a somewhat similar manner to the behavior of Nb islands on Au [START_REF] Eley | Approaching zero-temperature metallic states in mesoscopic superconductor-normal-superconductor arrays[END_REF]. Macroscopic coherence is then reached when the first percolating path connects one end of the sample to the other. For phase coherence to be established between neighboring puddles, the thermal energy needs to be smaller than the proximity effect energy [START_REF] Lobb | Theoretical interpretation of resistive transition data from arrays of superconducting weak links[END_REF][START_REF] Eley | Approaching zero-temperature metallic states in mesoscopic superconductor-normal-superconductor arrays[END_REF][START_REF] Likharev | Superconducting weak links[END_REF] for the local SNS junction:

k B T E J = hI c
2e where E J is the Josephson energy, and I c is the Josephson current running between neighboring puddles. Using the expression for I c in SNS junctions given by the Usadel equations in the diluted limit [START_REF] Likharev | Superconducting weak links[END_REF][START_REF] Tinkham | Introduction to Superconductivity[END_REF], one determines the temperature T cχ at which the macroscopic coherence is established:

T cχ = 2 h πe 2 k 2 B 2 0 (T cχ ) T cχ A ρ N 1 ξ N (T cχ ) e -[d/ξ N (T cχ )] , (3)
where ρ N is the resistivity of the normal metallic regions (N) and should be close to ρ Max in our case, A is the averaged section of the junctions, 0 is the SC gap in each puddle:

2 0 (T ) = 8π 2 7ζ (3) k 2 B T 2 cρ 1 - T T cρ (4)
for T close to T cρ , and ζ (3) 1.202. In the Usadel equations ξ N , the normal-state coherence length in the N region, is determined by the dirty limit:

ξ N (T ) = 1 3 hv F k B T l. ( 5
)
Notice that the clean-limit coherence length ξ 0 N = hv F /kT is much larger than ξ N , d, and l ∼ (ρ Min /ρ N )l 0 ∼ (ρ Min /ρ Max )l 0 ∼ 190 nm in our case (for example, ξ 0 N = 1400 nm and ξ N = 290 nm at 1 K) and thus the dirty-limit treatment is justified. Combining Eqs. ( 3)-( 5), the relation between T cρ and T cχ can be expressed as

T cχ = C T cχ 1 - T cχ T cρ e -[d(p) √ T cχ /α] , (6)
where C and α are constants. This equation can be numerically solved to analyze the data.

Let us now compare this expression to our experimental results in Fig. 6. Assuming d(p) for the model of spherical puddles forming a simple cubic lattice, the observed evolution of T cχ with p is compatible with that evaluated from Eq. ( 6) (the red curve in Fig. 6). The fitting parameters obtained are α = 100 nm/K 1/2 and C = 5.2 K 3/2 . The value of α in turns gives ξ N = α/ √ T = 120 nm at 0.75 K. This value is in reasonable agreement with what is expected in the disordered region [START_REF]In disordered regions, l a 162 nm, l b 16 nm, and l c 8 nm, so that ξ[END_REF]. The fitting result C 5.2 K 3/2 also compares favorably with its theoretical estimate: assuming A ∼ L 2 ∼ 9.4 × 10 -13 m 2 , v F = 1.8 × 10 5 m/s, l = 190 nm, and T cρ = 1.27 K, we obtain C theo 49 K 3/2 . Considering the randomness in the local distribution of puddles size, of their shape, as well as of the interpuddle distance that is not taken into consideration in our very crude model, C from experiment and theory agree reasonably with each other.

