Abstract
Quantum Griffiths singularity was theoretically proposed to interpret the phenomenon of divergent dynamical exponent in quantum phase transitions. It has been discovered experimentally in threedimensional (3D) magnetic metal systems and twodimensional (2D) superconductors. But, whether this state exists in lower dimensional systems remains elusive. Here, we report the signature of quantum Griffiths singularity state in quasionedimensional (1D) Ta_{2}PdS_{5} nanowires. The superconducting critical field shows a strong anisotropic behavior and a violation of the Pauli limit in a parallel magnetic field configuration. Currentvoltage measurements exhibit hysteresis loops and a series of multiple voltage steps in transition to the normal state, indicating a quasi1D nature of the superconductivity. Surprisingly, the nanowire undergoes a superconductormetal transition when the magnetic field increases. Upon approaching the zerotemperature quantum critical point, the system uncovers the signature of the quantum Griffiths singularity state arising from enhanced quenched disorders, where the dynamical critical exponent becomes diverging rather than being constant.
Introduction
Superconductivity in materials with lowdimensional electronic structure becomes an important topic during the past decades because they provide a rich avenue for investigating exotic physical properties and their potential applications in quantum computing devices^{1,2}. With the reduction of the dimensionality, fluctuation, disorder, and quantum correlation effects begin to have a special influence on the superconducting characteristics^{3}. As a result, many interesting phenomena arise, such as localization of Cooper pairs^{4}, transition temperature oscillations^{5,6}, and quantum phase transition (QPT) at zero temperature^{7,8,9}. In particular, one example of the QPT has been extensively studied that is the superconductorinsulator transition (SIT) or superconductingmetal transition (SMT), in which a continuous phase transition occurs at the zerotemperature limit as a function of external tuning parameters, such as external electric fields, carrier density, and outofplane magnetic fields^{1,9}. However, despite numbers of investigations in various systems, there still remain many open issues, such as unexplained inconsistencies among the critical exponents found in different physical systems^{1,10} and the appearance of intervening quantum metallic state between the superconducting and the insulating state^{2,11}. The latest remarkable observations of the quantum Griffiths singularity in thin Ga films^{12}, LaAlO_{3}/SrTiO_{3}(110) interface^{13}, monolayer NbSe_{2}^{14}, and ionic liquid gated ZrNCl and MoS_{2}^{15} shed a new light on the understanding of SMT in twodimensional (2D) system^{16}. Whether this phenomenon would appear in lower dimensional superconducting systems remains elusive.
Very recently, the newly discovered quasionedimensional (1D) transition metal chalcogenide superconductors with a formula M_{2}Pd_{x}Q_{5} (M = Ta, Nb; Q = S, Se) have attracted great attention because of their exotic superconducting characteristics^{17,18}. The most striking feature of these compounds is their remarkably large upper critical fields, which exceed the Pauli limit relative to their transition temperature^{19,20}. Theoretical investigations show that this should be due to the combination of strong spinorbit coupling and multiband effects in the extreme dirty limit^{21}. More interestingly, instead of using the sputtering or evaporating technique in fabricating granular and amorphous nanowires, the layered lowdimensional nature in such compounds offers a wonderful platform for investigating SMT in quasi1D singlecrystal nanowires^{17}.
In this study, we report the systematic transport measurements on quasi1D Ta_{2}PdS_{5} nanowires obtained by Scotch tape assisted micromechanical exfoliation of bulk crystals. The critical field of the system shows a strong anisotropic behavior and a violation of Pauli paramagnetic law under parallel magnetic field configuration. Moreover, the currentvoltage (IV) characteristics of the nanowires in the superconducting regime display a series of multiple voltage steps resulting from quantum phase slip; and a hysteresis arises when the applied current is swept up and down, which resembles a typical quasi1D behavior in superconductivity. Interestingly, the magnetotransport properties of the nanowires undergo a SMT with increasing magnetic field. As the temperature approaches zero, the dynamical critical exponent shows a divergent value, which is a signature of quantum Griffiths singularity state.
