⇦Chinese Physics Letters, 2022, Vol. 39, No. 12, Article code 127401Express Letter NMR Evidence for Universal Pseudogap Behavior in Quasi-Two-Dimensional FeSe-Based Superconductors B. L. Kang (康宝蕾)1†, M. Z. Shi (石孟竹)1†, D. Zhao (赵丹)1, S. J. Li (李顺姣)1, J. Li (李建)1, L. X. Zheng (郑立玄)1, D. W. Song (宋殿武)1, L. P. Nie (聂林鹏)1, T. Wu (吴涛)1,2,3,4,5*, and X. H. Chen (陈仙辉)1,2,3,4,5* Affiliations 1Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China 2Key Laboratory of Strongly coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, Hefei 230026, China 3CAS Center for Excellence in Superconducting Electronics (CENSE), Shanghai 200050, China 4Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China 5Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China Received 20 September 2022; accepted manuscript online 31 October 2022; published online 10 November 2022 †These authors contributed equally to this work.
*Corresponding authors. Email: wutao@ustc.edu.cn; chenxh@ustc.edu.cn Citation Text: Kang B L, Shi M Z, Zhao D et al. 2022 Chin. Phys. Lett. 39 127401    Abstract Recently, by intercalating organic ions into bulk FeSe superconductors, two kinds of layered FeSe-based superconductors [(TBA)$_{x}$FeSe and (CTA)$_{x}$FeSe] with superconducting transition temperatures ($T_{\rm c}$) above 40 K have been discovered. Due to the large interlayer distance ($\sim $15 Å), these new layered superconductors have a large resistivity anisotropy analogous to bismuth-based cuprate superconductors. Moreover, remarkable pseudogap behavior well above $T_{\rm c}$ is revealed by nuclear magnetic resonance (NMR) measurements on $^{77}$Se nuclei, suggesting a preformed pairing scenario similar to that of cuprates. Here, we report another new kind of organic-ion-intercalated FeSe superconductor, (PY)$_{x}$FeSe, with a reduced interlayer distance ($\sim $10 Å) compared to (TBA)$_{x}$FeSe and (CTA)$_{x}$FeSe. By performing $^{77}$Se NMR and transport measurements, we observe a similar pseudogap behavior well above $T_{\rm c}$ of $\sim $40 K and a large resistivity anisotropy of $\sim$$10^{\boldsymbol{4}}$ in (PY)$_{x}$FeSe. All these facts strongly support a universal pseudogap behavior in these layered FeSe-based superconductors with quasi-two-dimensional electronic structures.
cpl-39-12-127401-fig1.png
cpl-39-12-127401-fig2.png
cpl-39-12-127401-fig3.png
cpl-39-12-127401-fig4.png
 DOI:10.1088/0256-307X/39/12/127401 © 2022 Chinese Physics Society Article Text Cooper pairing and superconducting phase coherence are two indispensable prerequisites for realizing macroscopic superconductivity, which occurs simultaneously in Bardeen–Cooper–Schrieffer (BCS) superconductors. In contrast, Cooper pairing occurs prior to superconducting phase coherence in high-$T_{\rm c}$ cuprate superconductors, which has been used to account for the well-known pseudogap phenomenon.[1-3] In this sense, superconducting transition temperature ($T_{\rm c}$) is determined by phase coherence instead of Cooper pairing.[1] Although whether the preformed Cooper pairing can persist up to the pseudogap temperature is still under debate, evidence for fluctuating superconductivity is widely observed to be well above $T_{\rm c}$ in cuprates.[2,4-6] Recently, the evidence for fluctuating superconductivity above $T_{\rm c}$ was also reported in heavily hole-doped cuprates Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (Bi2212), which further strengthens the above picture and suggests a generic nature of superconductivity in cuprates.[7] How to understand the preformed Cooper pairing well above $T_{\rm c}$ is still an open question. In iron-based superconductors, whether preformed Cooper pairing exists remains elusive experimentally.