Abstract
Fundamentals of fermion-condensation physics are outlined. Fermion condensation is a phase transition occurring in a strongly correlated Fermi system upon a topological reconstruction of the Landau ground state and leading to the formation of a fermion condensate that possesses the dispersionless single-particle spectrum \(\epsilon({\mathbf{p}})=0\) in the momentum-space region adjacent to the Fermi surface and, accordingly, an anomalously enhanced density of single-particle states. A original method is developed for solving the set of nonlinear integral equations of fermion-condensation theory. This method makes it possible to analyze the problem of quantum chaos in strongly interacting multifermion systems. The computational technique used is demonstrated by applying it to superdense quark–gluon plasma, where the structure of exchange quark–quark interaction is well known. In electron systems featuring a fermion condensate, the magnitude of the gap appearing in the single-particle spectrum owing to Cooper pairing is shown to be much larger than that in Bardeen–Cooper–Schrieffer (BCS) theory. This explains both a high superconducting-transition temperature \(T_{c}\) and, with allowance for \(C_{4}\) crystal-lattice symmetry, the \(D\)-wave pairing-gap structure observed in cuprates. It is found that, in addition to the BCS gap \(\Delta\), the spectrum of single-particle excitations of superconducting systems where a fermion condensate is present develops a nonsuperconducting gap \(\Upsilon\) that owes its existence to the interaction of condensate particles with normal quasiparticles residing outside the condensate region in momentum space. The question of whether these results are pertinent to the two-gap structure recently unearthed in the excitation spectrum of cuprates upon analyzing ARPES data is addressed.
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REFERENCES
I. M. Lifshits, Sov. Phys. JETP 11, 1130 (1960).
L. D. Landau, Sov. Phys. JETP 3, 920 (1956).
V. A. Khodel and V. R. Shaginyan, JETP Lett. 51, 553 (1990).
G. E. Volovik, JETP Lett. 53, 222 (1991);
Springer Lect. Notes Phys. 718, 31 (2007).
P. Nozières, J. Phys. I (France) 2, 443 (1992).
V. A. Khodel, J. W. Clark, and M. V. Zverev, Phys. Rev. B 78, 075120 (2008).
A. Kaminski, T. Kondo, T. Takeuchi, and G. Gu, Philos. Mag. 95, 453 (2015).
M. V. Zverev, V. A. Khodel, and V. R. Shaginyan, J. Exp. Theor. Phys. 82, 567 (1996).
M. V. Zverev and V. V. Borisov, JETP Lett. 81, 503 (2005).
L. P. Pitaevskiĭ, Sov. Phys. JETP 10, 1267 (1959).
V. R. Shaginyan, JETP Lett. 81, 222 (2005).
V. R. Shaginyan, A. Z. Mzezane, V. A. Stephanovich, G. S. Japaridze, and E. V. Kirichenko, Phys. Scr. 99, 065801 (2019).
Y. S. Kushnirenko, A. A. Kordyuk, A. V. Fedorov, E. Haubold, T. Wolf, B. Büchner, and S. V. Borisenko, Phys. Rev. B 96, 100504(R) (2017).
A. B. Migdal, Theory of Finite Fermi Systems and Applications to Atomic Nuclei (Nauka, Moscow, 1965; Interscience, New York, 1967).
V. A. Khodel, V. R. Shaginyan, and P. Shuk, JETP Lett. 63, 752 (1996).
V. A. Khodel and M. V. Zverev, JETP Lett. 74, 502 (2001).
M. G. Alford, A. Schmitt, K. Rajagopal, and T. Schafer, Rev. Mod. Phys. 80, 1455 (2008).
C. J. Pethick, G. Baym, and H. Monien, Nucl. Phys. A 498, 313 (1989).
A. N. Kolmogorov, Probl. Peredachi Inform. 1, 3 (1965).
A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (Fizmatgiz, Moscow, 1962; Prentice-Hall, London, 1963).