Results
Sample characterization
Ta_{2}PdS_{5} single crystals were synthesized using chemical vapor transport (CVT) method^{22} (see Methods for details). The asgrown bulk crystals exhibit a long needlelike structure with a length up to centimeters. As shown in Fig. 1a, Ta_{2}PdS_{5} is composed of corrugated metal sulfide sheets, which form 1D chains along the < 010 > direction (needle direction or baxis)^{19,21}. Its crystal structure is centrosymmetric, with the space group of C2/m. Due to its lowdimensional structure, the Ta_{2}PdS_{5} bulk material can be cleaved into rectangularshape nanowires where the width ranges from 0.1 to 2 μm, with the thickness of 70–300 nm. Figure 1b shows the scanning electron microscope (SEM) image of the exfoliated nanowires on polydimethylsiloxane substrate, where the long axis of the nanowire is the baxis of the crystal. Figure 1c shows the brightfield transmission electron microscopy (TEM) image taken from a Ta_{2}PdS_{5} nanowire. Figures 1d, e respectively show the corresponding selectivearea electron diffraction (SAED) pattern and highresolution TEM (HRTEM) image, which confirm that the axial direction of the Ta_{2}PdS_{5} nanowire is < 010 > and the singlecrystal nature of the nanowire. Figures 1f–h show the elemental maps taken from a section of the nanowire (yellow dashed square in Fig. 1c) by energydispersive Xray spectroscopy (EDS), indicating that Ta, Pd, and S are distributed evenly in the nanowire.
Anisotropic superconductivity in Ta_{2}PdS_{5} nanowires
Fourterminal Ta_{2}PdS_{5} nanowire devices with various thickness were fabricated using ebeam lithography (EBL), followed by a metal deposition process (See Methods for details). A typical device structure is schematically illustrated in Fig. 2a (Optical image, inset of Fig. 2b). The measured fourprobe resistance is defined as R = V_{XX}/I_{DS}, where I_{DS} is the sourcedrain current and V_{XX} is the measured voltage drop between the middle two voltage probes. As depicted in Fig. 2b, fourterminal temperaturedependent resistance of the nanowire device shows a metallic behavior upon cooling and the superconductivity appears at T_{C} ∼ 3.3 K (Device 01 crosssectional area, 120 nm (thickness) × 300 nm (width)), where T_{C} is defined as the temperature corresponding to the middle point of the superconducting transition. T_{C} values of devices with different thickness are shown in Supplementary Figure 3 in which T_{C} decreases monotonically with the thickness. Note that in order to control the variables, we intentionally compare the samples with a similar channel width. We also measure the T_{C} of different lengths in one nanowire (Supplementary Figure 3) and different parts of the nanowire exhibit a similar T_{C}, indicative of good uniformity^{17}.
Next, we explore the anisotropy of the superconductivity in Ta_{2}PdS_{5}. Figures 2c, e display the temperaturedependent resistance for magnetic fields applied perpendicular and parallel to the baxis of Ta_{2}PdS_{5} nanowire device (inset Fig. 2d), respectively. In the case of the perpendicular geometry, the superconductivity rapidly disappears with the increase of magnetic field and is completely quenched when the magnetic field is larger than 6.5 T. For the parallel scenario, however, the superconductivity is robust against the magnetic field and it survives even under 9 T at T = 2 K. Figure 2d shows the angledependent upper critical field B_{C2}(T) at T = 2.4 K (similar device to device 01, the data of device 01 are shown in Supplementary Figure 4), where it exhibits large anisotropy. We define B_{C2}(T) as the magnetic field where the resistance drops to 50% of the normal resistance. We tried to fit the angulardependent B_{C2}(T) at small θ values using both 3D^{23,24} and 2D^{25,26} models, where neither of them fits the data well (See Supplementary Figure 6). Then, we further measured the angledependent B_{C2}(T) of Ta_{2}PdS_{5} samples with different thickness (Supplementary Figure 7). We find that the angledependent B_{C2} ~5 μm (Bulk) sample shows a very good fit to the 3D model, which is consistent with the previous study^{27}. However, the angledependent B_{C2} of thin nanowire samples do not fit well with either 3D or 2D model, indicating the reduced dimensionality of its superconductivity (See Supplementary Note 2 for details). As far as we know, up to now, there is no theoretical models/equations that can be used for the data fitting in the quasi1D superconducting system, which calls for a further theoretical investigation. In addition, the dependence of B_{C2} on temperature T for both the parallel and perpendicular magnetic fields are fitted well using the empirical equation^{17}:
where B_{C2}(0) = Φ_{0}/2πξ(0)^{2}. Then, the Ginsburg–Landau (GL) coherence length for parallel and perpendicular configuration can be estimated to be ξ_{//}(0) = 4.1 nm and ξ_{⊥}(0) = 7.6 nm, respectively. Considering the relatively small anisotropy in the ac plane (See Supplementary Note 3 for details), the coherence along a and caxis should be around 4.1 nm. Note that for the parallel configuration, the upper critical field at T = 0 K seemingly exceeds the Pauli paramagnetic limit of weak coupling Bardeen–Cooper–Schrieffer (BCS) superconductors B_{P}^{BCS }= Δ_{0}/\(\sqrt 2\)k_{B}T_{C} = 1.84T_{C }= 6.1 T (dashed line in Fig. 2f). Compare with spinmomentum lock induced Ising superconductivity in monolayer NbSe_{2}^{14,28} and ionic liquid gated MoS_{2}^{26}, the violation of Pauli paramagnetic limit in Ta_{2}PdS_{5} is resulted from the synergetic effect of strong spinorbit coupling and multiband effects^{21,29}.
