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Physical Review Letters

Superconductivity in a repulsively interacting two-band Fermi gas

Kazuhiko Kuroki, Hideo Aoki

Published May 2, 1994• 18 citations
Publisher

Abstract

Phase diagram of the two-band Fermi gas with repulsive intraband and interband interactions is obtained with the bosonization technique. In the forward-scattering model, there is a region for the superconductivity (SC) within a band due to charge fluctuations in the accompanying band. When the backward scattering is relevant the SC region becomes wider, while when the umklapp scattering is relevant the system is renormalized into two independent single bands, which is considered to cover the regime where superconductivity a\ifmmode\acute\else\textasciiacute\fi{} la single-band attractive Hubbard model is found from quantum Monte Carlo results in the multiband model on discrete lattices.

DOI
10.1103/physrevlett.72.2947

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Phase diagram of the two-band Fermi gas with repulsive intraband and interband interactions is obtained with the bosonization technique. In the forward-scattering model, there is a region for the superconductivity (SC) within a band due to charge fluctuations in the accompanying band. When the backward scattering is relevant the SC region becomes wider, while when the umklapp scattering is relevant the system is renormalized into two independent single bands, which is considered to cover the regime where superconductivity a\ifmmode\acute\else\textasciiacute\fi{} la single-band attractive Hubbard model is found from quantum Monte Carlo results in the multiband model on discrete lattices.
The phase diagram for spin 1/2 fermions with attractive interband interactions (- V ) is obtained for the two-band Hubbard model in the space of - V , intraband repulsion ( U ), and the band filling from the quantum Monte Carlo calculation along with the mean-field theory in one dimension. The competition of an off-diagonal long-range order with diagonal orders (CDW and SDW) is shown to result in a superconducting ground state arising from interband pairing (i) in the presence of U of right magnitude ( ∼ V ) and (ii) in non-half-filled bands.
We consider the multiband, purely repulsive Hubbard model on a class of systems in which there are two (or more) kinds of orbitals per unit cell such that one metallic band interacts with the other insulating band. From both perturbational canonical transformation and quantum Monte Carlo studies we have shown that superconductivity due to nonretarded attraction (negative U) is a generic feature of this class of metal-insulator composite many-body systems. Remarkably, the superconductivity arises, under appropriate conditions, for various types of insulating bands (a charge-transfer insulator, Mott-Hubbard insulator, etc.). Superconductivity is unambiguously identified from the pairing correlation function, which agrees with that of the attractive Hubbard model surprisingly well even in the nonperturbative regime. The superconductivity revealed here is in a sense an opposite limit to conventional superconductivity with retarded attraction from boson-exchange mechanisms. We also show that the present mechanism is distinct from existing multiband models such as d-${\mathit{p}}_{\mathrm{\ensuremath{\sigma}}}$ models. As we increase the magnitude of the attraction in the present model by changing some parameters (e.g., to make the accompanying band metallic), the similarity with the attractive Hubbard model becomes eventually degraded, so that the optimum condition for superconductivity is determined by this kind of tradeoff. We also discuss the relevance of the present model to high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductivity in cuprates and fullerenes.
We present a vector recursion based approach to study the effect of disorder on superconductivity in a system modeled by the two-band attractive Hubbard model. We use the augmented space formalism for the disorder averaging. In the presence of only intraband pairing in a two-band disordered system with disorder in either or both bands, our calculations reveal that the gap survives in the quasiparticle spectrum; similar to single band systems. However, for interband pairing the gap in the quasiparticle spectrum ceases to exist beyond a critical value of the disorder strength. In the presence of both interband and intraband pairing interaction, depending on the relative magnitude of the pairing strength, only a particular kind of pairing is possible for a half filled two-band system.
By means of the exact-diagonalization method we have studied the finite-size two-band model with the interband pair-transfer interaction by calculating the superconducting (SC) correlation function P s etc. in the ground state. Occurrence of SC was clearly indicated by the increase of P s . The diagram of the observed SC region was constructed in the plane of the relative position of the second band versus on-site Coulomb energy U . In the low-density limit it proved close to the region where a negative- U situation is realized by the pair-transfer interaction. On the high-density side, the SC region was found to be more extended than the latter in accord with the previous interband-ladder-diagram results. Inclusion of the exchange interaction was found to reduce the SC region in a restricted region where two bands substantially share electrons. The two-band situations in cuprates are argued to be relevant to the high T c through the present mechanism.
A two-band model of spinless fermions in one dimension is constructed. Density-density couplings, umklapp scattering, and interband transitions are included. Renormalization-group equations are derived and discussed. In addition, it is shown that with one condition on the couplings and the velocities the model may be transformed to two uncoupled sine-Gordon Hamiltonians, which makes it possible to obtain solutions in regions where the renormalization-group equations are not valid. An important property of the model is that there can be superconductivity with repulsive interactions.
A renormalization group treatment is applied to a model of (quasi)-two-dimensional semiconductor with a small band gap. Phase diagrams are derived based on the numerical solutions of the scaling equations. In the purely two-dimensional case, we find the singlet superconducting phase is induced by the repulsive interband interaction in the presence of the attractive intraband interaction. We also find the ferromagnetism and/or the ferroelectricity are stabilized in the presence of the repulsive interband and intraband interactions. The effects of the other kinds of interband and interplanar interactions are also discussed.