Hydrostatic pressure effect on the pseudogap in Y0.66Pr0.34Ba2Cu3O7–δ single crystals
DOI (Low Temperature Physics):
https://doi.org/10.1063/10.0046880Ключові слова:
high-temperature superconductors, praseodymium doping, superconducting transition temperature, fluctuation conductivity, pseudogap, Ginzburg numberАнотація
The influence of hydrostatic pressure (HP) up to ∼1.0 GPa on resistivity, ρ(T), fluctuation conductivity (FLC), σʹ (T), and pseudogap (PG), Δ*(T), of the Y1−xPrxBa2Cu3O7−δ (x = 0.34) single crystal was studied in detail. Defects created by magnetic inclusions of PrBCO were shown to play a significant role in the behavior of the sample. As expected, pressure decreased ρ(T) at a rate dln ρ/dP = ̶ (16.5 ± 0.2) % GPa–1 at T = 100 K and increased Tc at a rate dTc/dP = +2.88 K·GPa−1. From the FLC measurements, the values of the coherence length along the c-axis, ξc(0), were obtained, which decrease slightly under pressure. The PG analysis revealed a rather specific shape of Δ*(T) with a pronounced magnetic maximum at Tmax ~ 230 K. HP significantly increases Δ*(Tmax) as well as the slope of the descending linear section of Δ*(T) below Tmax. As a result, the shape of Δ*(T) becomes almost the same as in FeAs-based magnetic superconductors. A comparative analysis of the influence of pressure on the shape of Δ*(T) was conducted for different Pr content in the sample. Measurements of the Ginzburg number Gi = (TG − Tcmf) / Tcmf revealed completely opposite dependences of the longitudinal coherence length ξab(0) on pressure for x = 0.05 and 0.34.
Посилання
1. L. Taillefer, “Scattering and pairing in cuprate superconductors,” Annu. Rev. Condens. Matter Phys. 1, 51 (2010). https://doi.org/10.1146/annurev-conmatphys-070909-104117
2. S. Badoux, W. Tabis, F. Laliberté, G. Grissonnanche, B. Vignolle, D. Vignolles, J. Béard, D. A. Bonn, W. N. Hardy, R. Liang, N. Doiron-Leyraud, Louis Taillefer, and C. Proust, “Change of carrier density at the pseudogap critical point of a cuprate superconductor,” Nature (London) 531, 210 (2016). https://doi.org/10.1038/nature16983
3. R. Peters and J. Bauer, “Local origin of the pseudogap in the attractive hubbard model,” Phys. Rev. B 92, 014511 (2015). https://doi.org/10.1103/PhysRevB.92.014511
4. A. L. Solovjov and K. Rogacki, “Local pairs in high-temperature superconductors: The concept of pseudogap,” Low Temp. Phys. 49, 345 (2023) [Fiz. Nyzk. Temp. 49, 375 (2023)]. https://doi.org/10.1063/10.0017238
5. V. M. Loktev and V. Turkowski, “On the theory of temperature BCS–BEC crossover in two-dimensional square-lattice superconductors,” Low Temp. Phys. 51, 949 (2025) [Fiz. Nyzk. Temp. 51, 1054 (2025)]. https://doi.org/10.1063/10.0037101
6. P. G. de Gennes, Superconductivity of Metals and Alloys, (W. A. Benjamin, Inc., New York, 1966), p. 280.
7. E. Benckiser, M. W. Haverkort, S. Brück, E. Goering, S. Macke, A. Frañó, X. Yang, O. K. Andersen, G. Cristiani, H.-U. Habermeier, A. V. Boris, I. Zegkinoglou, P. Wochner, H.-J. Kim, V. Hinkov, and B. Keimer, “Orbital reflectometry of oxide heterostructures,” Nat. Mater. 10, 189 (2011). https://doi.org/10.1038/nmat2958
8. A. A. Kordyuk, “Pseudogap from ARPES experiment: Three gaps in cuprates and topological superconductivity,” Low Temp. Phys. 41, 319 (2015) [Fiz. Nizk. Temp. 41, 417 (2015)]. https://doi.org/10.1063/1.4919371
9. A. L. Solovjov, Superconductors — Materials, Properties and Applications, edited by A. Gabovich (InTech, Rijeka, 2012), Chap. 7, p. 137.