[8-13] The discovery of high-$T_{\rm c}$ superconductivity in a single-layer FeSe/SrTiO$_{3}$ film (FeSe/STO) sheds new light on this issue.[14] Although FeSe/STO exhibits a large superconducting gap of approximately 20 meV with a gap opening temperature of approximately 65 K, the zero-resistance temperature determined by transport measurement is always lower than 40 K.[15-18] These results strongly suggest a possible pseudogap behavior due to preformed Cooper pairing in FeSe/STO films. Recently, two kinds of organic-ion-intercalated FeSe-based superconductors have been successfully synthesized with $T_{\rm c}$ above 40 K, which exhibit a quasi-two-dimensional (quasi-2D) electronic structure analogous to bismuth-based cuprate superconductors.[19-21] Interestingly, a pseudogap behavior similar to that in cuprates has been revealed to be well above $T_{\rm c}$ by nuclear magnetic resonance (NMR) measurements, suggesting the existence of preformed Cooper pairing.[19] Meanwhile, the preformed Cooper pairing picture is further supported by angle-resolved photoemission spectroscopy (ARPES) and in situ transport measurements on single-layer FeSe/STO.[22,23] On the other hand, it is quite confusing that pseudogap behavior has not been reported in layered FeAs-based superconductors or other layered FeSe-based superconductors, including CsCa$_{2}$Fe$_{4}$As$_{4}$F$_{2}$[24] and (Li,Fe)OHFeSe.[25] To date, how to understand the origin of pseudogap behavior in organic-ion-intercalated FeSe-based superconductors and FeSe/STO films is still under debate. Whether the quasi-2D electronic structure is a necessary condition for observing pseudogap behavior also needs more investigation. In this work, a new kind of organic-ion-intercalated FeSe superconductor (PY)$_{x}$FeSe ($x\sim 0.15$) was successfully synthesized with $T_{\rm c} \sim 40$ K (see the Supplemental Material). Through the intercalation of organic ions 1-butyl-1-methylpyrrolidinium (PY$^{+}$), the distance between adjacent FeSe layers is expanded to 10.5 Å, which is smaller than the $\sim $15 Å of (CTA)$_{x}$FeSe and (TBA)$_{x}$FeSe but close to the 9.32 Å of (Li,Fe)OHFeSe. As is commonly believed, charge transfer from organic ions to FeSe layers plays an essential role in achieving a high-$T_{\rm c}$ superconductivity of approximately 40 K.[15,18,26,27] On the other hand, the enlarged interlayer distance would also weaken the interlayer coupling compared to bulk FeSe. As shown in Fig. 1, through the intercalation of various organic ions from (PY$^{+}$) to (TBA$^{+}$), the distance between adjacent FeSe layers is largely expanded with a similar layered structure. By measuring the Knight shift and nuclear spin-lattice relaxation rate, a pseudogap behavior similar to that in (CTA)$_{x}$FeSe and (TBA)$_{x}$FeSe is revealed below $T_{\rm p} \sim 60$ K in (PY)$_{x}$FeSe. Moreover, the electrical transport measurement also reveals a large resistivity anisotropy up to $\sim$$10^{4}$, supporting a quasi-2D electronic structure. These results indicate that the pseudogap behavior in these new layered FeSe-based superconductors is tied to a quasi-2D electronic structure instead of the interlayer distance, which may explain the absence of pseudogap behavior in other layered iron-based superconductors with moderate resistivity anisotropy [e.g., (Li,Fe)OHFeSe].
cpl-39-12-127401-fig1.png
Fig. 1. Crystal structures of (a) FeSe, (b) (PY)$_{x}$FeSe, (c) (CTA)$_{x}$FeSe, and (d) (TBA)$_{x}$FeSe. Accurate molecular selection enables fine tuning of the interlayer distance $d$. Temperature dependence of the magnetic susceptibility measured in field-cooling (FC) and zero-field-cooling (ZFC) modes under a magnetic field of 5 Oe applied out of plane for (e) FeSe, (f) (PY)$_{x}$FeSe, (g) (CTA)$_{x}$FeSe, and (h) (TBA)$_{x}$FeSe.