IV characteristics of Ta_{2}PdS_{5} nanowire devices and the estimation of penetration depth
In order to further understand the superconductivity in Ta_{2}PdS_{5} nanowires, we performed fourterminal currentvoltage (IV) measurements in the superconducting transition region. Figure 3 shows the measured IV curves at varying temperatures (Fig. 3a) and magnetic fields (Fig. 3b) on a linear scale driven by current. A series of sharp voltage steps were observed as the nanowires transit from the superconducting to the normal state. These voltage steps are reproducible, becoming more pronounced and sharper at lower temperatures (magnetic fields) and finally vanished with the gradual increase of temperature (magnetic field). Usually, the multiple voltage steps in the IV characteristics are considered to be typical features of quasi1D superconductors. It has been reported in thin superconducting polycrystalline Nb nanowires^{30,31} and singlecrystal Sn nanowires^{32}. These voltage steps were interpreted as a consequence of spatially localized weak spots or resistive phase slip centers (PSCs), which arise from the local imperfections or defects in the nanowire that support a smaller critical current. A voltage step in the wire is created when the applied excitation current exceeds the local critical current of a specific PSC. The spatial extension of the PSC is typically on the order of a few micrometers in length^{32}, which is at the same level of our device length. In addition, when we sweep the current upstream and back down, a sequence of hysteresis loop has been observed in the superconducting regime (Figs. 3c, d), which also disappears as the temperature or magnetic field increases. As the phaseslip centers in superconducting nanowires act qualitatively like weaklink in Josephson junctions, a superconducting nanowire can be viewed as the coupled combination of Josephson junctions and the rest of the superconducting filament^{33}. Hence, such a hysteresis in IV characteristics is a hybrid effect resulting from both selfheating hotspots and the runaway and retrapping of the phase point in the tilted washboardlike potential of the underdamped Josephson junction^{34}. We have also compared the IV relation of Ta_{2}PdS_{5} nanowires with thickness changes from ~5 μm (bulk) to 110 nm (See Supplementary Figure 9). For ~5 μm thick (Bulk) sample, there is only one step in the IV curves and the voltage is zero under low current bias until the current reaches a certain value I_{C} (Note that the data points in Supplementary Figure 9(a) at V~1 μV are the noise approaching the measurement limit). As the thickness of the device goes down, multiple voltage steps and enhanced Ohmic finite resistance emerge, which is mainly due to the 1D confinement effect as predicted by thermalactivated phase slip model^{32,35,36} (See Supplementary Note 4 for details). In addition, we have fit the temperaturedependent critical current to the Bardeen’s formula^{37,38} for quasi1D superconductors I(T) = I_{C}(0) (1−(T/T_{C0})^{2})^{3/2}, where T_{C0} is the transition temperature T in the absence of currents and fields (See Supplementary Figure 10a for details). We found that the experimental data fit the equation well, evidencing the quasi1D superconductivity in Ta_{2}PdS_{5} nanowires. Note that our observation of multisteps and hysteresis in IV curves in Ta_{2}PdS_{5} nanowires is consistent with the scenario generally expected in quasi1D nanowires as well^{17}. At first glance, it seems contrary to the fact that the GL coherence length of Ta_{2}PdS_{5}, as calculated above and described in Supplementary Note 3, is much smaller than the sample size. However, it has been suggested that for typeII superconductors the required actual size for the quasi1D superconductivity can be determined by their penetration depth^{17,38}, unlike in typeI superconductors where the diameter of the wires needs to be less than its GL coherence length.
