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Physical Review

New Mechanism for Superconductivity

J. M. Luttinger

Published Oct 7, 1966• 74 citations
Publisher

Abstract

A new mechanism which leads to superconductivity even for particles with purely repulsive forces between them is described. The general theory is given for weak short-ranged pair forces between the particles and for arbitrary (convex) Fermi surfaces. It is shown that the transition temperature due to this mechanism is in general quite low, though it may be enhanced somewhat by very special Fermi-surface geometry.

DOI
10.1103/physrev.150.202

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•Jan 1, 2019•0 citations
A new mechanism which leads to superconductivity even for particles with purely repulsive forces between them is described. The general theory is given for weak short-ranged pair forces between the particles and for arbitrary (convex) Fermi surfaces. It is shown that the transition temperature due to this mechanism is in general quite low, though it may be enhanced somewhat by very special Fermi-surface geometry.
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.
We show that superconductive pairing is possible in the presence of an arbitrarily strong short-range repulsion between electrons if the gap is an odd function of k-kF{\mathit{k}}_{\mathit{F}}kF​. We discuss how the behavior of \ensuremath{\Delta}(k-kF{\mathit{k}}_{\mathit{F}}kF​) close to the Fermi surface is related to (i) the low-energy tunneling density of states, and (ii) the attractive part of the potential. We show that some features of the tunneling data in high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates, including the fact that the maximum hardly moves when T approaches Tc{\mathit{T}}_{\mathit{c}}Tc​, are natural consequences of this type of pairing.
In this short review, 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 note 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 Ranninger et al. and its generalizations.
We discuss the mechanisms of unconventional superconductivity and superfluidity in 3D and 2D fermionic systems with purely repulsive interaction at low densities. We construct phase diagrams of these systems and find the areas of the superconducting state in free space, as well as on the lattice in the framework of the Fermi-gas model with hard-core repulsion, the Hubbard model, the Shubin-Vonsovsky model, and the t−Jt-Jt−J model. We demonstrate that the critical superconducting temperature can be greatly increased in the spin-polarized case or in a two-band situation already at low densities. The proposed theory is based on the Kohn-Luttinger mechanism or its generalizations and explains or predicts anomalous ppp-, ddd-, and fff-wave pairing in various materials, such as high-temperature superconductors, the idealized monolayer and bilayer of doped graphene, heavy-fermion systems, layered organic superconductors, superfluid 3^33He, spin-polarized 3^33He mixtures in 4^44He, ultracold quantum gases in magnetic traps, and optical lattices.
Various BCS-like pairing theories are still invariably used to describe the unusual superconducting/superfluid states and properties of condensed matters without clarifying the fermionic or bosonic nature of Cooper pairs and the relevant mechanisms of superconductivity and superfluidity. We show that the bosonization of Cooper pairs and the novel superconductivity and superfluidity resulting from the condensation of an attractive Bose gas of Cooper pairs into a superfluid state in high-Tc cuprates and other exotic systems occur under the condition εF≲2εA (where εF is the Fermi energy, εA is the energy of the effective attraction between fermions). We argue that the simple BCS criterion (i.e. formation of an energy gap on the Fermi surface) is insufficient for the occurrence of unconventional superconductivity (superfluidity) and the superconducting/superfluid transition in attractive Bose systems is more λ-like than the usual Bose–Einstein condensation. The new and specific criteria for unconventional superconductivity and superfluidity are formulated. Mean-field theory of the three- and two-dimensional superfluid Bose condensates of Cooper pairs describes reasonably well the novel superconducting states (i.e., two distinct superconducting phases below the bulk superconducting transition temperature Tc and a vortex-like state above Tc) and properties (such as λ-like transition at Tc, first-order phase transition and gapless bosonic excitations somewhat below Tc or even far below Tc) of high-Tc cuprates in full agreement with the experimental findings. The unusual superconducting/superfluid states and properties of heavy-fermion and organic compounds, Sr2RuO4, 3He, 4He and atomic Fermi gases are explained more clearly by this theory.