It is well known that NMR is a bulk-sensitive technique to probe pseudogap behavior since it provides a direct measure of local spin susceptibility ($\chi_{\rm s}$).[28,29] In cuprate superconductors, the pseudogap manifests as a simultaneous reduction in the Knight shift ($K$) and nuclear spin-lattice relaxation rate (1/$T_{1}$).[30,31] Usually, the total Knight shift can be divided into two parts with $K_{\rm tot}=K_{\rm s} + K_{\rm orb}$, where $K_{\rm orb}$ is a temperature-independent orbital shift and $K_{\rm s}$ is a temperature-dependent spin shift. The spin shift is related to the uniform spin susceptibility with $K_{\rm s} = A\chi_{\rm s}$, where $A$ is the hyperfine coupling tensor between nuclear and electronic spins. The nuclear spin-lattice relaxation rate is related to dynamical spin susceptibility and can be expressed as $1 / {T_{1}T}\sim \sum_q {\gamma_{n}^{2}{ \vert }{A_{\bot }\left( q \right)\vert }^{2}{\chi''\left( q,\omega \right)} / \omega}$, where $A_{\bot }\left( q \right)$ is the transverse hyperfine form factor and $\chi''\left( q,\omega \right)$ is the imaginary part of the dynamical susceptibility in the direction perpendicular to the external field. In a conventional Fermi-liquid picture, $1/T_{1}T$ and $K_{\rm s}$ follow a simple Korringa relation with $1/T_{1}T \sim K_{\rm s}^{2} \sim N(E_{\rm F})^{2}$, where $N(E_{\rm F})$ is the density of states at Fermi energy. In this context, both $K_{\rm s}$ and $1/T_{1}T$ can be used to measure the suppression of $N(E_{\rm F})$ due to the formation of a pseudogap. In Fig. 2, the $^{77}$Se NMR evidence for pseudogap behavior in three organic-ion-intercalated FeSe-based superconductors is summarized, including the new result of (PY)$_{x}$FeSe and the previously reported results of (CTA)$_{x}$FeSe and (TBA)$_{x}$FeSe.[19] To improve the signal-to-noise ratio, 50% $^{77}$Se isotope-enriched samples were used in the measurement of (PY)$_{x}$FeSe and (TBA)$_{x}$FeSe. As shown in Figs. 2(a)–2(c), the temperature-dependent Knight shift of $^{77}$Se nuclei shows a clear deviation from its high-temperature behavior below 60 K, which was ascribed to preformed Cooper pairing in previous work.[19] The absence of any change in the NMR spectral profile indicates that the shift of the NMR spectrum to a low frequency below 60 K comes from an intrinsic suppression of the uniform spin susceptibility (also see the Supplemental Material).[19] As shown in Figs. 2(d)–2(f), a similar deviation from the high-temperature behavior is also observed in the temperature-dependent $1/T_{1}T$ below $\sim $60 K. The similar temperature-dependent behavior in both the Knight shift and $1/T_{1}T$ confirms that the observed pseudogap behavior should originate from quasiparticle-like excitations. More analysis of the temperature-dependent evolution of the Korringa ratio over the whole temperature range will be discussed elsewhere. In summary, the above NMR results display a universal pseudogap behavior in these organic-ion-intercalated FeSe-based superconductors with the characteristic temperature $T_{\rm p} \sim 60$ K. In addition, the observed pseudogap behavior in NMR measurements is almost independent of field orientation or strength in our present field range (see the Supplemental Material), which is consistent with the large pairing gap ($\sim $16 meV) observed by scanning tunneling microscopy/spectroscopy (STM/S) experiments.[19]
cpl-39-12-127401-fig2.png
Fig. 2. (a)–(c) Temperature dependence of the Knight shift $^{77}K_{ab}$ for (PY)$_{x}$FeSe, (CTA)$_{x}$FeSe, and (TBA)$_{x}$FeSe with an external magnetic field applied along $ab$ plane. (d)–(f) Temperature evolution of the spin-lattice relaxation rate divided by temperature, 1/$^{77}T_{1}^{ab}T$, for (PY)$_{x}$FeSe, (CTA)$_{x}$FeSe, and (TBA)$_{x}$FeSe with an external magnetic field applied along $ab$ plane. The external magnetic field is $\sim $12 T. The data of (CTA)$_{x}$FeSe and (TBA)$_{x}$FeSe are taken from Ref. [19].
cpl-39-12-127401-fig3.png
Fig. 3. The anisotropy ratio of electrical transport $\rho_{c}/\rho_{ab}$ for (a) (PY)$_{x}$FeSe, (b) (CTA)$_{x}$FeSe, and (c) (TBA)$_{x}$FeSe. The inset shows the temperature dependence of in-plane and out-of-plane resistivity in the temperature range of 20–300 K. The results indicate an extremely large anisotropy ratio of up to $10^{4}$ in these intercalated FeSe-based superconductors, which suggests a quasi-2D electronic structure. The data of (CTA)$_{x}$FeSe and (TBA)$_{x}$FeSe are taken from Ref. [19].