We then extract the magnetic properties of Ta_{2}PdS_{5} to estimate the penetration depth. The obtained magnetic moment versus magnetic field of Ta_{2}PdS_{5} is shown in Fig. 3e, exhibiting a typical behavior of typeII superconductors^{39,40}. From the initial magnetization curve (Fig. 3f), B_{C1}(1.8 K) = 1.8 Oe can be acquired. Using the equation^{20} B_{C}(T) = B_{C}(0)[1−(T/T_{C})^{2}], we can obtain the low temperature B_{C1}(0) = 2.6 Oe. Utilizing the B_{C2a´}(0) = 4.7 T in Supplementary Note 3^{39}, the GL parameter can be estimated to be 220 following the equation^{20,25} B_{C2}(0)/B_{C1}(0) = 2κ(0)^{2}/ln κ(0). Using^{20,25} κ(0) = λ(0)/ξ(0), we can obtain the penetration depth λ(0) of Ta_{2}PdS_{5} nanowire ~1848 nm, which is much larger than the device thickness of 120 nm. Note that the penetration depth we estimated here is similar to other quasi1D superconductors like Nb_{2}PdS_{5} ~785 nm [ref.^{41}], Nb_{2}PdS_{5}~410 nm [ref.^{20}] and Sc_{3}CoC_{4} ~970 nm [ref.^{39}]. Thus, we believe that the superconductivity in Ta_{2}PdS_{5} is quasi1D.
Superconductormetal transition and quantum Griffiths state
Next, we study the magnetoresistance of the Ta_{2}PdS_{5} in a perpendicular magnetic field configuration. Figure 4a reveals the temperaturedependent resistance of a nanowire device (crosssectional area 300 nm × 100 nm) under various magnetic fields. With the increase of the magnetic field, the superconducting transition shifts monotonically to lower temperatures similar to Fig. 2c. As the magnetic field continues to increase, the superconductor gradually changes to a localized metal, indicating a magnetic field induced SMT. This SMT behavior is further explored in magnetoresistance isotherms in Fig. 4b where R_{S}(B) curves cross each other. Intriguingly, the crossing point of SMT seemingly changes as the temperature varies. To investigate the SMT behavior in Ta_{2}PdS_{5} nanowires, we measure the sample in the dilution temperature environment. Figure 4c shows the magnetoresistance isotherms of the device under an ultralow temperature ranging from 0.12 to 1.2 K. A series of crossing points have also been observed. We summarize the crossing points in both high and lowtemperature regimes in Fig. 4d, where the black squares are crossing points of every two adjacent R_{S}(B) curves. Also, as shown by the red dots in Fig. 4d, the R_{S} plateaus where dR_{S}(T)/dT changes sign for a given magnetic field have been extracted from R_{S}(T) curves in Fig. 4a. We have also used the empirical equation to fit the crossing points (blue dashed line in Fig. 4d). In the hightemperature regime, the data fit the equation well; while in the ultralowtemperature region, B_{C} diverges from the tendency of the empirical equation (T < 0.7 K). The experimental data of B_{C}(0) > 6.2 T is substantially larger than the fitted result from the empirical equation (B_{C}(0) = 6.06 T).
Typically, for SIT, the critical resistance corresponding to the border between the superconducting and insulating region at low temperatures should be the quantum unit of resistance (h/4e^{2} ∼ 6450 Ω), and the critical exponent remains to be a constant^{42}. Theoretical investigations^{43} show that unpaired electrons could originate from the pairbreaking mechanism of dissipation effect, giving rise to a much smaller critical resistance than h/4e^{2}. This explains our experimental data that the critical resistance of Ta_{2}PdS_{5} nanowire is much smaller than the quantum resistance h/4e^{2}. More recently, theoretical studies also show that quenched disorders could dramatically change the scaling behavior of SMT and result in an activated scaling behavior identical to that of the quantum random transversefield Ising model^{44}. In that system, the activated scaling behavior, called quantum Griffiths singularity, exhibits continuously varying dynamical exponent z when approaching the infiniterandomness quantum critical point. Recent experiments on 2D superconducting Ga thin film, monolayer NbSe_{2} and ionic liquid gated ZrNCl and MoS_{2} have envisaged the similar continuous line of “critical” points and the divergence of the dynamical critical exponent in SMT, which experimentally reveals the existence of quantum Griffiths singularity state in SMT in 2D superconductors^{12,14}.