10. M. Hücker, N. B. Christensen, A. T. Holmes, E. Blackburn, E. M. Forgan, Ruixing Liang, D. A. Bonn, W. N. Hardy, O. Gutowski, M. v. Zimmermann, S. M. Hayden, and J. Chang, “Competing charge, spin, and superconducting orders in underdoped YBa2Cu3Oy,” Phys. Rev. B 90, 054514 (2014). https://doi.org/10.1103/PhysRevB.90.054514
11. H. Eskes and G. A. Sawatzky, “Single-, triple-, or multiple-band hubbard models,” Phys. Rev. B 44, 9656 (1991). https://doi.org/10.1103/PhysRevB.44.9656
12. G. Jackeli and N. M. Plakida, “Charge dynamics and optical conductivity of the t−J model,” Phys. Rev. B 60, 5266 (1999). https://doi.org/10.1103/PhysRevB.60.5266
13. R. J. Birgeneau and G. Shirane, Physical Properties of High Temperature Superconductors, edited by D. M. Ginsberg (World Scientific, Singapore, 1989), p. 152.
14. M. A. Kastner, R. J. Birgeneau, G. Shirane, and Y. Endoh, “Magnetic, transport, and optical properties of monolayer copper oxides,” Rev. Mod. Phys. 70, 897 (1998). https://doi.org/10.1103/RevModPhys.70.897
15. G. R. Stewart, “Superconductivity in iron compounds,” Rev. Mod. Phys. 83, 1589 (2011). https://doi.org/10.1103/RevModPhys.83.1589
16. I. I. Mazin, “Superconductivity gets an iron boost,” Nature (London) 464, 183 (2010). https://doi.org/10.1038/nature08914
17. A. J. Drew, Ch. Niedermayer, P. J. Baker, F. L. Pratt, S. J. Blundell, T. Lancaster, R. H. Liu, G. Wu, X. H. Chen, I. Watanabe, V. K. Malik, A. Dubroka, M. Rössle, K. W. Kim, C. Baines, and C. Bernhard, “Coexistence of static magnetism and superconductivity in SmFeAsO1−xFx as revealed by muon spin rotation,” Nat. Mater. 8, 310 (2009). https://doi.org/10.1038/nmat2396
18. R. M. Fernandes, D. K. Pratt, W. Tian, J. Zarestky, A. Kreyssig, S. Nandi, M. G. Kim, A. Thaler, N. Ni, P. C. Canfield, R. J. McQueeney, J. Schmalian, and A. I. Goldman, “Unconventional pairing in the iron arsenide superconductors,” Phys. Rev. B 81, 140501(R) (2010). https://doi.org/10.1103/PhysRevB.81.140501
19. V. Mishra and U. Chatterjee, J. C. Campuzano and M. R. Norman, “Effect of the pseudogap on the transition temperature in the cuprates and implications for its origin,” Nat. Phys. 10, 357 (2014). https://doi.org/10.1038/nphys2926
20. Y. Ma, P. Ye, and Z.-Y. Weng, “Low-temperature pseudogap phenomenon: Precursor of high-Tc superconductivity,” New J. Phys. 16, 083039 (2014). https://doi.org/10.1088/1367-2630/16/8/083039
21. S. A. Kivelson and S. Lederer, “Linking the pseudo-gap in the cuprates with local symmetry breaking: A commentary,” PNAS 116, 14395 (2019). https://doi.org/10.1073/pnas.1908786116
22. N. J. Robinson, P. D. Johnson, T. M. Rice, and A. M. Tsvelik, “Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering,” Rep. Prog. Phys. 82, 126501 (2019). https://doi.org/10.1088/1361-6633/ab31ed