A second argument for this granular scenario comes from a previous specific-heat study performed on a sample cooled at the rate of 10 K/min [START_REF] Garoche | Influence of the Cooling Rate on the Superconducting Properties of the Organic Solid Di-Tetramethyltetraselenafulvalenium-Perchlorate, (TMTSF) 2 ClO 4[END_REF] (corresponding to 1p = 57%; see Fig. 4). This study revealed a broad SC anomaly starting around 1.1 K and reaching a maximum around 0.85 K. This temperature for the maximum specific heat matches T cχ , whereas the onset of the broad transition roughly corresponds to the border between the light-blue and light-red regions in Fig. 6, namely the temperature domain where the pair condensation begins to be significant thermodynamically speaking. Furthermore, specific-heat data have revealed that the entropy involved in the SC pairing of this sample cooled at 10 K/min [START_REF] Garoche | Influence of the Cooling Rate on the Superconducting Properties of the Organic Solid Di-Tetramethyltetraselenafulvalenium-Perchlorate, (TMTSF) 2 ClO 4[END_REF] is only 50 ± 10% of the total electronic specific heat. This feature is in fair agreement with the ≈40% value for the bulk SC volume fraction derived in Fig. 4. These agreements provide additional support for our scenario. As demonstrated above, the proximity effect together with percolation represent a reasonable approach for understanding the development of the superconducting state in regime II. FIG. 6. Dependencies of T cρ (purple circles) and T cχ (blue circles) on the disordered volume fraction 1p for sample no. 1. Note that T cχ is practically equivalent to T c,ρ=0 . For comparison, we plot T c from the specific-heat study [START_REF] Garoche | Influence of the Cooling Rate on the Superconducting Properties of the Organic Solid Di-Tetramethyltetraselenafulvalenium-Perchlorate, (TMTSF) 2 ClO 4[END_REF], with 1p values estimated from the curves in Fig. 4. For these data, the upper error bar corresponds to the onset of the transition, and the lower error bar to the peak in the electronic specific heat. In the light-blue region, superconductivity develops within individual puddles. On the border between the light-blue and light-red regions, the proximity effect starts to induce SC coherence between puddles. The large scale phasecoherent superconductivity establishes progressively in the light-red region as a result of the interpuddle proximity effect coupling. The broken curves indicate the region used for the analysis based on the proximity effect: T cρ is assumed to be constant (1.27 K) as shown with the magenta curve and T cχ is calculated by solving Eq. ( 6). The red curve is obtained by fitting the theory to the T cχ data in the range 1p > 40%. The resulting fitting parameters are C = 5.2 K 3/2 and α = 100 nm/K 1/2 . Third, another support for our scenario is provided by the ac susceptibility data. Indeed, it is striking that a magnetic signal is only perceptible below T cχ , when the measured resistivity is only a small fraction of that of the normal state. This signifies that the part of the sample contributing to the initial resistivity drop is, in all likelihood, formed of small isolated SC puddles which size (L 970 nm) is smaller than or of the order of the SC penetration depth (λ > 1000 nm [START_REF] Le | Muon-spin-rotation and relaxation studies in (TMTSF) 2 X compounds[END_REF][START_REF] Greer | Muon spin rotation study of the (TMTSF) 2 ClO 4 system[END_REF]), so that these are invisible to ac susceptibility measurements. The dissipation is then due to currents circulating in the normal (disordered) regions [START_REF]The sample dimensions are smaller than the skin depth δ at the considered frequencies: δ 2 cm[END_REF].

As the temperature is lowered, in between T cχ and T cρ , intergrain coupling starts, so that SC clusters form, resulting in a first percolating path at T c,ρ=0 T cχ , but also in a sizable shielded volume. Then χ ac begins to decrease, while χ ac increases due to enhanced dissipation: as the SC volume expands, the current density in the remaining normal regions becomes also larger. More generally, as has been mentioned in the early studies of filamentary superconductors [START_REF] Oda | The Meissner effect of polysulfur nitride, (SN) x[END_REF][START_REF] Maxwell | Filamentary Structure in Superconductors[END_REF][START_REF] Strongin | Ac susceptibility measurements on transition metal superconductors containing rare earth and ferromagnetic metal solutes[END_REF][START_REF] Oda | susceptibility of polysulfur nitride (SN) x[END_REF], the peak of χ ac reflects a multiphases compound. Here, it arises from a balance between the normal and SC regions: the peak occurs at a temperature T peak when approximately half of the sample is shielded, as shown by the value of χ ac | T peak -0.5. This explains why, at higher cooling rates, T peak shifts to lower temperatures: at high cooling rates the initial density of SC puddles is lower, so that the coupling needs to be stronger, or the temperature lower, to achieve the same SC volume in the sample.

