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arXiv:2112.03950 · Physical review. B./Physical review. B

Unconventional superconductivity due to interband polarization

Valentin Crépel, Tommaso Cea, Liang Fu, F. Guinea

Published Mar 16, 2022• 36 citations
arXivHTMLPDF

Abstract

An important question about unconventional superconductors is how attractions can emerge in a purely repulsive electronic system. Here, the authors study comprehensively one such electronic mechanism, where pairing is induced by a third electron undergoing a virtual interband transition. Their exact solution of an illustrative Hubbard model establishes superconductivity due to interband polarization in both the weak and strong coupling regimes. Relevance of this pairing mechanism for twisted bilayer graphene is also discussed.

DOI
10.1103/physrevb.105.094506

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An important question about unconventional superconductors is how attractions can emerge in a purely repulsive electronic system. Here, the authors study comprehensively one such electronic mechanism, where pairing is induced by a third electron undergoing a virtual interband transition. Their exact solution of an illustrative Hubbard model establishes superconductivity due to interband polarization in both the weak and strong coupling regimes. Relevance of this pairing mechanism for twisted bilayer graphene is also discussed.
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In superconducting phases, repulsive interactions between the electrons usually lead to higher-angular momentum Cooper pairing. Here, the authors employ the weak-coupling renormalization group approach to study unconventional superconducting phases emerging in the extended, repulsive Hubbard model on paradigmatic two-dimensional lattices. Among their findings are extended regions of chiral topological superconductivity on the square, triangular, and honeycomb lattices. They provide detailed superconducting phase diagrams as well as the coupling strengths that quantify the corresponding critical temperatures depending on the band-structure parameters, band filling, and interaction parameters. The importance of the resolution and accuracy of the numerical integration for the method is discussed and a way to higher numerical efficiency provided.
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.
Stacking two layers of graphene with a relative twist angle gives rise to Moir\'e patterns, which can strongly modify electronic behavior and may lead to unconventional superconductivity. A synthetic version of twisted bilayers can be engineered with cold atoms in optical lattices. Here, the bilayer structure is mimicked through coupling between atomic sublevels, and the twist is achieved by a spatial modulation of this coupling. In the present paper, we investigate the superconducting behavior of fermionic atoms in such a synthetic twisted bilayer lattice. Attractive interactions between the atoms are treated on the mean-field level, and the superconducting behavior is analyzed via the self-consistently determined pairing gap. A strong enhancement of the pairing gap is found when a quasi-flat band structure occurs at the Fermi surface, reflecting the prominent role played by the twist on the superconductivity. The tunability of interactions allows for the switching of superconducting correlations from intra (synthetic) layer to inter (synthetic) layer. This includes also the intermediate scenario, in which the competition between inter- and intra-layer coupling completely destroys the superconducting behavior, resulting in re-entrant superconductivity upon tuning of the interactions.
Motivated by the recent novel electronic features extracted from the magic-angle graphene superlattices, we studied the ground state superconducting pairing correlations within the Hubbard model on a twisted bilayer honeycomb lattice. Using Constrained-Path Quantum Monte Carlo method, we found that the [Formula: see text] pairing correlation dominates over other pairing patterns among various electron fillings and interaction strengths, and the effective pairing interaction was enhanced as the on-site Coulomb interaction increased. We further examined the effect of the nearest neighbor interaction [Formula: see text], and the effective pairing interaction with [Formula: see text] pairing symmetry was also enhanced by either a repulsive or attractive interaction. Our intensive numerical results confirm the interaction driven superconductivity with a dominant [Formula: see text] pairing symmetry in twisted bilayer graphene.
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.