23. I. Esterlis, S. A. Kivelson, and D. J. Scalapino, “Pseudogap crossover in the electron-phonon system,” Phys. Rev. B 99, 174516 (2019). https://doi.org/10.1103/PhysRevB.99.174516
24. V. J. Emery and S. A. Kivelson, “Importance of phase fluctuations in superconductors with small superfluid density,” Nature (London) 374, 434 (1995). https://doi.org/10.1038/374434a0
25. Q. Chen, I. Kosztin, B. Janko, and K. Levin, “Pairing fluctuation theory of superconducting properties in underdoped to overdoped cuprates,” Phys. Rev. Lett. 81, 4708 (1998). https://doi.org/10.1103/PhysRevLett.81.4708
26. J. R. Engelbrecht, A. Nazarenko, M. Randeria, and E. Dagotto, “Pseudogap above Tc in a model with pairing,” Phys. Rev. B 57, 13406 (1998). https://doi.org/10.1103/PhysRevB.57.13406
27. B. P. Stojkovic and D. Pines, “Theory of the longitudinal and Hall conductivities of the cuprate superconductors,” Phys. Rev. B 55, 8576 (1997). https://doi.org/10.1103/PhysRevB.55.8576
28. A. V. Chubukov and J. Schmalian, “Temperature variation of the pseudogap in underdoped cuprates,” Phys. Rev. B 57, R11085 (1998). https://doi.org/10.1103/PhysRevB.57.R11085
29. D. J. Scalapino, “A common thread: The pairing interaction for unconventional superconductors,” Rev. Mod. Phys. 84, 1383 (2012). https://doi.org/10.1103/RevModPhys.84.1383
30. K. Efetov, H. Meier, and C. Pèpin, “Pseudogap state near a quantum critical point,” Nat. Phys. 9, 442 (2013). https://doi.org/10.1038/nphys2641
31. P. W. Anderson, “The resonating valence bond state in La2CuO4 and superconductivity,” Science 235, 1196 (1987). https://doi.org/10.1126/science.235.4793.1196
32. M. Randeria, “Ultracold Fermi gases: Preparing for condensation,” Nat. Phys. 6, 561 (2010). https://doi.org/10.1038/nphys1748
33. J. Corson, R. Mallozzi, J. Orenstein, J. N. Eckstein, and I. Bozovic, “Vanishing of phase coherence in underdoped Bi2Sr2CaCu2O8+δ,” Nature (London) 398, 221 (1999). https://doi.org/10.1038/18402
34. R.-H. He, M. Hashimoto, H. Karapetyan, J. D. Koralek, J. P. Hinton, J. P. Testaud, V. Nathan, Y. Yoshida, Hong Yao, K. Tanaka, W. Meevasana, R. G. Moore, D. H. Lu, S.-K. Mo, M. Ishikado, H. Eisaki, Z. Hussain, T. P. Devereaux, S. A. Kivelson, J. Orenstein, A. Kapitulnik, and Z.-X. Shen, “from a single-band metal to a high-temperature superconductor via two thermal phase transitions,” Science 331, 1579 (2011). https://doi.org/10.1126/science.1198415
35. A. S. Kolisnyk, M. V. Shytov, E. V. Petrenko, A. V. Terekhov, L. V. Bludova, A. Sedda, E. Lähderanta, and A. L. Solovjov, “Effect of a magnetic field up to 9 T on the temperature dependence of the pseudogap in YBa2Cu3O7–δ films,” Low Temp. Phys. 52, 3 (2026) [Fiz. Nyzk. Temp. 52, 5 (2026)]. https://doi.org/10.1063/10.0042157
36. A. L. Solovjov, K. Rogacki, N. V. Shytov, E. V. Petrenko, L. V. Bludova, A. Chroneos, and R. V. Vovk, “Influence of strong electron irradiation on fluctuation conductivity and pseudogap in YBa2Cu3O7−δ single crystals,” Phys. Rev. B 111, 174508 (2025). https://doi.org/10.1103/PhysRevB.111.174508