To verify the dimensionality of the electronic structure, the in-plane and out-of-plane resistivities ($\rho_{ab}$ and $\rho_{c}$) were also measured in these organic-ion-intercalated FeSe-based superconductors. As shown in Fig. 3, it is clear that all the three samples exhibit a similar temperature-dependent resistivity anisotropy ($\rho_{c}/\rho_{ab}$). Although the anisotropy ratio of (PY)$_{x}$FeSe reaches $\sim$$10^{4}$ at 50 K, this value is one order of magnitude smaller than $\sim $$10^{5}$ for (CTA)$_{x}$FeSe and (TBA)$_{x}$FeSe.[19] Considering the smaller interlayer distance in (PY)$_{x}$FeSe, this result is quite reasonable. As shown in the inset of Fig. 3, while the in-plane resistivity $\rho_{ab}$ displays metallic behavior over almost the whole temperature range, the out-of-plane resistivity $\rho_{c}$ of the three samples exhibits a similar hump behavior from 150 K to 200 K, suggesting a possible electronic crossover.[32] It should be noted that, regardless of the interlayer distance, the large value of the anisotropy ratio above $\sim$$10^{4}$ strongly supports a generic quasi-2D electronic structure in these organic-ion-intercalated FeSe-based superconductors, which exhibit a great similarity to bismuth-based cuprate superconductors.[20,21] We think that this should be an important prerequisite for the emergence of pseudogap behavior in these samples. Next, we will discuss the correlation between the anisotropy ratio and pseudogap behavior by involving more iron-based superconductors. As shown in Fig. 4, the relationship between $\rho_{c}/\rho_{ab}$ and interlayer distance $d$ is summarized for several selected layered iron-based superconductors and cuprates. Empirically, the anisotropy ratio, which reflects the 2D nature of the electronic structure, should be enhanced by increasing the interlayer distance. However, in practice, it usually depends on what kind of blocking layer is used in the layered structure. For example, with a comparable interlayer distance of $\sim $$10$ Å, the anisotropy ratio of Ca$_{10}$(Pt$_{4}$As$_{8}$)((Fe$_{0.86}$ Pt$_{0.14})_{2}$As$_{2})_{5}$ with metallic blocking layers is much smaller than that of (Li,Fe)OHFeSe and (PY)$_{x}$FeSe with insulating blocking layers. Therefore, the 2D nature of the electronic structure also depends on the nature of the blocking layers.
cpl-39-12-127401-fig4.png
Fig. 4. A summarized $\rho_{c}/\rho_{ab}$ plot for a series of layered high-$T_{\rm c}$ superconductors. The data points labeled in filled squares, open triangles, and open circles represent FeSe-based superconductors, FeAs-based superconductors, and cuprates, respectively. The $d$ of cuprates is defined as the Cu–O single-layer, double-layer or tri-layer separations. The data points except for (PY)$_{x}$FeSe are taken from Refs. [19,32-56].
Our new results indicate that the newly discovered organic-ion-intercalated FeSe-based superconductors [(PY)$_{x}$FeSe, (CTA)$_{x}$FeSe, and (TBA)$_{x}$FeSe] display a generic quasi-2D electronic structure with an anisotropy ratio above $\sim $$10^{4}$, in which universal pseudogap behavior is observed. In contrast, pseudogap behavior is absent in (Li,Fe)OHFeSe with an anisotropy ratio of only approximately $10^{3}$. Furthermore, most FeAs-based superconductors also exhibit a smaller anisotropy ratio than organic-ion-intercalated FeSe-based superconductors. As shown in Fig. 4, the anisotropy ratio of CsCa$_{2}$Fe$_{4}$As$_{4}$F$_{2}$, which has the largest anisotropy ratio among all FeAs-based superconductors, is only $\sim$$10^{3}$. Accordingly, there has been no evidence for the existence of pseudogap behavior in FeAs-based superconductors. These facts suggest that the extremely 2D electronic structure should play a crucial role in the emergence of pseudogap behavior in these organic-ion-intercalated FeSe-based superconductors. In addition, the nearly same pairing temperature of $\sim $60 K in these organic-ion-intercalated FeSe-based superconductors is ascribed to the similar electron doping level and quasi-2D electronic structure in these materials. This could also be used to explain the possible pseudogap behavior in the FeSe/STO film due to a 2D electronic structure.