Finally, the T → 0 limit of χ ac is a measure of the dissipation and hence an indirect probe of the disordered volume fraction. This is illustrated in Fig. 5(c). As can be seen, χ ac (T → 0) is almost constant and close to 0 until 1p 0.3 [or equivalently, the cooling rate 1 K/min; see Fig. 2(d)], before drastically increasing with the disordered volume fraction. The fact that χ ac does not vanish even for T → 0 provides yet another strong indication that normal regions persist in this limit.

Let us remark that this behavior is at variance with the behavior of cuprate high-T c superconductors (HTSCs). Indeed, in these compounds, the two peaks observed in the measurements of χ ac have been attributed to the onset of intra-and intergrain superconducting currents. Moreover, the initial drop in χ ac is steep in temperature, simultaneous with the resistive T c , and corresponds to the penetration of the field within each superconducting grain [START_REF] Müller | AC susceptibility of high temperature superconductors in a critical state model[END_REF][START_REF] Nikolo | Superconductivity: A guide to alternating current susceptibility measurements and alternating current susceptometer design[END_REF]. Finally, χ ac always goes to -1 in the low-temperature limit. In our case, however, the shielding is not always total, the drop in χ ac is broad in temperature, and only begins at T cχ where the resistivity measurements show that the percolation threshold is almost reached. In the present case, given the large size of the normal regions, the magnetic signal is more likely to be due to currents within the normal regions than to the penetration of currents in the SC regions, contrary to HTSCs.

V. CONCLUSION

Our precise study of the normal and superconducting properties of (TMTSF) 2 ClO 4 by simultaneous transport and magnetic measurements, using a carefully controlled cooling procedure and covering cooling rates of four orders of magnitude, has revealed a crossover between a defect controlled d-wave and granular superconductivity in an inhomogeneous conductor with increasing cooling rate.

At cooling rates up to about 1 K/min, nonmagnetic disorder originates from small-volume clusters of disordered anions. The clusters are randomly distributed and act as local scattering centers. Superconductivity is suppressed by this disorder and the behavior of T c versus the residual resistivity can be explained by the Abrikosov-Gorkov theory adapted to impure dwave superconductors. Above 1 K/min and up to 18 K/min, T c for the resistivity onset remains independent of the cooling rate whereas T c for the onset of the ac susceptibility signal keeps decreasing. In this fast-cooling-rate regime, the system behaves as a set of randomly distributed SC (anion-ordered) puddles embedded in a normal conducting background with disordered anions. The fraction of the sample volume comprising ordered anions has been derived using the theory for an effective medium composed of two regions with different residual resistivities. Zero resistance and diamagnetic shielding are achieved through proximity effect links between the bulk SC puddles. The volume fraction of bulk SC puddles is about 30% smaller than the macroscopic screened sample volume measured by the real part of ac susceptibility. This feature provides an additional argument supporting the proximity effect picture in the fast-cooling regime. We emphasize that the case of (TMTSF) 2 ClO 4 investigated in the present study is likely to be relevant for other 1D or 2D molecular superconductors when disorder arises either from molecular disorder or from the competition between other ground states [START_REF] Senoussi | Signatures of granular superconductivity and Josephson effects in macroscopic measurements: the case of new superconductors[END_REF][START_REF] Müller | Magnetic-Field Induced Crossover of Superconducting Percolation Regimes in the Layered Organic Mott System κ-(BEDT-TTF) 2 Cu[N(CN) 2 ]Cl[END_REF][START_REF] Powell | Dependence of the superconducting transition temperature of organic molecular crystals on intrinsically nonmagnetic disorder: A signature of either unconventional superconductivity or the atypical formation of magnetic moments[END_REF]. Similarly, the granular behavior at high disorder concentration can occur in other unconventional superconductors, particularly when the disorder is introduced chemically and forms clusterlike structures. Thus the present study provides a guideline and an insight toward future investigation of impurity effects in a wide variety of unconventional superconductors.

