Abstract
The two-band memory-function conductivity formula is derived from the quantum kinetic equation in the pseudogap state of underdoped cuprates. The conduction electrons are described by using the adiabatic version of the nested Fermi liquid model, and the effects of Mott correlations are taken into account phenomenologically. The linear dependence of the low-temperature effective number of conduction electrons on the doping level δ (for not too large δ) is found to be in agreement with experimental observation. The momentum distribution function turns out to play an important role in describing temperature effects. The closing of the antiferromagnetic pseudogap at temperatures of the order of room temperature is shown to be a direct consequence of a relatively large width of the quasiparticle peak in this distribution function. The coupling of conduction electrons to external magnetic fields is included in the two-band transport equations in the usual semiclassical way. It is shown that the low-temperature Hall number is proportional to δ as well (again for not too large δ) and that it exhibits singular behaviour when the Fermi surface changes from the hole-like shape into the electron-like shape.
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D.B. Tanner, F. Gao, K. Kamarás, H.L. Liu, M.A. Quijada, D.B. Romero, Y.-D. Yoon, A. Zibold, H. Berger, G. Margaritondo, L. Forró, R.J. Kelly, M. Onellion, G. Cao, J.E. Crow, O. Beom-Hoan, J.T. Markert, J.P. Rice, D.M. Ginsberg, Th. Wolf, Physica C 341–348, 2193 (2000)
V.J. Emery, Phys. Rev. Lett. 58, 2794 (1987)
N. Plakida, High-Temperature Cuprate Supercoductors (Springer-Verlag, Berlin, 2010)
S. Uchida, T. Ido, H. Takagi, T. Arima, Y. Tokura, S. Tajima, Phys. Rev. B 43, 7942 (1991)
M.C. Schabel, C.-H. Park, A. Matsuura, Z.-X. Shen, D.A. Bonn, R. Liang, W.N. Hardy, Phys. Rev. B 57, 6090 (1998)
T. Yoshida, X.J. Zhou, K. Tanaka, W.L. Yang, Z. Hussain, Z.-X. Shen, A. Fujimori, S. Sahrakorpi, M. Lindroos, R.S. Markiewicz, A. Bansil, S. Komiya, Y. Ando, H. Eisaki, T. Kakeshita, S. Uchida, Phys. Rev. B 74, 224510 (2006)
A. Kanigel, M.R. Norman, M. Randeria, U. Chatterjee, S. Souma, A. Kaminski, H.M. Fretwell, S. Rosenkranz, M. Shi, T. Sato, T. Takahashi, Z.Z. Li, H. Raffy, K. Kadowaki, D. Hinks, L. Ozyuzer, J.C. Campuzano, Nat. Phys. 2, 447 (2006)
X.J. Zhou, T. Cuk, T. Devereaux, N. Nagaosa, Z.-X. Shen, in Handbook of High-Temperature Superconductivity, edited by J.R. Schrieffer, J.S. Brooks (Springer, New York, 2007), p. 87
J.R. Schrieffer, Theory of Superconductivity (Benjamin, New York, 1964)
A.A. Abrikosov, Fundamentals of the Theory of Metals (Nort-Holland, Amsterdam, 1988)
N.W. Ashcroft, N.D. Mermin, Solid State Physics (Saunders, New York, 1976)
T.P. Devereaux, R. Hackl, Rev. Mod. Phys. 79, 175 (2007)
I. Kupčić, S. Barišić, Phys. Rev. B 75, 094508 (2007)
J. Ruvalds, A. Virosztek, Phys. Rev. B 43, 5498 (1991)
P. Monthoux, D. Pines, Phys. Rev. B 47, 6069 (1993)
D.K. Sunko, S. Barišić, Eur. Phys. J. B 46, 269 (2005)