37. A. L. Solovjov, L. V. Omelchenko, V. B. Stepanov, R. V. Vovk, H.-U. Habermeier, H. Lochmajer, P. Przysłupski, and K. Rogacki, “Specific temperature dependence of pseudogap in YBa2Cu3O7−δ nanolayers,” Phys. Rev. B 94, 224505 (2016). https://doi.org/10.1103/PhysRevB.94.224505
38. A. L. Solovjov, L. V. Omelchenko, R. V. Vovk, and S. N. Kamchatnaya, “Pseudogap and fluctuation conductivity in Y1–xPrxBa2Cu3O7–δ single crystals with different concentrations of praseodymium,” Low Temp. Phys. 43, 841 (2017) [Fiz. Nizk. Temp. 43, 1050 (2017)]. https://doi.org/10.1063/1.4995634
39. A. L. Solovjov, L. V. Omelchenko, E. V. Petrenko, Yu. A. Kolesnichenko, A. S. Kolesnik, S. Dzhumanov, and R. V. Vovk, “Effects of annealing on the fluctuation conductivity and pseudogap in slightly doped HoBa2Cu3O7–δ single crystals,” Low Temp. Phys. 49, 108 (2023) [Fiz. Nyzk. Temp. 49, 115 (2023)]. https://doi.org/10.1063/10.0016484
40. R. V. Vovk and A. L. Solovjov, “Electric transport and pseudogap in high-temperature superconducting compounds of system 1-2-3 under conditions of all-round compression,” Low Temp. Phys. 44, 81 (2018) [Fiz. Nizk. Temp. 44, 111 (2018)]. https://doi.org/10.1063/1.5020905
41. H. Nagasawa and T. Sugawara, “The magnetism of praseodymium metal,” J. Phys. Soc. Jpn. 23, 701 (1967). https://doi.org/10.1143/JPSJ.23.701
42. M. P. Guillaume, P. Fischer, B. Roessli, A. Podlesnyak, J. Schefer, and A. Furrer, “Magnetic order of Pr ions in related perovskite-type Pr123 compounds,” J. Appl. Phys. 75, 6331 (1994). https://doi.org/10.1063/1.355390
43. J.-M. Triscone, Ø Fischer, O. Brunner, L. Antognazza, A. D. Kent, and M. G. Karkut, “YBa2cu3o7/PrBa2Cu3O7 superlattices: Properties of ultrathin superconducting layers separated by insulating layers,” Phys. Rev. Lett. 64, 804 (1990). https://doi.org/10.1103/PhysRevLett.64.804
44. R. V. Vovk, Z. F. Nazyrov, I. L. Goulatis, and A. Chroneos, “Metal-to-insulator transition in Y1−xPrxBa2Cu3O7−δ single crystals with various praseodymium contents,” Physica C 485, 89 (2013). https://doi.org/10.1016/j.physc.2012.09.017
45. R. Fehrenbacher and T. M. Rice, “Unusual electronic structure of PrBa2Cu3O7,” Phys. Rev. Lett. 70, 3471 (1993). https://doi.org/10.1103/PhysRevLett.70.3471
46. A. I. Liechtenstein and I. I. Mazin, “Quantitative model for the superconductivity suppression in R1-xPrxBa2Cu3O7 with different rare earths,” Phys. Rev. Lett. 74, 1000 (1995). https://doi.org/10.1103/PhysRevLett.74.1000
47. Y. Yu, G. Cao, and Z. Jiao, “Hole distribution and Tc suppression in Y1−xPrxBa2Cu3O7,” Phys. Rev. B 59, 3845 (1999). https://doi.org/10.1103/PhysRevB.59.3845