When considering the competition between SC and SDW in the two materials (TMTSF) 2 PF 6 and (TMTSF) 2 ClO 4 , it becomes clear that the corresponding driving mechanisms are different. For (TMTSF) 2 PF 6 under pressure, from the high-pressure SC side, SDW develops as a consequence of a decrease of the unnesting term in the band structure (improving nesting in turn). Only in a narrow pressure regime close to the critical pressure can SC coexist with SDW albeit in distinct domains in the sample. In (TMTSF) 2 ClO 4 on the other hand, the intermediate state consists of a mixture of anion-ordered puddles embedded in the anion-disordered background whose volume fraction depends on the cooling rate.

It would be particularly interesting to pursue this study to further understand how the electronic granularity arises from disorder. Comparing ac susceptibility measurementsin zero and finite magnetic field-in the different crystal orientations or STM measurements such as those performed on electronically inhomogeneous NbN thin films [START_REF] Carbillet | Confinement of superconducting fluctuations due to emergent electronic inhomogeneities[END_REF] could for example provide information on the size of the SC puddles and the mechanism responsible for their formation. Finally, let us note that the flexibility brought by the cooling procedure in tuning both the density and the dimensions of SC puddles and proximity effect bridges makes (TMTSF) 2 ClO 4 a promising candidate in which more advanced investigations of mesoscopic superconductivity could be undertaken. One could, for instance, probe the quantum-critical metallic states that have been predicted to arise in such systems [START_REF] Spivak | Theory of quantum metal to superconductor transitions in highly conducting systems[END_REF], study how grain superconductivity and proximity effect each contribute to the specific heat, as this issue has not yet been clearly settled [START_REF] Poran | Quantum criticality at the superconductor-insulator transition revealed by specific heat measurements[END_REF], or study the localization-delocalization transition both in the three-and two-dimensional limits [START_REF] Gantmakher | Localized-delocalized electron quantum phase transitions[END_REF].

FIG. 1 2

 12 FIG. 1. Normal and superconducting properties of (TMTSF) 2 ClO 4 for sample no. 1 at various cooling rates. (a) Interlayer resistivity ρ c * vs T at 0.020 K/min showing the drop of the elastic resistivity ρ c * = 0.23 cm at T AO as indicated by the red arrow. (b) Change in the imaginary part of the ac susceptibility. (c) Change in the real part of the ac susceptibility. (d) ρ c * (T ) simultaneously measured with the data in (b) and(c). The inset presents ρ c * (T ) on a broader temperature range for 0.020, 0.52, 2.5, 7.6, and 18 K/min. For the 0.020-and 18-K/min data, the results of the fitting, performed using the procedure explained in the text, are presented with the broken curves.

2 FIG. 2 .

 22 FIG. 2. Cooling-rate dependence of superconducting properties for sample no. 1, and its comparison to that of sample no. 2. (a) Cooling-rate dependence of the various critical temperatures: the blue circles correspond to T cχ , the purple closed squares to T cρ , and the purple open squares to T c,ρ=0 . The red circles indicate T cχ for sample no. 2. (b) Cooling-rate dependence of the relative shielded volume fraction v shield for samples no. 1 (blue) and no. 2 (red). (c) Cooling-rate dependence of the residual resistivity ρ c * 0 . (d) Low-temperature dissipation, as measured by χ ac for sample no. 1. The χ ac data have been averaged in the temperature range 0.1 K < T < 0.3 K.

Sample no. 1 Sample no. 1 FIG. 3 .

 113 FIG. 3. Dependence of T c 's and relative shielded volume fraction v shield on ρ c * 0 for sample no. 1. (a) T cρ as a function of ρ c * 0 , compared with T c,ρ=0 and T cχ . The dotted curve presents results of fittings of T cρ with the AG formula [Eq. (2)]. The fitting has been performed in the range 0 < ρ c * 0 < 0.05 cm. The inset shows the same data in a wider range. (b) v shield as a function of ρ c * 0 . The inset shows the same data in a wider range.

  FIG. 5. (a) T cρ , (b) ρ c * 0 , and (c) low-temperature dissipation as measured by χ ac , plotted against the disordered volume fraction 1p derived through Eq. (1). Deviation from the linear dependence (broken lines; fitted in the range 1p < 20% in all panels) occurs when the first finite disordered cluster emerges. At complete disorder (not accessible before the onset of the SDW ground state above 18 K/min), the resistivity would amount to ρ Max = 0.26 cm, as indicated by the open circle. The χ ac data in (c) have been averaged in the temperature range 0.1 K < T < 0.3 K.