V. A. Khodel and M. V. Zverev, JETP Lett. 85, 404 (2007).
V. A. Khodel, J. W. Clark, and M. V. Zverev, JETP Lett. 105, 267 (2017).
V. A. Khodel, J. W. Clark, and M. V. Zverev, JETP Lett. 108, 260 (2018).
V. A. Khodel, J. Low Temp. Phys. 191, 14 (2018).
R. A. Cooper, Y. Wang, B. Vignolle, O. J. Lipscombe, S. M. Hayden, Y. Tanabe, T. Adachi, Y. Koike, M. Nomara, H. Takagi, C. Proust, and N. E. Hussey, Science (Washington, DC, U. S.) 323, 603 (2009).
N. E. Hussey, R. A. Cooper, X. Xu, I. Mouzopoulou, Y. Wang, B. Vignolle, and C. Proust, Phys. Trans. R. Soc. A 369, 1626 (2011).
N. E. Hussey, H. Gordon-Moys, J. Kokaly, and R. H. McKenzie, J. Phys.: Conf. Ser. 449, 012004 (2013).
V. A. Khodel, J. W. Clark, and M. V. Zverev, Phys. Lett. A 318, 3281 (2018).
J. G. Bednorz and K. A. Müller, Z. Phys. B 64, 189 (1986);
Rev. Mod. Phys. 60, 585 (1988).
M. K. Wu, J. R. Ashburn, C. J. Torng, P. H. Hor, R. L. Meng, L. Goa, Z. J. Huang, Y. Q. Wang, and C. W. Chu, Phys. Rev. Lett. 58, 908 (1987).
S. T. Belyaev, Sov. Phys. JETP 7, 289 (1958);
Sov. Phys. JETP 7, 299 (1958).
M. Yu. Mel’nikov, A. A. Shashkin, V. T. Dolgopolov, A. X. Y. Zhu, S. V. Kravchenko, S.H. Huang, and C. W. Liu, Phys. Rev. B 99, 081106 (R) (2019).
S. V. Kravchenko, G. V. Kravchenko, J. G. Furneaux, V. M. Pudalov, and M. D’Iorio, Phys. Rev. B 50, 8039 (1994).
E. Abrahams, S. V. Kravchenko, and M. P. Sarachik, Rev. Mod. Phys. 73, 251 (2001).
S. V. Kravchenko and M. P. Sarachik, Rep. Prog. Phys. 67, 1 (2004).
A. Punnnoose and A. M. Finkel’stein, Science (Washington, DC, U. S.) 310, 289 (2005).
B. L. Altshuler and A. G. Aronov, Mod. Probl. Condens. Matter Sci. 10, 1 (1985).
A. Punnnoose and A. M. Finkel’stein, Phys. Rev. Lett. 88, 016802 (2002).
A. A. Shashkin, A. A. Kapustin, E. V. Deviatov, V. T. Dolgopolov, and Z. D. Kvon, Phys. Rev. B 76, 241302 (R) (2007).
B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen, Nature (London, U.K.) 518, 179 (2015).
ACKNOWLEDGMENTS
We are grateful to G.E. Volovik, R. Green, V.T. Dolgopolov, A. Kaminski, Ya. Kopelevich, S.V. Kravchenko, L.P. Pitaevsky, and V.R. Shaginyan for stimulating discussions on the problems addressed in this article. Special thanks are due to A. Kaminski for his kind permission to use here Fig. 8 from [7], and to S.V. Kravchenko, who presented Fig. 7 at our disposal.
Funding
V.A. Khodel and J.W. Clark gratefully acknowledge the support of McDonnell Center for the Space Sciences, and J.W. Clark is also indebted to Centro de Investigação em Matemática e Aplicações, University of Madeira, for the hospitality extended to him.
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Khodel, V.A., Clark, J.W. & Zverev, M.V. Fermion Condensation: Theory and Experiment. Phys. Atom. Nuclei 83, 101–117 (2020). https://doi.org/10.1134/S1063778820020167
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DOI: https://doi.org/10.1134/S1063778820020167