Abstract
Motivated by a scarcity of simple and analytically tractable models of superconductivity from strong repulsive interactions, we introduce a simple tight-binding lattice model of fermions with repulsive interactions that exhibits unconventional superconductivity (beyond BCS theory). The model resembles an idealized trilayer. The Cooper pair consists of electrons on opposite sides of the dielectric, which mediates the attraction. In the strong coupling limit, we use degenerate perturbation theory to show that the model reduces to a superconducting hard-core Bose-Hubbard model. Above the superconducting critical temperature, an analog of pseudo-gap physics results where the fermions remain Cooper paired with a large single-particle energy gap.
Highlights
We present a simple tight-binding lattice model of fermions with a strong repulsive interaction that admits a well-controlled analytical description of its superconductivity
Using degenerate perturbation theory in the limit of a strong repulsive interaction, we show that the model reduces to an s-wave superconducting hard-core boson model
When an electron is at site 1 or 2, the covalent bond is damaged since the repulsive interaction U prevents fermions from hopping onto site 3
Summary
Understanding unconventional superconductivity [1,2,3,4,5,6,7,8,9] arising from electron-electron interactions is a long-standing problem that has recently been most thoroughly discussed in the context of cuprate [10,11,12,13,14,15,16] and iron-based [17,18,19,20,21,22,23] superconductors. Simplest, previously-studied models have found either no attraction [41,42,43] or the strength of the attraction (quantified by the pair-binding energy) approaches zero [41].2 Another interesting direction has been to consider electron attraction that results from proximity to a dielectric or semiconductor [44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60]. We present a simple (and perhaps minimal) tight-binding lattice model of fermions with a strong repulsive interaction that admits a well-controlled analytical description of its superconductivity. Using degenerate perturbation theory in the limit of a strong repulsive interaction, we show that the model reduces to an s-wave superconducting hard-core boson model
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