ACKNOWLEDGMENTS

S.Y. acknowledges Y. Maeno, Y. Sugimoto, T. Higuchi, and K. Ishida for experimental support and fruitful discussion. D.J. acknowledges fruitful exchanges with B. Castaing, who made him aware of the Landau effective conductor model used in this work, and with J. P. Pouget for discussions on x-ray data. We had several discussions with H. Bouchiat, D. Roditchev, and T. Cren on the topic of mesoscopic superconductivity. This work has been supported by Japan Society for the Promotion of Science (JSPS) Grant-in-Aids KAKENHI Grants No. JP26287078 and No. JP17H04848, as well as by JSPS Grant-in-Aids for Scientific Research on Innovative Areas "Topological Materials Science" (KAKENHI Grants No. JP15H05852 and No. JP15K21717).


Pradorn Sureephong

Nopasit Chakpitak

Yacine Ouzrout

Gilles Neubert

Abdelaziz Bouras

Knowl

Knowledge Management System Architecture for the Industry Cluster

Keywords: knowledge management, architecture, industry cluster

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

In developing country, Small and Medium Enterprises (SMEs) are very important to their economy due to more than 70% of firms in industry sector are small to medium size. Thus, governments try to support these companies in various ways such as financial support, government policy or import/export promotion. However, large number of SMEs still can not survive in the competition.

After the concept of industry cluster [START_REF] Porter | Competitive Advantage of Nations[END_REF] was tangibly applied in Thailand in 1998. Thai SMEs trended to link to each other to maintain their competitiveness in the market. Successful companies gain benefits from being a member of the cluster. The major key success factors are knowledge sharing and collaboration within the cluster. This knowledge was collected in form of tacit and explicit knowledge in expert and institutions within cluster. Thus, applying knowledge management theory through cluster development should assist industry cluster to be able to achieve their goal efficiently. Although, many papers claimed that knowledge is very important for cluster development but no demonstrate empirical method to initiate or improve knowledge sharing for cluster. Then, the objective of this paper is to propose a knowledge management system architecture and methodology for the industry cluster.

A. Industry Cluster

The knowledge-based economy is affected by the increasing use of information technologies. Most of industries try to use available information to gain competitive advantages. Knowledge-based economy is based on the production, distribution and use of knowledge and information [START_REF] Malmberg | How) do (firms in) cluster create knowledge?[END_REF]. From the study of ECOTEC in 2005 [START_REF] Dti | A practical guide to cluster development[END_REF] about the critical success factors in cluster development, first two critical success factors are collaboration in networking partnership and knowledge creation for innovative technology in the cluster which are about 78% and 74% of articles mentioned as success criteria accordingly. This knowledge is created through various forms of local inter-organizational collaborative interaction [START_REF] Malmberg | On the goal of global demand in local innovation processes[END_REF]. There are many literatures regarding cluster developing in economic and management aspect. However, there are a few of literatures which study about cluster development in knowledge management context. Therefore, the fundamental of this study is about enhancing cluster by using knowledge management theory.

The concept of industry cluster was popularized by Prof. Michael E. Porter in his book named "Competitive Advantages of Nations" [START_REF] Porter | Competitive Advantage of Nations[END_REF]. Then, industry cluster becomes currently trend in economic development planning. However, there is considerable debate regarding the definition of the industry cluster. Based-on Porter's definition about industry cluster [START_REF] Porter | On Competition[END_REF], in this study the cluster is "geographically proximate group of companies and associated institutions (for example universities, government agencies, and related association) in a particular field, linked by commonalities and complementarities". Until now, literatures of the industry cluster and cluster building has been rapidly growing both in academic and policy-making circles [START_REF] Dti | A practical guide to cluster development[END_REF].