D. Bergeron, Y. Hankevych, B. Kyung, A.-M.S. Tremblay, Phys. Rev. B 84, 085128 (2011)
J.R. Schrieffer, X.G. Wen, S.C. Zhang, Phys. Rev. B 39, 11663 (1989)
J. Friedel, M. Kohmoto, Eur. Phys. J. B 30, 427 (2002)
S. Chakravarty, C. Nayak, S. Tewari, Phys. Rev. B 68, 100504(R) (2003)
I. Kupčić, Physica C 391, 251 (2003)
S.I. Mirzaei, D. Stickler, J.N. Hancock, C. Berthod, A. Georges, E. van Heumen, M.K. Chan, X. Zhao, Y. Li, M. Greven, N. Barišić, D. van der Marel, Proc. Natl. Acad. Sci. USA 110, 5774 (2013)
S. Ono, S. Komiya, Y. Ando, Phys. Rev. B 75, 024515 (2007)
I. Kupčić, Phys. Rev. 91, 205428 (2015)
I. Kupčić, G. Nikšić, Z. Rukel, D. Pelc, Phys. Rev. B 94, 075434 (2016)
I. Kupčić, Z. Rukelj, S. Barišić, J. Phys.: Condens. Matter 25, 145602 (2013)
A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover Publications, New York, 1975)
I.E. Dzyaloshinskii, A.I. Larkin, Zh. Eksp. Teor. Fiz. 65, 411 (1973)
I.E. Dzyaloshinskii, A.I. Larkin, Sov. Phys. JETP 38, 202 (1974)
G.D. Mahan, Many-particle Physics (Plenum Press, New York, 1990)
I. Kupčić, Phys. Rev. 95, 035403 (2017)
I. Kupčić, Phys. Rev. 90, 205426 (2014)
P.A. Lee, T.M. Rice, P.W. Anderson, Solid State Commun. 14, 703 (1974)
A. Bjeliš, S. Barišić, J. Phys. Lett. 36, L169 (1975)
S.A. Brazovskii, I.E. Dzyaloshinskii, Zh. Eksp. Teor. Fiz. 71, 2338 (1976)
S.A. Brazovskii, I.E. Dzyaloshinskii, Sov. Phys.–JETP 44, 1233 (1976)
R.H. McKenzie, Phys. Rev. B 52, 16428 (1995)
I. Kupčić, Z. Rukelj, S Barišić, J. Phys.: Condens. Matter 26, 195601 (2014)
J.M. Tranquada, in Handbook of High-Temperature Superconductivity, edited by J.R. Schrieffer, J.S. Brooks (Springer, New York, 2007), p. 257
M.V. Sadovskii, Zh. Eksp. Teor. Fiz. 66, 1720 (1973)
M.V. Sadovskii, Sov. Phys.–JETP 39, 845 (1974)
M.V. Sadovskii, Zh. Eksp. Teor. Fiz. 77, 2070 (1979)
M.V. Sadovskii, Sov. Phys.–JETP 50, 989 (1979)
H. Kontani, Rep. Prog. Phys. 71, 1 (2008)
Ž. Bonačić Lošić, P. Županovic, A. Bjeliš, J. Phys.: Condens. Matter 18, 3655 (2006)
E. Pavarini, I. Dasgupta, T. Saha-Dasgupta, O. Jepsen, O.K. Andersen, Phys. Rev. Lett. 87, 047003 (2001)
Y. Ando, S. Komiya, K. Segawa, Y. Kurita, Phys. Rev. Lett. 93, 267001 (2004)
J.M. Ziman, Electrons and Phonons (Oxford University Press, London, 1972)
H. Kontani, K. Kanki, K. Ueda, Phys. Rev. B 59, 14723 (1999)
P.M. Platzman, P.A. Wolff, Waves and Interactions in Solid State Plasmas (Academic Press, New York, 1973)
N.P. Ong, Phys. Rev. B 43, 193 (1991)
D. Pines, P. Noziéres, The Theory of Quantum Liquids I (Addison-Wesley, New York, 1989)
G. Nikšić, I. Kupčić, O.S. Barišić, D.K. Sunko, S. Barišić, J. Supercond. Nov. Magn. 27, 969 (2014)
L.P. Gor’kov, G.B. Teitel’baum, Phys. Rev. Lett. 97, 247003 (2006)
I. Kupčić, Physica B 344, 27 (2004)
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Kupčić, I., Jedovnicki, I. Memory-function conductivity formula and transport coefficients in underdoped cuprates. Eur. Phys. J. B 90, 63 (2017). https://doi.org/10.1140/epjb/e2017-70737-0
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DOI: https://doi.org/10.1140/epjb/e2017-70737-0