Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

Abstract

In a short review-article we first discuss the results, which are mainly devoted to the generalizations of the famous Kohn-Luttinger mechanism of superconductivity in purely repulsive fermion systems at low electron densities. In the context of repulsive-U Hubbard model and Shubin-Vonsovsky model we consider briefly the superconducting phase diagrams and the symmetries of the order parameter in novel strongly correlated electron systems including idealized monolayer and bilayer graphene. We stress that purely repulsive fermion systems are mainly the subject of unconventional low-temperature superconductivity. To get the high temperature superconductivity in cuprates (with T C of the order of 100 K) we should proceed to the t-J model with the Van der Waals interaction potential and the competition between short-range repulsion and long-range attraction. Finally we stress that to describe superconductivity in metallic hydrogen alloys under pressure (with T C of the order of 200 K) it is reasonable to reexamine more conventional mechanisms connected with electron-phonon interaction. These mechanisms arise in the attractive-U Hubbard model with static onsite or intersite attractive potential or in more realistic theories (which include retardation effects) such as Migdal-Eliashberg strong coupling theory or even Fermi-Bose mixture theory of Alexandrov, Ranninger and its generalizations. I) IntroductionRecent discovery of Cooper pairing at 190 K in metallic hydrogen sulfide H 2 S under high pressure revives our hopes to move forward from high-temperature to room-temperature superconductivity [1][2][3][4][5]. In the same time there are many interesting low-temperature superconducting systems with anomalous types of pairing and a nontrivial structure of the order parameter.In the beginning of the review-article we discuss the mechanisms of unconventional superconductivity in 3D and 2D fermionic systems with purely repulsive interaction at low densities. We briefly discuss the phase-diagrams of these systems in free space and on the lattice and find the areas of the superconductive state in the framework of the Fermi-gas model with hard core repulsion, the Hubbard model [6] and the Shubin-Vonsovsky model [7,8]. We demonstrate that the critical superconductive temperature can be greatly increased in the spinpolarized case or in a two-band situation already at low densities.The proposed theory is based on the Kohn-Luttinger mechanism of superconductivity [9] and its generalizations and explains or predicts p-, d-, f-and anomalous s-wave pairing in various materials such as the idealized monolayer and bilayer graphene, heavy-fermion systems, layered

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“…As a first guess we might conjecture that the lower carrier concentration in SrTiO 3 could contribute to the larger value. However, for a one-band model, Kagan finds theoretically [33] that…”

Anomalous superconductivity and superfluidity in repulsive fermion systems

“…As a result, we proceed from (42) an integral Gor'kov equation for the superconducting gap ∆(p). Passing to the integration with respect to [123,124]. For all points that belong to one thin line in (b), the indicated value of |λ| is constant.…”

“…calculated in Ref. [124] for the point of the phase diagram at which the s-wave pairing is realized at large electron densities. This dependence demonstrates the presence of eight nodal points at which the gap vanishes.…”

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“…The phase-diagram of this model presented in Fig. 2 shows regions of superconducting phases with different pairing symmetry: p-wave, s-wave and [20,21,24] on the 2D square lattice.…”

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