[14-18] Recent ARPES and in situ transport measurements further support the preformed Cooper pairing picture in the FeSe/STO film.[22,23] On the other hand, a similar pseudogap behavior due to preformed Cooper pairing has also been revisited in overdoped Bi2212.[7] The quantitative theoretical calculation indicates that a von Hove singularity close to the Fermi level may further boost the 2D superconducting fluctuations. Whether superconducting fluctuations due to phase fluctuations are enough to account for the pseudogap behavior up to 60 K still needs more theoretical investigations in these organic-ion-intercalated FeSe-based superconductors. On the other hand, the physics of BCS-BEC crossover has also been discussed in iron chalcogenide superconductors recently,[8,57-60] which may be one possible picture to account for the above-mentioned preformed Cooper pairing. In the BCS-BEC crossover regime, the coherence length of Cooper pair ($\xi$) is required to be comparable to $1/k_{\rm F}$, where $k_{\rm F}$ is the Fermi wave vector. Equivalently, the ratio of the pairing gap $\varDelta$ to the bandwidth or Fermi energy $E_{\rm F}$ is also required to be of order unity ($\varDelta /E_{\rm F} \sim 1$). Except for bulk FeSe, in most heavily electron-doped FeSe-based superconductors including K$_{0.8}$Fe$_{2}$Se$_{2}$ and (Li,Fe)OHFeSe, the $\varDelta /E_{\rm F}$ is closer to the BCS limit rather than the BCS-BEC crossover regime.[59,61] In our case, since the organic-ion-intercalated FeSe-based superconductors own a comparable pairing gap and similar electron doping level with (Li,Fe)OHFeSe, the BCS-BEC crossover is also less possible for the emergence of preformed Cooper pairing. In summary, our present work reveals a universal pseudogap behavior tied to quasi-2D electronic structures in newly discovered organic-ion-intercalated FeSe-based superconductors. These results also offer a natural explanation for the mysterious superconducting behavior in the FeSe/STO film, suggesting a generic nature of 2D superconductivity in this system. Finally, the similar pseudogap behavior observed in both bismuth-based cuprates and layered FeSe-based superconductors with quasi-2D electronic structures should be key to understanding the nature of high-$T_{\rm c}$ superconductivity. Acknowledgments. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11888101 and 12034004), the National Key R&D Program of China (Grant No. 2017YFA0303000), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB25000000), the Anhui Initiative in Quantum Information Technologies (Grant No. AHY160000), and the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302800). References Importance of phase fluctuations in superconductors with small superfluid densityVanishing of phase coherence in underdoped Bi2Sr2CaCu2O8+δUniversal Correlations between T c and n s m * (Carrier Density over Effective Mass) in High- T c Cuprate SuperconductorsNernst effect in high- T c superconductorsFluctuations and critical temperature reduction in cuprate superconductorsDiamagnetism and Cooper pairing above T c in cupratesSuperconducting Fluctuations in Overdoped Bi 2 Sr 2 CaCu 2 O 8 + δ Giant superconducting fluctuations in the compensated semimetal FeSe at the BCS–BEC crossoverQuantum Vortex Core and Missing Pseudogap in the Multiband BCS-BEC Crossover Superconductor FeSeSuperconducting fluctuations in FeSe investigated by precise torque magnetometrySuperconductivity-induced transverse plasma mode and phonon anomaly in