48. M. A. Obolenskii, R. V. Vovk, A. V. Bondarenko, and N. N. Chebotaev, “Localization effects and pseudogap state in YBa2Cu3O7−δ single crystals with different oxygen content,” Low Temp. Phys. 32, 571 (2006) [Fiz. Nizk. Temp. 32, 746 (2006)]. https://doi.org/10.1063/1.2215373
49. A. L. Solovjov, M. A. Tkachenko, R. V. Vovk, and A. Chroneos, “Fluctuation conductivity and pseudogap in HoBa2Cu3O7–δ single crystals under pressure with transport current flowing under an angle 45o to the twin boundaries,” Physica C 501, 24 (2014). https://doi.org/10.1016/j.physc.2014.03.004
50. J. D. Thompson, “Low-temperature pressure variations in a self-clamping pressure cell,” Rev. Sci. Instrum. 55, 231 (1984). https://doi.org/10.1063/1.1137730
51. Y. Ando, S. Komiya, K. Segawa, S. Ono, and Y. Kurita, “Electronic phase diagram of high-Tc cuprate superconductors from a mapping of the in-plane resistivity curvature,” Phys. Rev. Lett. 93, 267001 (2004). https://doi.org/10.1103/PhysRevLett.93.267001
52. A. L. Solovjov, L. V. Omelchenko, E. V. Petrenko, R. V. Vovk, V. V. Khotkevych, and A. Chroneos, “Peculiarities of pseudogap in Y0.95Pr0.05Ba2Cu3O7−δ single crystals under pressure up to 1.7 GPa,” Sci. Rep. 9, 20424 (2019). https://doi.org/10.1038/s41598-019-55959-1
53. A. L. Solovjov, L. V. Bludova, A. S. Kolesnik, E. V. Petrenko, M. V. Shytov, A. Sedda, E. Lähderanta, D. Sergeyev, and R. V. Vovk, “Hydrostatic pressure effect on the pseudogap in Y0.77Pr0.23Ba2Cu3O7–δ single crystals,” Low Temp. Phys. 52, 425 (2026) [Fiz. Nyzk. Temp. 52, 475 (2026)]. https://doi.org/10.1063/10.0043141
54. E. V. L. de Mello, M. T. D. Orlando, J. L. González, E. S. Caixeiro, and E. Baggio-Saitovich, “Pressure studies on the pseudogap and critical temperatures of a high-Tc superconductor,” Phys. Rev. B 66, 092504 (2002). https://doi.org/10.1103/PhysRevB.66.092504
55. H. Huang, H. Jang, M. Fujita, T. Nishizaki, Y. Lin, J. Wang, J. Ying, J. S. Smith, C. Kenney-Benson, G. Shen, W. L. Mao, C.-C. Kao, Y.-J. Liu, and J.-S. Lee, “Modification of structural disorder by hydrostatic pressure in the superconducting cuprate YBa2Cu3O6.73,” Phys. Rev. B 97, 174508 (2018). https://doi.org/10.1103/PhysRevB.97.174508
56. A. L. Solovjov, L. V. Omelchenko, R. V. Vovk, O. V. Dobrovolskiy, Z. F. Nazyrov, S. N. Kamchatnaya, and D. M. Sergeyev, “Hydrostatic-pressure effects on the pseudogap in slightly doped YBa2Cu3O7−δ single crystals,” Physica B 493, 58 (2016). https://doi.org/10.1016/j.physb.2016.04.015
57. F. Rullier-Albenque, P. A. Vieillefond, H. Alloul, A. W. Tyler, P. Lejay, and J. F. Marucco, “Universal Tc depression by irradiation defects in underdoped and overdoped cuprates,” Europhys. Lett. 50, 81 (2000). https://doi.org/10.1209/epl/i2000-00238-x
58. H. J. Liu, Q. Wang, G. A. Saunders, D. P. Almond, B. Chapman, and K. Kitahama, “Hydrostatic-pressure effects on the a-axis resistance of monocrystalline Bi2.2(Sr,Ca)2.8Cu2O8 + y,” Phys. Rev. B 51, 9167 (1995). https://doi.org/10.1103/PhysRevB.51.9167