Inspired by the new discovery of quantum Griffiths singularity in SMT, we analyze multiple crossing points in Ta_{2}PdS_{5} nanowires using the scaling analysis method, according to which the resistance in the vicinity of a critical point follows^{7,45}
where the δ = B − B_{C} is the deviation from the critical field, R_{C} is the critical resistance, f(x) is the scaling function with f(0) = 1, δ is tuning parameter, z is the dynamic critical exponent, and ν is the correlation length critical exponent. One “critical” point (B_{C}, R_{C}) of a certain small critical transition region is defined as the crossing points of several adjacent R_{S}(B) curves (See Supplementary Figure 11 for details). The deduced magnetic field dependence of the effective “critical” exponent zν is shown in Fig. 5. In the relative hightemperature regime, zν value increases slowly with the magnetic field, while in the ultralowtemperature regime, zν grows quickly as the temperature decreases. Here we note that one zν value corresponds to a temperature region rather than a certain temperature. Next, we try to fit the extracted zν values versus B using the activated scaling law zν = CB_{C}* − B^{−ηψ}, where C is a constant, η ≈ 1.2 is the correlation length exponent and ψ ≈ 1 is the tunneling critical exponent in quasione dimension^{12,14,46}. The activated scaling law fits the data well (the solid pink line in Fig. 5, where B_{C}* = 6.148 T), indicating the existence of infiniterandomness quantum critical points in Ta_{2}PdS_{5} nanowires. As mentioned before, the enhanced quenched disorders^{13} at low temperatures are the main inducement of the quantum Griffiths singularity in Ta_{2}PdS_{5}. Although the Ta_{2}PdS_{5} nanowires are single crystalline with good uniformity, there may still be some defects. In addition, the interface effect coming from the device fabrication and scattering from the substrate could also introduce disorders in the system. All of these above could be the origin of the enhanced quenched disorders at low temperatures^{14}, resulting in the infinite zν value when the critical point B_{C}* is approached.
Discussion
With the reduced dimensionality of angledependent B_{C2} of thin Ta_{2}PdS_{5} nanowires, the appearance of multiple IV steps, the enhanced Ohmic finite resistance when the thickness of the device reduces, the good fittings of the temperaturedependent critical current to the Bardeen’s formula^{37,38} for quasi1D superconductors, and the zν value to the 1D equation^{46} zν = CB_{C}* − B^{−1.2}, the quasi1D superconductivity is suggested to present in Ta_{2}PdS_{5} nanowires. Considering the crystal lattice constants^{19} a = 1.2 nm, b = 0.3 nm, and c = 1.5 nm, the GL coherence lengths along different crystal axes are larger than the lattice constants (ξ_{a´}(0) = 8.4 nm, ξ_{b}(0) = 4.2 nm, and ξ_{c´}(0) = 8.6 nm, see Supplementary Note 3 for details). Note that the GL coherence length along different directions is also smaller than our nanowire thickness (~120 nm). However, the actual effective superconducting thickness of Ta_{2}PdS_{5} nanowire should be smaller than the sample thickness^{3}, which may make the superconductivity in Ta_{2}PdS_{5} nanowires quasi1D. Nevertheless, the penetration depth of ~1848 nm calculated above is significantly larger than the sample thickness, satisfying the condition required for quasi1D superconductivity in typeII superconductors^{17,38}. Also, from previous experiments on quasi1D superconducting nanowires, the diameter of the systems ranges from 10 to 1000 nm^{32,34,38,47,48,49} and our sample thickness is within that range. We need to further mention that the unique weak coupled TaS chains^{19,27,50} along the baxis, which are responsible for the superconductivity also make the superconductivity in Ta_{2}PdS_{5} nanowires quasi1D^{39,51}. Considering all the facts listed above, we conclude that the superconductivity in Ta_{2}PdS_{5} nanowire is quasi1D in nature (also see Supplementary Note 5 for all listed facts for quasi1D superconductivity in Ta_{2}PdS_{5} nanowires).
