Generalizedη-pairing models and transition temperature in flat-band superconductors

Certain flat band tight-binding models have exact η-pairing ground states in which superconductivity can be analytically studied.  We generalize the η-pairing models to include generalized bipartite crystalline lattices [1], extending the flat-band superconducting models in [2] to realistic materials.  Our formalism allows for an analytic calculation of charge +1 and +2 excitations above the ground state, the superfluid weight, and a perturbative calculation of the maximum transition temperature and the location of the van Hove singularity.  We apply our results in the context of recent work performed in flat band superconductors such as twisted trilayer graphene [3], demonstrating the need for modifications to BCS theory in the presence of strong coupling.

[1] Calugaru et al., arXiv:2106.05272

[2] Tovmasyan et al., PRB 94, 245149 (2016)

[3] Hao et al., Science Vol. 371, No. 6534 (2021)