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International Journal of Modern Physics B

SUPERCONDUCTIVITY AND SUPERFLUIDITY IN FERMI SYSTEMS WITH REPULSIVE INTERACTIONS

M. A. BARANOV, Andrey V. Chubukov, M. Yu. Kagan

Published Jul 20, 1992• 105 citations
Publisher

Abstract

We study the possibility of a pairing instability in Fermi systems with a purely repulsive interaction potential. The effective interaction between particles at the Fermi surface is shown to contain a contribution from the fermionic background. This contribution is attractive and in many cases it overshadows the interactive potential in the pairing channels with nonzero orbital angular momenta. In particular, we show that 3D Fermi gas with repulsive interaction is unstable against p-pairing. Both the value of T c and its field dispersion are consistent with the experimental data for pure 3 He . It is also shown that in a magnetic field and in the two-band model there is the possibility of a significant mcrease of T c . We also consider the situation in two dimensions, where the effect of the fermionic background is much weaker than in the 3D case. Nevertheless, we show that the positive-U Hubbard model may have an intrinsic instability at arbitrarily small carrier densities. In particular, the Hubbard model with hopping between nearest neighbors is unstable against d-wave pairing with dxy symmetry of the gap wave function. The superconducting states we study correspond to the actual minima of the Free energy.

DOI
10.1142/s0217979292001249

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We study the possibility of a pairing instability in Fermi systems with a purely repulsive interaction potential. The effective interaction between particles at the Fermi surface is shown to contain a contribution from the fermionic background. This contribution is attractive and in many cases it overshadows the interactive potential in the pairing channels with nonzero orbital angular momenta. In particular, we show that 3D Fermi gas with repulsive interaction is unstable against p-pairing. Both the value of T c and its field dispersion are consistent with the experimental data for pure 3 He . It is also shown that in a magnetic field and in the two-band model there is the possibility of a significant mcrease of T c . We also consider the situation in two dimensions, where the effect of the fermionic background is much weaker than in the 3D case. Nevertheless, we show that the positive-U Hubbard model may have an intrinsic instability at arbitrarily small carrier densities. In particular, the Hubbard model with hopping between nearest neighbors is unstable against d-wave pairing with dxy symmetry of the gap wave function. The superconducting states we study correspond to the actual minima of the Free energy.
We demonstrate the possibility of triplet p-wave pairing at low electron density a large number of models such as 3D and 2D Fermi-gas models with hard-core repulsion, 3D and 2D Hubbard models, and the Shubin-Vonsovsky model. The critical temperature for p-wave pairing can be considerably higher in the spin-polarized case or even in a two-band situation at low density and can reach experimentally observable values of 1–5 K. We also discuss briefly the d-wave pairing and high-Tc superconductivity with Tc ∼ 100 K which arise in the extended Hubbard model and in the generalized t-J model when close to half-filling.
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.
An effective interaction between fermions in a Bose-Fermi mixture is derived. It is induced by density fluctuations of the bosonic background. The contributions from states containing both one and two virtual phonons are taken into account self-consistently. The time dependence of the effective interaction has been removed by assuming that the velocity of the fermions at the Fermi surface is much larger than the sound velocity in the Bose gas. This assumption is more appropriate for the actual experimental situations than the usual approximation of neglecting retardation effects. The effective interaction turns out to be attractive and, as a consequence, can give rise to a superconducting phase in the Fermi component of the mixture. The fermions are considered in only one magnetic state, so that pairing can be effective only in odd-lll channels. It has been found that the onset of the superconducting phase can occur at temperatures (>100nK)(>100\mathrm{nK})(>100nK) of the same order of magnitude as the Fermi temperature $(\ensuremath{\sim}300\mathrm{nK}),$ and the energy gap in the excitation spectrum is a small fraction $(\ensuremath{\sim}1%)$ of the Fermi energy.
The search for superconductivity with unconventional pairing symmetry has been a central focus in the study of strongly correlated electron systems. In this work, we report a numerically exact study of the spin-triplet pairing in a two-dimensional Hubbard model with repulsive interactions, employing the determinant quantum Monte Carlo method. The model includes next-nearest-neighbor and third-nearest-neighbor hopping terms and maintains spin balance. By tuning the fermion filling close to a type-II Van Hove singularity (VHS) in the model, we numerically investigate the ordering tendencies of several possible pairing channels with different symmetries. Our numerical results provide clear evidence of the spin-triplet ppp-wave pairing instability approaching low temperatures, as revealed by the vertex contribution to the pairing susceptibility. This signature becomes increasingly pronounced as the interaction strength increases in the weak to intermediate regime. We further find that, near the type-II VHS, the dominant spin-spin correlations in the system are ferromagnetic, suggesting its close relation to the spin-triplet pairing instability. Our findings offer a reliable approach to realize spin-triplet ppp-wave superfluidity in the repulsive Hubbard model from an unbiased numerical perspective.
The attractive (U < 0) and repulsive (U > 0) Hubbard models have been studied using the Fermi liquid perturbation approach. The attractive Hubbard model (U < 0) is an adequate model for 3 He , an incompressible and strongly paramagnetic liquid [Formula: see text], [Formula: see text] for |U|N F = 0.9) with a pseudogap in the charge response. A pairing instability and superfluidity for U < 0 exists in the spin channel only: spin-triplet with l = 0, or spin-singlet with l = 1 (p-wave orbital state j = s + l = 1), where l is the orbital momentum of a pair. The repulsive Hubbard model (U > 0) represents a highly compressible and nearly antiferromagnetic liquid [Formula: see text], [Formula: see text] for UN F = 0.9) with a pseudogap in the spin response. However, for U > 0 a pairing instability and superconductivity exist in the charge channel only: spin-singlet with l = 0 (s-wave), or with l = 2 (d-wave) in the case of an anisotropic Fermi surface.