Charge order and Mott insulating ground states in small-angle twisted bilayer graphene

TL;DR

This paper investigates the electronic ordered states in small-angle twisted bilayer graphene, revealing charge density waves and Mott insulators depending on coupling strength, with implications for symmetry breaking and experimental observations.

Contribution

It provides a detailed analysis of charge order and Mott insulating states across different coupling regimes in twisted bilayer graphene, highlighting the role of non-local interactions.

Findings

Charge density waves break translational and rotational symmetry in weak coupling.

Mott insulating states break symmetries and depend on local electron occupation.

Symmetry breaking may explain reduced Landau level degeneracy observed experimentally.

Abstract

In this work, we determine states of electronic order of small-angle twisted bilayer graphene. Ground states are determined for weak and strong couplings which are representatives for varying distances of the twist-angle from its magic value. In the weak-coupling regime, charge density waves emerge which break translational and $C_{3}$-rotational symmetry. In the strong coupling-regime, we find rotational and translational symmetry breaking Mott insulating states for all commensurate moir\'e band fillings. Depending on the local occupation of superlattice sites hosting up to four electrons, global spin-(ferromagnetic) and valley symmetries are also broken which may give rise to a reduced Landau level degeneracy as observed in experiments for commensurate band fillings. The formation of those particular electron orders is traced back to the important role of characteristic non-local interactions which connect all localized states belonging to one hexagon formed by the AB- and BA-stacked regions of the superlattice.