The observation of quantum Griffiths singularity state in Ta_{2}PdS_{5} also suggests that the critical phenomenon below the quantum critical point is described by exponentially small but nonzero probability of largeordered regionsrare regions, which can be viewed as the superconducting puddles surviving in the normal state background with a long time and length scale as the temperature approaches 0 K^{15,52}. Instead of one or two crossing points in the magnetoresistance isotherms cross in the SIT or SMT, recent observations of the quantum Griffiths singularity in thin Ga^{12} films and monolayer NbSe_{2}^{14} have shown one cross point in the hightemperature regime and a series of crossing points in the ultralowtemperature regime. Interestingly, our study in quasi1D Ta_{2}PdS_{5} nanowire has shown that the crossing point moves continuously in both high and lowtemperature regimes. As a result, the dynamical exponent z continuously varies in both high and lowtemperature regimes. The reason for this may be due to the fact that the thermal fluctuations at such a temperature regime (2–4 K) are unable to smear out the inhomogeneity caused by quenched disorders^{12,53,54}. However, the exquisite physics in this system needs further theoretical and experimental investigations.
In summary, we have demonstrated the systematic study of magnetotransport properties of quasi1D Ta_{2}PdS_{5} nanowires. The strong anisotropic superconducting behavior and hysteretic multiple voltage steps in its IV relation indicate its typical quasi1D nature in superconductivity. Importantly, the nanowire undergoes a SMT and shows signatures of quantum Griffiths singularity state when approaching zerotemperate quantum critical point. These findings shed lights on the understanding of the superconductormetal and metalinsulator transitions. In addition, the appealing physical properties unveiled in this study demonstrate Ta_{2}PdS_{5} to be a promising platform for possible applications in quantum computing devices.
Methods
Sample preparation
Single crystals of Ta_{2}PdS_{5} were synthesized by the CVT method using iodine as a transport agent. Before the crystal growth, a quartz tube containing iodine and the stoichiometric ratio of Ta, Pd, and S powders with 1% excess of S was evacuated and sealed. The sealed tube was then placed in a double zone furnace horizontally and grew for 2 weeks with the temperature gradient of 775–850 ^{o}C, after which needlelike single crystals of Ta_{2}PdS_{5} were formed at the lowtemperature end.
Material characterizations
The structural and compositional characteristics of the nanowires were investigated using TEM (FEI Tecnai F20, 200 kV, equipped with EDS). The nanowires were dry transferred onto Lacey carbon films supported by a copper grid.
Device fabrication
Ta_{2}PdS_{5} nanowires with different thickness were obtained through mechanical exfoliation onto prepatterned SiO_{2}(285 nm)/Si substrates from bulk crystals. The electrical contacts of Ta_{2}PdS_{5} devices were fabricated along the baxis of the crystal by EBL using Polymethylmethacrylate/Methyl methacrylate bilayer polymer. Ti/Au (5 nm/150 nm) electrodes were then deposited using magnetron sputtering.
Transport measurements
Fourterminal temperaturedependent magnetotransport and IV measurement measurements were carried out in a Physical Property Measurement System (PPMS) system (Quantum Design) using lockin amplifier (SR830), Agilent 2912 and Keithley 2182. Ultralowtemperature magnetotransport measurements were performed in an Oxford 3He/4Hedilution refrigerator equipped with a superconducting magnet using SR830.
Data availability
All of the experimental data supporting this study are available from the corresponding author.
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Acknowledgements
This work was supported by the National Key Research and Development Program of China (grant no. 2018YFA0305601 and 2017YFA0303302) and National Natural Science Foundation of China (11474058, 61674040, and 11874116), and the Australian Research Council. Part of the sample fabrication was performed at Fudan Nanofabrication Laboratory. The singlecrystal growth at Tulane was supported by the US Department of Energy (DOE) under grant no. DESC0014208. We thank Jiwei Ling and Prof. Haiwen Liu for helpful discussions.
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F.X. conceived the idea and supervised the experiments. E.Z., Z.F., L.A., J.S., C.H., S.L., Z.L., and X.Z. carried out the device fabrication. E.Z. performed lowtemperature measurements and data analysis. J.Z., E.Z., N.K., H.X., W.W., and L.H. conducted the magnetotransport measurements at dilution temperature. J.L. and Z.M. synthetized Ta_{2}PdS_{5} single crystals. YC.Z. and J.Z. performed structural characterization and analysis. E.Z. and F.X. wrote the paper with the help from all other authors.
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Zhang, E., Zhi, J., Zou, YC. et al. Signature of quantum Griffiths singularity state in a layered quasionedimensional superconductor. Nat Commun 9, 4656 (2018). https://doi.org/10.1038/s4146701807123y
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