59. Q. Wang, G. A. Saunders, H. J. Liu, M. S. Acres, and D. P. Almond, “Electrical resistance under pressure in textured Bi2Sr2CaCu2O8 + y: Enhancement of the energy gap and thermodynamic fluctuations,” Phys. Rev. B 55, 8529 (1997). https://doi.org/10.1103/PhysRevB.55.8529
60. L. M. Ferreira, P. Pureur, H. A. Borges, and P. Lejay, “Effects of pressure on the fluctuation conductivity of YBa2Cu3O7,” Phys. Rev. B 69, 212505 (2004). https://doi.org/10.1103/PhysRevB.69.212505
61. R. V. Vovk, Z. F. Nazyrov, M. A. Obolenskii, I. L. Goulatis, A. Chroneos, and V. M. Pinto Simoes, “Phase separation in oxygen deficient ΗοBa2Cu3O7−δ single crystals: Effect of high pressure and twin boundaries,” Philos. Mag. 91, 2291 (2011). https://doi.org/10.1080/14786435.2011.552893
62. B. Oh, K. Char, A. D. Kent, M. Naito, M. R. Beasley, T. H. Geballe, R. H. Hammond, and A. Kapitulnik, “Upper critical field, fluctuation conductivity, and dimensionality of YBa2Cu3O7−x,” Phys. Rev. B 37, 7861 (1988). https://doi.org/10.1103/PhysRevB.37.7861
63. T. Kondo, A. D. Palczewski, Y. Hamaya, T. Takeuchi, J. S. Wen, Z. J. Xu, G. Gu, and A. Kaminski, “Formation of gapless Fermi arcs and fingerprints of order in the pseudogap state of cuprate superconductors,” Phys. Rev. Lett. 111, 157003 (2013). https://doi.org/10.1103/PhysRevLett.111.157003
64. M. R. Norman, H. Ding, M. Randeria, J. C. Campuzano, T. Yokoya, T. Takeuchi, T. Takahashi, T. Mochiku, K. Kadowaki, P. Guptasarma, and D. G. Hinks, “Destruction of the Fermi surface in underdoped high-Tc superconductors,” Nature (London) 392, 157 (1998). https://doi.org/10.1038/32366
65. A. L. Solovjov and V. M. Dmitriev, “Resistive studies of the pseudogap in YBCO films with consideration of the transition from BCS to bose–einstein condensation,” Low Temp. Phys. 32, 99 (2006) [Fiz. Nizk. Temp. 32, 139 (2006)]. https://doi.org/10.1063/1.2171509
66. S. Hikami and A. I. Larkin, “Magnetoresistance of high temperature superconductors,” Mod. Phys. Lett. B 2, 693 (1988). https://doi.org/10.1142/S0217984988000369
67. W. Lang, G. Heine, P. Schwab, X. Z. Wang, and D. Bäuerle, “Paraconductivity and excess Hall effect in epitaxial YBa2Cu3O7−δ films induced by superconducting fluctuations,” Phys. Rev. B 49, 4209 (1994). https://doi.org/10.1103/PhysRevB.49.4209
68. G. D. Chryssikos, E. I. Kamitsos, J. A. Kapoutsis, A. P. Patsis, V. Psycharis, A. Koufoudakis, Ch. Mitros, G. Kallias, E. Gamari-Seale, and D. Niarchos, “X-ray diffraction and infrared investigation of RBa2Cu3O7 and R0.5Pr0.5Ba2Cu3O7 compounds (R, Y and lanthanides),” Physica C 254, 44 (1995). https://doi.org/10.1016/0921-4534(95)00553-6
69. O. Tchernyshyov, “Noninteracting cooper pairs inside a pseudogap,” Phys. Rev. B 56, 3372 (1997). https://doi.org/10.1103/PhysRevB.56.3372
