Phase diagram and orbital Chern insulator in twisted double bilayer graphene

TL;DR

This paper explores the phase diagram and orbital Chern insulator states in twisted double bilayer graphene, revealing conditions for topological phases and orbital magnetization behavior through theoretical calculations.

Contribution

It introduces a comprehensive phase diagram for TDBG, incorporating interactions and revealing conditions for orbital Chern insulator states at half-filling.

Findings

Orbital Chern insulator appears at half-filling when valley splitting exceeds bandwidth.

Orbital magnetization remains negative across the half-filling gap, with no sign reversal.

The study provides insights relevant for ongoing experimental investigations.

Abstract

Compared with twisted bilayer graphene, twisted double bilayer graphene (TDBG) provides another important platform to realize the moir\'e flat bands. In this paper, we first calculate the valley Chern number phase diagram of TDBG in the parameter space spanned by the twist angle and the interlayer electric potential. To include the effects of interactions, we then phenomenologically introduce the spin-splitting and valley-splitting. We find that when the valley splitting is larger than the bandwidth of the first conduction band so that a gap is opened and the spin splitting is relatively weak, the orbital Chern insulator emerges at half-filling, associated with a large orbital magnetization (OM). Further calculations suggest that there is no sign reversal of the OM when the Fermi energy goes from the bottom to the top of the half-filling gap, as the OM remains negative in both AB-AB stacking and AB-BA stacking. The implications of our results for the ongoing experiments are also discussed.