the c -axis response of the bilayer compound RbCa 2 Fe 4 As 4 F 2 Pseudogap and Strong Pairing Induced by Incipient and Shallow Bands in the Quasi-Two-Dimensional KCa$_{2}$Fe$_{4}$As$_{4}$F$_{2}$Ultrafast Optical Spectroscopy Evidence of Pseudogap and Electron-Phonon Coupling in an Iron-Based Superconductor KCa$_2$Fe$_4$As$_4$F$_2$Interface-Induced High-Temperature Superconductivity in Single Unit-Cell FeSe Films on SrTiO3Phase diagram and electronic indication of high-temperature superconductivity at 65 K in single-layer FeSe filmsInterface-induced superconductivity and strain-dependent spin density waves in FeSe/SrTiO3 thin filmsDirect Observation of High-Temperature Superconductivity in One-Unit-Cell FeSe FilmsInterface charge doping effects on superconductivity of single-unit-cell FeSe films on SrTiO 3 substratesPreformed Cooper Pairs in Layered FeSe-Based SuperconductorsEvolution of the resistivity anisotropy in Bi 2 Sr 2 − x La x CuO 6 + δ single crystals for a wide range of hole dopingAnisotropic resistivities of single-crystal Bi 2 Sr 2 CaCu 2 O 8 + δ with different oxygen contentSpectroscopic evidence of superconductivity pairing at 83 K in single-layer FeSe/SrTiO3 filmsIncoherent Cooper Pairing and Pseudogap Behavior in Single-Layer FeSe / SrTi O 3 Crystal structure and superconductivity at about 30 K in ACa2Fe4As4F2 (A = Rb, Cs)Coexistence of superconductivity and antiferromagnetism in (Li0.8Fe0.2)OHFeSeHigh-temperature superconductivity in potassium-coated multilayer FeSe thin filmsEvolution of High-Temperature Superconductivity from a Low- T c Phase Tuned by Carrier Concentration in FeSe Thin FlakesNMR Studies of the Normal State of High Temperature SuperconductorsNuclear magnetic relaxation and resonnance line shift in metals Y 89 NMR evidence for a fermi-liquid behavior in YBa 2 Cu 3 O 6 + x Pseudogap behavior in single-crystal Bi 2 Sr 2 CaCu 2 O 8 + δ probed by Cu NMR ( Li 0.84 Fe 0.16 ) OHFe 0.98 Se superconductor: Ion-exchange synthesis of large single-crystal and highly two-dimensional electron propertiesElectrical and Thermal Transport Properties of Layered Superconducting Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 Single CrystalSuperconductivity at 32 K and anisotropy in Tl0.58 Rb0.42 Fe1.72 Se2 crystalsExtreme anisotropy and anomalous transport properties of heavily electron doped Li x ( NH 3 ) y Fe 2 Se 2 single crystalsTransport and anisotropy in single-crystalline SrFe 2 As 2 and A 0.6 K 0.4 Fe 2 As 2 ( A = Sr , Ba) superconductorsAnisotropic thermodynamic and transport properties of single-crystalline CaKFe 4 As 4 Anisotropic superconductivity and magnetism in single-crystal RbEuFe 4 As 4 Temperature dependence of the upper critical field of FeSe single crystalsGiant anisotropy in superconducting single crystals of CsCa 2 Fe 4 As 4 F 2 Anisotropic transport properties of single-crystal La 2 − x Sr x CuO 4 : Evidence for the dimensional crossoverCompositional dependence of transport anisotropy in large (La, Sr)2CuO4 single crystals and second peak in magnetization curvesLogarithmic Divergence of both In-Plane and Out-of-Plane Normal-State Resistivities of Superconducting La 2 − x Sr x Cu O 4 in the Zero-Temperature LimitInsulator-to-Metal Crossover in the Normal State of La 2 − x Sr x CuO 4 Near Optimum DopingNormal-state transport properties of slightly overdoped Y Ba 2 Cu 3 O y crystals prepared by a crystal-pulling techniqueInterplane charge transport in YBa 2 Cu 3 O 7 − y : Spin-gap effect on in-plane and out-of-plane resistivityMeasurement of anisotropic resistivity and Hall constant for single-crystal YBa 2 Cu 3 O 7 − x Out-of-plane conductivity in single-crystal YBa 2 Cu 3 O 7 Diverging resistivity anisotropy with decreasing temperature in 60-K YBa 2 Cu 2 O 7 − y Normal-state transport properties of Bi 2 + x Sr 2 − y CuO 6 + δ crystalsCrystal growth and anisotropic