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Physical review. B, Condensed matter

Superconductivity originating from a repulsive potential: Proposal of a new exciton mechanism of high- Tc superconductivity in the dilute electron gas

Yasutami Takada

Published Jun 1, 1989• 20 citations
Publisher

Abstract

We investigate the possibility of superconductivity and estimate the transition temperature ${T}_{c}$ in a system in which the bare electron-electron interaction $V(q)$ is arbitrary but basically repulsive. We employ the recently developed variational method which is believed to be the best one for the purpose at present. Through this study, we consider a concept of the Cooper pair originating not from an attractive but rather a repulsive bare potential. We find a special form for $V(q)$ to obtain ${T}_{c}$ over 200 K in the dilute electron-gas system. We discuss the band structure near the Fermi surface to produce such $V(q)'\mathrm{s}$ and propose a new exciton mechanism.

DOI
10.1103/physrevb.39.11575

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We investigate the possibility of superconductivity and estimate the transition temperature Tc{T}_{c}Tc​ in a system in which the bare electron-electron interaction V(q)V(q)V(q) is arbitrary but basically repulsive. We employ the recently developed variational method which is believed to be the best one for the purpose at present. Through this study, we consider a concept of the Cooper pair originating not from an attractive but rather a repulsive bare potential. We find a special form for V(q)V(q)V(q) to obtain Tc{T}_{c}Tc​ over 200 K in the dilute electron-gas system. We discuss the band structure near the Fermi surface to produce such V(q)′sV(q)'\mathrm{s}V(q)′s and propose a new exciton mechanism.
Motivation With few exceptions [131] it is widely accepted that the conventional Bardeen–Cooper–Schrieffer (BCS) theory [12] and its intermediate-coupling Eliashberg extension [14] do not suffice to explain high-temperature superconductivity. As shown in the preceding chapters the true origin of high-temperature superconductivity could be found in a proper combination of the bare Coulomb repulsion with the bare electron–phonon interaction in the framework of the many-body polaron theory [51] beyond the BCS–Eliashberg approximation. Nevertheless some researchers have maintained that the repulsive electron–electron interaction alone should provide pairing at high temperatures without phonons despite substantial experimental evidence that the EPI is an important player and needs to be included in the successful theory of high- T c superconductivity. Following the original proposal by P. W. Anderson, many authors [22, 74] argued that the electron–electron interaction in high-temperature superconductors was strong but repulsive providing high T c without phonons via superexchange and/or spin fluctuations in the d -wave pairing channel ( l = 2). A motivation for this concept can be found in the earlier works by Kohn and Luttinger (KL) [132, 133] who showed that the Cooper pairing of fermions with any weak repulsion was possible since the two-particle interaction induced by many-body effects is attractive for pairs with large orbital momenta, l ≫ 1.
It is important to understand the mechanism of high-temperature superconductivity. It is obvious that the interaction with large energy scale is responsible for high critical temperature T c . The Coulomb interaction is one of candidates that bring about high-temperature superconductivity because its characteristic energy is of the order of eV. There have been many works for the Hubbard model including three-band d-p model with the on-site Coulomb repulsion to investigate a possibility of high-temperature superconductivity. It is, of course, not trivial whether the on-site Coulomb interaction leads to a pairing interaction between two electrons. We argue that high-temperature superconductivity is possible in the strongly correlated region by using the variational Monte Carlo method for the two-dimensional t-U-J-V model. The exchange interaction J and the nearest-neighbour attractive interaction V cooperate with U and will act to enhance the critical temperature.
Superconductivity arises from a very complicated set of interactions between the electrons in a metal. This chapter considers a very simplified model of the interaction of a pair of electrons in a metal, it is an instructive example of how quantum mechanics works and the main features of this model are at the starting point of the modern theory of superconductivity. In a metal one has a repulsive Coulomb interaction between the electrons, together with an attractive interaction between the electrons and ions. The total interaction between any two electrons is a composite of this attraction plus the Coulomb repulsion. In some metals, this total interaction is attractive for electrons near the Fermi surface.
The understanding of the mechanisms responsible for superconductivity in strongly correlated systems is an interesting and important subject in condensed matter physics. Several theoretical proposals were considered for these systems. The Coulomb interaction between electrons allow a new approach to study this problem. In this paper, we use a usual Hubbard model with a local repulsive interaction to describe a 2D system. The system of equations are solved using the Green's functions method, within a Hubbard-I mean field approximation, which allows to treat the strong interaction limit. We consider both cases of attractive and repulsive interactions and obtain the zero temperature phase diagram of the model. Our results show, in the repulsive case, the existence of a superconducting ground state mediated by the kinetic electronic energy and described by a non-local order parameter. A minimum value of the repulsive interaction UminU_{min}Umin​ is required to create a pairing state. At finite temperatures, for strong interactions, the critical temperature TcT_cTc​ shows a saturation similar to the Bose-Einstein condensation observed for strong attractive interactions.
We present a review of theoretical investigations into the Kohn-Luttinger nonphonon superconductivity mechanism in various 3D and 2D repulsive electron systems described by the Fermi-gas, Hubbard, and Shubin-Vonsovsky models. Phase diagrams of the superconducting state are considered, including regions of anomalous s-, p-, and d-wave pairing. The possibility of a strong increase in the superconducting transition temperature T c even for a low electron density is demonstrated by analyzing the spin-polarized case or the two-band situation. The Kohn-Luttinger theory explains or predicts superconductivity in various materials such as heterostructures and semimetals, superlattices and dichalcogenides, high-T c superconductors and heavy-fermion systems, layered organic superconductors, and ultracold Fermi gases in magnetic traps. This theory also describes the anomalous electron transport and peculiar polaron effects in the normal state of these systems. The theory can be useful for explaining the origin of superconductivity and orbital currents (chiral anomaly) in systems with the Dirac spectrum of electrons, including superfluid 3He-A, doped graphene, and topological superconductors.