70. R. Haussmann, “Properties of a Fermi liquid at the superfluid transition in the crossover region between BCS superconductivity and bose–einstein condensation,” Phys. Rev. B 49, 12975 (1994). https://doi.org/10.1103/PhysRevB.49.12975
71. L. G. Aslamazov and A. L. Larkin, “The influence of fluctuation pairing of electrons on the conductivity of the normal metal,” Phys. Lett. A 26, 238 (1968). https://doi.org/10.1016/0375-9601(68)90623-3
72. Y. B. Xie, “Superconducting fluctuations in the high-temperature superconductors: Theory of the dc resistivity in the normal state,” Phys. Rev. B 46, 13997 (1992). https://doi.org/10.1103/PhysRevB.46.13997
73. J. B. Bieri, K. Maki, and R. S. Thompson, “Nonlocal effect in magnetoconductivity of high-Tc superconductors,” Phys. Rev. B 44, 4709(R) (1991). https://doi.org/10.1103/PhysRevB.44.4709
74. M. Akhavan, “The question of Pr in HTSC,” Physica B 321, 265 (2002). https://doi.org/10.1016/S0921-4526(02)00860-8
75. B. Leridon, A. Défossez, J. Dumont, J. Lesueur, and J. P. Contour, “Conductivity of underdoped YBa2Cu3O7−δ: Evidence for incoherent pair correlations in the pseudogap regime,” Phys. Rev. Lett. 87, 197007 (2001). https://doi.org/10.1103/PhysRevLett.87.197007
76. E. Stajic, A. Iyengar, K. Levin, B. R. Boyce, and T. R. Lemberger, “Cuprate pseudogap: Competing order parameters or precursor superconductivity,” Phys. Rev. B 68, 024520 (2003). https://doi.org/10.1103/PhysRevB.68.024520
77. Y. Yamada, K. Anagawa, T. Shibauchi, T. Fujii, T. Watanabe, A. Matsuda, and M. Suzuki, “Interlayer tunneling spectroscopy and doping-dependent energy-gap structure of the trilayer superconductor Bi2Sr2Ca2Cu3O10+δ,” Phys. Rev. B 68, 054533 (2003). https://doi.org/10.1103/PhysRevB.68.054533
78. K. W. Wang and W. Y. Ching, “A structural-based microscopic theory on high-temperature cuprate superconductors,” Physica C 416, 47 (2004). https://doi.org/10.1016/j.physc.2004.09.003
79. A. L. Solovjov, L. V. Omelchenko, A. V. Terekhov, K. Rogacki, R. V. Vovk, E. P. Khlybov and A. Chroneos, “Fluctuation conductivity and possible pseudogap state in FeAs-based superconductor EuFeAsO0.85F0.15,” Mater. Res. Express 3, 076001 (2016). https://doi.org/10.1088/2053-1591/3/7/076001
80. A. L. Solovjov, L. V. Omelchenko, R. V. Vovk, O. V. Dobrovolskiy, S. N. Kamchatnaya, and D. M. Sergeyev, “Peculiarities in the pseudogap behavior in optimally doped YBa2Cu3O7−δ single crystals under pressure up to 1 GPa,” Curr. Appl. Phys. 16, 931 (2016). https://doi.org/10.1016/j.cap.2016.05.014
81. A. Kapitulnik, M. R. Beasley, C. Castellani, and C. Di Castro, “Thermodynamic fluctuations in the high-Tc perovskite superconductors,” Phys. Rev. B 37, 537 (1988). https://doi.org/10.1103/PhysRevB.37.537
82. J. S. Schilling and S. Klotz, Physical Properties of High Temperature Superconductors, edited by D. M. Ginsberg (World Scientific Singapore, 1992), Vol. 3, p. 59.