resistivity of Bi 2 Sr 2 − x La x CuO y Metallic In-Plane and Divergent Out-of-Plane Resistivity of a High- T c Cuprate in the Zero-Temperature LimitAnisotropic Resistivities of Precisely Oxygen Controlled Single-Crystal Bi 2 Sr 2 CaCu 2 O 8 + δ : Systematic Study on “Spin Gap” EffectTemperature Dependence of the Resistivity Tensor in Superconducting Bi 2 Sr 2.2 Ca 0.8 Cu 2 O 8 CrystalsSingle-crystal growth of Bi2Sr2Ca2Cu3O10+δ (Bi-2223) by TSFZ methodDoping dependence of anisotropic resistivities in the trilayered superconductor Bi 2 Sr 2 Ca 2 Cu 3 O 1 0 + δ Field-induced superconducting phase of FeSe in the BCS-BEC cross-overShallow pockets and very strong coupling superconductivity in FeSexTe1−xTuning across the BCS-BEC crossover in the multiband superconductor Fe 1+ y Se x Te 1− x : An angle-resolved photoemission studyThermodynamics of transition to BCS-BEC crossover superconductivity in FeSe$_{1-x}$S$_x$Superconductivity of the FeSe/SrTiO3 Interface in View of BCS–BEC Crossover*
[1] Emery V J and Kivelson S A 1995 Nature 374 434
[2] Corson J, Mallozzi R, Orenstein J, Eckstein J N, and Bozovic I 1999 Nature 398 221
[3] Uemura Y J et al. 1989 Phys. Rev. Lett. 62 2317
[4] Wang Y Y, Li L, and Ong N P 2006 Phys. Rev. B 73 024510
[5] Tallon J L, Storey J G, and Loram J W 2011 Phys. Rev. B 83 092502
[6] Li L, Wang Y Y, Komiya S, Ono S, Ando Y, Gu G D, and Ong N P 2010 Phys. Rev. B 81 054510
[7] He Y, Chen S D, Li Z X, Zhao D, Song D, Yoshida Y, Eisaki H, Wu T, Chen X H, Lu D H, Meingast C, Devereaux T P, Birgeneau R J, Hashimoto M, Lee D H, and Shen Z X 2021 Phys. Rev. X 11 031068
[8] Kasahara S, Yamashita T, Shi A, Kobayashi R, Shimoyama Y, Watashige T, Ishida K, Terashima T, Wolf T, Hardy F, Meingast C, Von Lohneysen H, Levchenko A, Shibauchi T, and Matsuda Y 2016 Nat. Commun. 7 12843
[9] Hanaguri T, Kasahara S, Boker J, Eremin I, Shibauchi T, and Matsuda Y 2019 Phys. Rev. Lett. 122 077001
[10] Takahashi H, Nabeshima F, Ogawa R, Ohmichi E, Ohta H, and Maeda A 2019 Phys. Rev. B 99 060503
[11] Xu B, Munzar D, Dubroka A, Sheveleva E, Lyzwa F, Marsik P, Wang C N, Wang Z C, Cao G H, and Bernhard C 2020 Phys. Rev. B 101 214512
[12] Hao J H, Hong W S, Zhou X X, Xiang Y, Dai Y M, Yang H, Li S L, Luo H Q, and Wen H H 2021 arXiv:2111.04422 [cond-mat.supr-con]
[13] Zhang C, Wu Q Y, Hong W S, Liu H, Zhu S X, Song J J, Zhao Y Z, Wu Y Z, Liu Z T, Liu S Y, Yuan Y H, Huang H, He J, Li S L, Liu H Y, Duan Y X, Luo H Q, and Meng J Q 2021 arXiv:2109.06460 [cond-mat.supr-con]
[14] Wang Q Y, Li Z, Zhang W H, Zhang Z C, Zhang J S, Li W, Ding H, Ou Y B, Deng P, Chang K, Wen J, Song C L, He K, Jia J F, Ji S H, Wang Y Y, Wang L L, Chen X, Ma X C, and Xue Q K 2012 Chin. Phys. Lett. 29 037402
[15] He S L et al. 2013 Nat. Mater. 12 605
[16] Tan S Y, Zhang Y, Xia M, Ye Z R, Chen F, Xie X, Peng R, Xu D F, Fan Q, Xu H C, Jiang J, Zhang T, Lai X C, Xiang T, Hu J P, Xie B P, and Feng D L 2013 Nat. Mater. 12 634
[17] Zhang W H et al. 2014 Chin. Phys. Lett. 31 017401
[18] Zhang W H, Li Z, Li F S, Zhang H M, Peng J P, Tang C J, Wang Q Y, He K, Chen X, Wang L L, Ma X C, and Xue Q K 2014 Phys. Rev. B 89 060506
[19] Kang B L, Shi M Z, Li S J, Wang H H, Zhang Q, Zhao D, Li J, Song D W, Zheng L X, Nie L P, Wu T, and Chen X H 2020 Phys. Rev. Lett. 125 097003
[20] Ono S and Ando Y 2003 Phys. Rev. B 67 104512
[21] Chen X H, Yu M, Ruan K Q, Li S Y, Gui Z, Zhang G C, and Cao L Z 1998 Phys. Rev. B 58 14219
[22] Xu Y, Rong H T, Wang Q Y, Wu D S, Hu Y, Cai Y Q, Gao Q, Yan H T, Li C, Yin C H, Chen H, Huang J W, Zhu Z H, Huang Y, Liu G D, Xu Z Y, Zhao L, and Zhou X J 2021 Nat. Commun. 12 2840
[23] Faeth B D et al. 2021 Phys. Rev. X 11 021054
[24] Wang Z C, He C Y, Tang Z T, Wu S Q, and Cao G H 2017 Sci. Chin. Mater. 60 83
[25] Lu X F, Wang N Z, Wu H, Wu Y P, Zhao D, Zeng X Z, Luo X G, Wu T, Bao W, Zhang G H, Huang F Q, Huang Q Z, and Chen X H 2015 Nat. Mater. 14 325