The characteristic of the industry cluster is depending on definition, type of industry, and collaboration. However, the general cluster should have these characters to support the development, i.e. connectivity, collaboration, competition, and collective efficiency [START_REF] Dawson | UNIDO Report, consultants and UNIDO Project Teams in India, Nicaragua[END_REF]. However, the concept of industry cluster development is quite different form organization development in many aspects. Cluster is composed of firms in specific industry, academic institutes, financial institutes, government From cluster green book [START_REF] Sölvell | The Cluster Initiative Green Book", Garamond, Arial Narrow, Book Antiqa[END_REF], CDA is a critical success factor in cluster. From the statistic, 89% of successful cluster have full-time CDA.

B. Knowledge Management System

Knowledge management is the discipline that helps spread knowledge of individuals or groups across organizations in ways that directly affect performance. Knowledge management envisions getting the right information within the right context to the right person at the right time for the right business purpose [START_REF] Th | Knowledge Engineering and Management: The CommonKADS Methodology[END_REF].

Knowledge Management System (KMS) is a system for managing knowledge in organizations, supporting creation, capture, and storage and sharing of expertise in the form of information. Jennex and Olfman [START_REF] Jennex | Organizational memory/knowledge effects on productivity, a longitudinal study[END_REF] classified the KMS in to two groups based on amount of common context of understanding.

1) The process/task based approach: focuses on the use of knowledge by participants in a process, task or project in order to improve the effectiveness of that process, task or project. This approach identifies the information and knowledge needs of the process, where they are located, and who needs them. The KMS is designed to capture tacit knowledge and to make knowledge available when needed to whom needs it.

2) The infrastructure/generic system based approach: focuses on building a base system to capture and distribute knowledge for use throughout the organization. It concern of the technical details needed to provide good mnemonic functions associated with the identification, retrieval, and use of knowledge. The approach focuses on network capacity, database structure and organization, and knowledge information classification.

Even though several models related to KM technologies have been developed, but they could not be used directly to meet the objective of this study. For example, the seven layer KMS architecture [START_REF] Tiwana | The knowledge management toolkit[END_REF] which mirrors the OSI Model used in data communication [START_REF] Chua | Knowledge management system architecture: a bridge between KM consultants and technologist[END_REF] is oriented to the infrastructure/generic system based approach. The KM spectrum [START_REF] Binney | The knowledge management spectrumunderstanding the KM landscape[END_REF] and the Ovum KM tools architectural model [START_REF] Woods | Knowledge management: applications, markets and technologies[END_REF] are process/task based approach. They are comprehensive in scope but lack of actual deployment examples and obscure reference to fundamental KM process [START_REF] Chua | Knowledge management system architecture: a bridge between KM consultants and technologist[END_REF]. Most of literatures proposed KMS architecture to support KM activities within single organization or community. As we mentioned earlier that the cluster development is different from usual organization so we tried to propose specific KMS architecture for the cluster that integrated process/task based and infrastructure/generic system based approach together.

II. METHODOLOGY

Our methodology was separated into two main parts. Firstly, knowledge engineering process which is more in the process/task based approach. Secondly, knowledge system development process is oriented in the infrastructure/generic based system approach. This integration combined technical and non-technical aspects of knowledge management theory within this architecture.

1) Knowledge Engineering (KE) process: is strongly emphasized on the conceptual modeling of knowledge intensive activities. The often geographical techniques have proved to be very useful in clarifying the major tacit knowledge, in a way enabling and stimulating fruitful communications with variety of people (managers, experts, end users, customers) who often do not have background in information technology [START_REF] Th | Knowledge Engineering and Management: The CommonKADS Methodology[END_REF].

There are several knowledge engineering methods such as CommonKADS [START_REF] Th | Knowledge Engineering and Management: The CommonKADS Methodology[END_REF], SPEDE [START_REF] Shadbolt | From knowledge engineering to knowledge management[END_REF], and MOKA [START_REF] Preston | Knowledge acquisition for knowledge-based engineering system[END_REF]. However, we selected CommonKADS as knowledge engineering methodology in this study become it provided a model suite (Fig. 1) and template knowledge models for solving problems. Besides, it is now a European de facto standard for knowledge analysis and knowledge-intensive system development.

