Correlated states in magic angle twisted bilayer graphene under the optical conductivity scrutiny

María J Calderón,Elena Bascones

doi:10.1038/s41535-020-00258-6

Abstract

Moiré systems displaying flat bands have emerged as novel platforms to study correlated electron phenomena. Insulating and superconducting states appear upon doping magic angle twisted bilayer graphene (TBG), and there is evidence of correlation induced effects at the charge neutrality point (CNP) which could originate from spontaneous symmetry breaking. Our theoretical calculations show how optical conductivity measurements can distinguish different symmetry breaking states, and reveal the nature of the correlated states. In the specific case of nematic order, which breaks the discrete rotational symmetry of the lattice, we find that the Dirac cones are displaced, not only in momentum space but also in energy, inducing finite Drude weight at the CNP. We also show that the sign of the Drude weight anisotropy induced by a nematic order depends on the degree of lattice relaxation, the doping and the nature of the symmetry breaking.

Highlights

Instabilities in correlated materials arise when the interaction energy overcomes the kinetic energy gain
The changes in the band structure responsible for the modification of the density of states (DOS) observed in STM when the flat bands are partially filled, with respect to the one in fully empty or filled flat bands, can be addressed by optical conductivity measurements in the far-infrared regime
We present results for the optical conductivity calculated in linear response as given by Kubo formula, following the derivation for multiorbital systems in ref. 21, see “Methods” and Supplementary Eq 20

Summary

Introduction

Instabilities in correlated materials arise when the interaction energy overcomes the kinetic energy gain. A plethora of insulating and superconducting states appear as the system is doped[2,3,4,5,6,7] and band widening has been observed in STM experiments when the chemical potential μ lies within the flat bands, in particular, in undoped systems (namely, at the charge neutrality point (CNP))[8,9,10,11]. Correlations have to be included to explain both the insulating states which appear at integer fillings and the doping dependence of the band widening[13,14,15,16]. The nature of these states is highly debated. An important issue, yet unknown, is whether the correlated states affect only the flat bands or involve higher energy bands, split by a few tens of meV gaps from the flat bands

Methods

Results

Conclusion