[26] Miyata Y, Nakayama K, Sugawara K, Sato T, and Takahashi T 2015 Nat. Mater. 14 775
[27] Lei B, Cui J H, Xiang Z J, Shang C, Wang N Z, Ye G J, Luo X G, Wu T, Sun Z, and Chen X H 2016 Phys. Rev. Lett. 116 077002
[28] Berthier C, Julien M H, Horvatic M, and Berthier Y 1996 J. Phys. I (France) 6 2205
[29] Korringa J 1950 Phys. (Amsterdam) 16 601
[30] Alloul H, Ohno T, and Mendels P 1989 Phys. Rev. Lett. 63 1700
[31] Ishida K, Yoshida K, Mito T, Tokunaga Y, Kitaoka Y, Asayama K, Nakayama Y, Shimoyama J, and Kishio K 1998 Phys. Rev. B 58 R5960(R)
[32] Dong X L, Jin K, Yuan D N, Zhou H X, Yuan J, Huang Y L, Hua W, Sun J L, Zheng P, Hu W, Mao Y Y, Ma M W, Zhang G M, Zhou F, and Zhao Z X 2015 Phys. Rev. B 92 064515
[33] Wu D P, Meng X D, Zhai Y Y, Yu H M, Yu J, and Qi Y 2019 Materials 12 474
[34] Wang H D, Dong C H, Li Z J, Mao Q H, Zhu S S, Feng C M, Yuan H Q, and Fang M H 2011 Europhys. Lett. 93 47004
[35] Sun S S, Wang S H, Yu R, and Lei H C 2017 Phys. Rev. B 96 064512
[36] Chen G F, Li Z, Dong J, Li G, Hu W Z, Zhang X D, Song X H, Zheng P, Wang N L, and Luo J L 2008 Phys. Rev. B 78 224512
[37] Meier W R, Kong T, Kaluarachchi U S, Taufour V, Jo N H, Drachuck G, Bohmer A E, Saunders S M, Sapkota A, Kreyssig A, Tanatar M A, Prozorov R, Goldman A I, Balakirev F F, Gurevich A, Bud'ko S L, and Canfield P C 2016 Phys. Rev. B 94 064501
[38] Smylie M P, Willa K, Bao J K, Ryan K, Islam Z, Claus H, Simsek Y, Diao Z, Rydh A, Koshelev A E, Kwok W K, Chung D Y, Kanatzidis M G, and Welp U 2018 Phys. Rev. B 98 104503
[39] Vedeneev S I, Piot B A, Maude D K, and Sadakov A V 2013 Phys. Rev. B 87 134512
[40] Wang Z C, Liu Y, Wu S Q, Shao Y T, Ren Z, and Cao G H 2019 Phys. Rev. B 99 144501
[41] Nakamura Y and Uchida S 1993 Phys. Rev. B 47 8369
[42] Kimura T, Kishio K, Kobayashi T, Nakayama Y, Motohira N, Kitazawa K, and Yamafuji K 1992 Physica C 192 247
[43] Ando Y, Boebinger G S, Passner A, Kimura T, and Kishio K 1995 Phys. Rev. Lett. 75 4662
[44] Boebinger G S, Ando Y, Passner A, Kimura T, Okuya M 1, Shimoyama J, Kishio K, Tamasaku K, Ichikawa N, and Uchida S 1996 Phys. Rev. Lett. 77 5417
[45] Terasaki I, Sato Y, Miyamoto S, Tajima S, and Tanaka S 1995 Phys. Rev. B 52 16246
[46] Takenaka K, Mizuhashi K, Takagi H, and Uchida S 1994 Phys. Rev. B 50 6534
[47] Tozer S W, Kleinsasser A W, Penney T, Kaiser D, and Holtzberg F 1987 Phys. Rev. Lett. 59 1768
[48] Hagen S J, Jing T W, Wang Z Z, Horvath J, and Ong N P 1988 Phys. Rev. B 37 7928
[49] Brawner D A, Wang Z Z, and Ong N P 1989 Phys. Rev. B 40 9329
[50] Martin S, Fiory A T, Fleming R M, Schneemeyer L F, and Waszczak J V 1990 Phys. Rev. B 41 846
[51] Wang N L, Buschinger B, Geibel C, and Steglch F 1996 Phys. Rev. B 54 7449
[52] Ando Y, Boebinger G S, Passner A, Wang N L, Geibel C, and Steglich F 1996 Phys. Rev. Lett. 77 2065
[53] Watanabe T, Fujii T, and Matsuda A 1997 Phys. Rev. Lett. 79 2113
[54] Martin S, Fiory A T, Fleming R M, Schneemeyer L F, and Waszczak J V 1988 Phys. Rev. Lett. 60 2194
[55] Fujii T, Watanabe T, and Matsuda A 2001 J. Cryst. Growth 223 175
[56] Fujii T, Terasaki I, Watanabe T, and Matsuda A 2002 Phys. Rev. B 66 024507
[57] Kasahara S, Watashige T, Hanaguri T, Kohsaka Y, Yamashita T, Shimoyama Y, Mizukami Y, Endo R, Ikeda H, Aoyama K, Terashima T, Uji S, Wolk T, H, von L, Shibauchi T, and Matsuda Y 2014 Proc. Natl. Acad. Sci. USA 111 16309
[58] Lubashevsky Y, Lahoud E, Chashka K, Podolsky D, and Kanigel A 2012 Nat. Phys. 8 309
[59] Rinott S, Chashka K, Ribak A, Rienks E D, Taleb-Ibrahimi A, Fevre P L, Bertran F, Randeria M, and Kanigel A 2017 Sci. Adv. 3 e1602372
[60] Mizukami Y, Haze M, Tanaka O, Matsuura K, Sano D, Böker J, Eremin I, Kasahara S, Matsuda Y, and Shibauchi T 2021 arXiv:2105.00739v1 [cond-mat.supr-con]
[61] Zhang S Y, Miao G Y, Guan J Q, Xu X F, Liu B, Yang F, Wang W H, Zhu X T, and Guo J D 2019 Chin. Phys. Lett. 36 107404