Together, the organization, task, and agent models analyze the organizational environment and the corresponding critical success factors for a knowledge system. The knowledge and communication models yield the conceptual description of problem-solving functions and data that were handled and delivered by a knowledge system. The design model converts it into a technical specification that is the basics for software system implementation.

2) Knowledge system development processes: are relative to knowledge engineering process. The outputs from CommonKADS model suite are specific requirements for designing knowledge system. Integrating these components to create knowledge management system model requires thinking in term of info-structure, rather than infrastructure [START_REF] Tiwana | The knowledge management toolkit[END_REF]. The KMS architecture for the industry cluster was adapted from three-tier KMS architecture [START_REF] Chua | Knowledge management system architecture: a bridge between KM consultants and technologist[END_REF] identifies three distinct services supported by knowledge management technologies. They are collaboration services, knowledge services and presentation services as shown in Fig. 2.

1) Collaboration services: refer to the basic technology platform and features needed to implement KM. The two main infrastructure services provided by technology are storage and communication.

1.1 Storage: known as knowledge repository such as drawings, audio, video or multimedia documents. The knowledge server which allow user to build content, create references and establish links among documents is technology that support KM processes, particularly knowledge creation and knowledge reuse.

1.2 Communication: related to collaboration and sharing activities in the cluster. This communication services are designed by specification output from communication model of CommonKADS. They could support communication between users (ex. email) among user (ex. synchronous meeting and asynchronous discussion forum) and workflow management.

2) Knowledge services: intended to help achieve the goals of KM directly. Three primary goals are to promote the process of generating new knowledge, encourage the flow of knowledge among organization members and ensure the ease of access to knowledge repository [START_REF] Martin | Knowledge management within the context of management: An evolving relationship[END_REF] 2.1 Knowledge creation: is capability to capture and codify knowledge held by experts. This process was done by domain experts or knowledge engineer with the knowledge elicitation techniques provided by CommonKADS.

2.2 Knowledge sharing: is an important goal of KM technologies that support the knowledge sharing process which is collaborative tools, such as shared spaces, calendaring, workflow management service, etc.

2.3 Knowledge reuse: is a synonym with "information retrieval" in the information management literature. The emerging technology aim to provide enhanced search capabilities as user's needs and automatic generation of meta-data [START_REF] Marwick | Knowledge management technology[END_REF]. Technologies that support knowledge reuse process are content management system (CMS) or concept mapping.

3) Presentation services: concerned with enhancing the interface between the user and the information /knowledge source.

3.1 Personalization: involves gathering userinformation and delivering the appropriate content and service to meet the specific need of a user [START_REF] Bonett | Personalization of web services: Opportunities and challenges[END_REF]. This service refer to the rule that determine how users and content are matched, base on their attributes and values. Fig. 2. Knowledge system for the industry cluster.

3.2 Visualization: help users better understand the information and knowledge available by making subject-based browsing and navigation easier [START_REF] Marwick | Knowledge management technology[END_REF]. 4) Cluster Development Service: concerned with facilities for CDA to analyze and assess collaboration and sharing in the system. Technologies that support these services are social network analysis (SNA), accounting system, user's activities tracking, etc.

4.1 Cluster visualization: helps CDAs to visualize their cluster character such as social network map, cluster map, etc.

4.2 Collaboration accounting: show the quality of communication and sharing by taking account from users' activities via KMS.

III. INVESTIGATIONS AND RESULTS

The initial investigations have been done with 10 firms within the two biggest handicraft associations in Thailand and Northern Thailand. NOrthern Handicraft Manufacturer and EXporter (NOHMEX) association is the biggest handicraft association in Thailand which includes 161 manufacturers and exporters. Another association which is the biggest handicraft association in Chiang Mai is named Chiang Mai Brand. It is a group of qualified manufacturers who have capability to export their products and passed requirements of Thailand's ministry of commerce. Until 2007, there are 99 authorized enterprises to use Chiang Mai brand on their products.

Regarding the study on cluster mapping by KIASIA [START_REF] Kiasia | Cluster mapping project[END_REF], this project was funded by National Economic and Social Development Board (NESDB) to survey and analyze the current condition of clusters through the country. One of the recommendations that issued to Thai government is to establish knowledge database on cluster development to bring together cluster development information from various organizations. This will create more complete data on cluster development that can be used for monitoring operations and the progress of the development or related parties. Another recommendation is strengthening Cluster Development Agents (CDAs) within 5 years.

