Low-energy optical sum-rule in moir\'e graphene

TL;DR

This paper develops an exact analytical theory for the low-energy optical spectral weight in twisted bilayer graphene at integer fillings, revealing its vanishing in the strong-coupling limit and exploring effects of strain and tunneling.

Contribution

It provides the first exact analytical description of Coulomb interaction effects on optical spectral weight in moiré graphene at all integer fillings.

Findings

Optical spectral weight vanishes at integer fillings in the strong-coupling limit.

Strain and tunneling effects modify the optical spectral weight.

Results connect optical properties to superconducting tendencies in moiré graphene.

Abstract

Few layers of graphene at small twist-angles have emerged as a fascinating platform for studying the problem of strong interactions in regimes with a nearly quenched single-particle kinetic energy and non-trivial band topology. Starting from the strong-coupling limit of twisted bilayer graphene with a vanishing single-electron bandwidth and interlayer-tunneling between the same sublattice sites, we present an {\it exact} analytical theory of the Coulomb interaction-induced low-energy optical spectral weight at all {\it integer} fillings. In this limit, while the interaction-induced single-particle dispersion is finite, the optical spectral weight vanishes identically at integer fillings. We study corrections to the optical spectral weight by systematically including the effects of experimentally relevant strain-induced renormalization of the single-electron bandwidth and interlayer tunnelings between the same sublattice sites. Given the relationship between the optical spectral weight and the diamagnetic response that controls superconducting $T_c$, our results highlight the relative importance of specific parent insulating phases in enhancing the tendency towards superconductivity when doped away from integer fillings.