The Kohn-Luttinger mechanism and phase diagram of the superconducting state in the Shubin-Vonsovsky model
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IC PROPERTIES OF SOLID
The Kohn–Luttinger Mechanism and Phase Diagram of the Superconducting State in the Shubin–Vonsovsky Model M. Yu. Kagana,*, V. V. Val’kovb,c, V. A. Mitskanb,c, and M. M. Korovuskinb,c a
Kapitza Institute for Physical Problems, Russian Academy of Sciences, Moscow, 119334 Russia Kirenskii Physics Institute, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia cReshetnev Siberian Aerospace University, Krasnoyarsk, 660014 Russia *email: [email protected]
b
Received March 27, 2013
Abstract—Using the Shubin–Vonsovsky model in the weakcoupling regime W > U > V (W is the bandwidth, U is the Hubbard onsite repulsion, and V is the Coulomb interaction at neighboring sites) based on the Kohn– Luttinger mechanism, we determined the regions of the existence of the superconducting phases with the dxy, p, s, and d x2 –y2 symmetry types of the order parameter. It is shown that the effective interaction in the Cooper channel considerably depends not only on singlesite but also on intersite Coulomb correlations. This is dem onstrated by the example of the qualitative change and complication of the phase diagram of the supercon ducting state. The superconducting (SC) phase induction mechanism is determined taking into account polarization contributions in the secondorder perturbation theory in the Coulomb interaction. The results obtained for the angular dependence of the superconducting gap in different channels are compared with anguleresolved photoemission spectroscopy (ARPES) results. The influence of longrange hops in the phase diagram and critical superconducting transition temperature in different channels is analyzed. The condi tions for the appearance of the Kohn–Luttinger superconductivity with the d x2 –y2 symmetry and high critical temperatures Tc ~ 100 K near the halffilling are determined. DOI: 10.1134/S1063776113120030
1. INTRODUCTION 3He
and ultra Extensive studies of superfluidity in cold quantum Fermi gases and superconductivity in cuprates, heavyFermion intermetallic compounds, semimetals and superlattices have stimulated interest in nonconventional mechanisms of the Cooper pairing. One of the most popular nonphonon mechanisms of superconductivity is the Kohn–Luttinger mechanism [1], proposed in 1965. It was shown in [1] that, due to the presence of the longrange component in the effec tive potential of interaction of particles via the fermi onic background, any threedimensional electron sys tem with the bare repulsive interaction between parti cles is certainly unstable with respect to the transition to the superconducting state with a large orbital moment of the relative motion of a Cooper pair (l Ⰷ 1). The Kohn–Luttinger mechanism is closely related to Friedel oscillations [2]. It is well known that due to the sharp boundary 2kF in the electron density distri bution in the momentum space at the Fermi level, the impurity potentials in a metal do not decease mono tonically but oscillate (Friedel oscillations [3]). Kohn and Luttinger showed [1] th
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