As we are in the beginning of this study, CommonKADS was used as a knowledge engineering methodology in the context level (organization model, task model, and agent model) in order to understand organization environment and corresponding critical success factors for knowledge system.

As shown in Fig. 3, Organization Model (OM-1 to OM-5), we found that handicraft cluster has its own vision as "Knowledge sharing hub for handicraft exporter". And companies defined their problems, such as intellectual property problem, lack of collaboration, CDA development, product innovation, and product exporting. However, this cluster has many opportunities and solutions as well. We used "product exporting" and "product innovation" as our mock-up problems due to these problems are a knowledge intensive and feasible in business and technical aspect.

From the Task Model (TM-1 to TM-2), we analyzed the feasibility of each tasks that related to product exporting and product innovation processes. This model makes it possible to rank and prioritize the different knowledge-improvement scenarios.

Agent Model (AM-1) proposed organizational recommendations, improvements, and actions. From the experts' point of view, they proposed actions for solving product exporting and product innovation problems as follow, 1) Develop information system that provides knowledge from experts about product selection, marketing information, or economic data from government organization. 2) Archive past lesson learn or experiences with in electronic forum 3) Create best practice of each task and store in knowledge-based system 4) Increasing the collaboration and information sharing within the cluster. a. Between core business and supporting organization (cluster level) b. Between firms in the core business (core business level) 5) Create tools to support the capability of cluster development agency (CDA) to facilitate the cluster.

From knowledge engineering process in context level, we proposed our knowledge management system architecture for support cluster as shown in Fig. 4 The proposed architecture consisted of three parts, knowledge system part, ontology part, and knowledge engineering part. The Knowledge system part interacts with users (CDA, cluster members, knowledge engineers, and administrator) and also includes collaboration tools, repository, user's database, content management, etc. In the presentation service, CDA's tools are included for helping CDA to facilitate the cluster, such as social network analysis, cluster mapping. Knowledge acquisition part focused on supporting knowledge engineering process. During the manipulation stage, when user accesses the knowledge based, the ontology can support task of KM as well as searching. The knowledge based and the ontology is linked one to another via the ontology module. In the maintenance stage, knowledge engineers or domain experts can add, update, revise, and delete the knowledge or domain ontology via knowledge acquisition module.

IV. CONCLUSION

In our preliminary study on handicraft cluster and knowledge engineering in context level, we acquired basic requirements for design knowledge management system for cluster. However, we are in the beginning of the research. In our perspectives of this study, we will finalize the specification of the sharable knowledge/information and the conditions of sharing among the cluster members. Then, we will capture and maintain the knowledge (for reusing when required) and work on the specific infrastructure to enhance the collaboration. At the end of the study, we will develop the knowledge management system for the handicraft cluster regarding to acquire requirements specification from the cluster.

Fig. 1 .

 1 Fig. 1. CommonKADS model suite.

Fig. 3 .

 3 Fig. 3. A road map for carrying out knowledge oriented organization and task analysis.

Fig. 4 .

 4 Fig. 4. Proposed knowledge management system architecture for the industry cluster.

Knowledge Management System Architecture for the Industry Cluster

	agencies, and associations. Due to, there is no hierarchy,
	penalty, or incentive. Besides, the main goal of cluster is
	P. Sureephong 1 , N. Chakpitak 1 not the maximum profit but improving competitiveness of 1 entire industry. Cluster Development Agent (CDA) is a College of Arts, Media and Technology, Chiang Mai University, Chiang Mai, Thailand , Y. Ouzrout 2 , G. Neubert 2 , A. Bouras 2 2 LIESP Laboratory, University Lumiere Lyon 2, Lyon, France person who plays a role as a facilitator in the cluster.

ACKNOWLEDGMENT

The authors would like to thank Euro-Asia Collaboration and NetWorking in Information Engineering System Technology (EAST-WEST) project which aim to increase the collaboration between European countries and Asian countries in term of economics, knowledge, innovation or human resource development.