Trigonal Warping, Satellite Dirac Points and Multiple Field Tuned Topological Transitions in Twisted Double Bilayer Graphene

TL;DR

This paper investigates how electric fields induce topological phase transitions in twisted double bilayer graphene, revealing the role of trigonal warping and satellite Dirac points in tuning valley Chern numbers and electronic phases.

Contribution

It demonstrates the control of valley Chern numbers via electric fields and elucidates the impact of trigonal warping and satellite Dirac points on topological transitions.

Findings

Valley Chern number can be tuned through two topological transitions.

Satellite Dirac points with opposite chirality form around the central Dirac cone.

A narrow parameter regime exhibits transitions through three insulating phases with distinct valley Hall conductivities.

Abstract

We show that the valley Chern number of the low energy band in twisted double bilayer graphene can be tuned through two successive topological transitions, where the direct bandgap closes, by changing the electric field perpendicular to the plane of the graphene layers. The two transitions with Chern number changes of -3 and +1 can be explained by the formation of three satellite Dirac points around the central Dirac cone in the moir\'e Brillouin zone due to the presence of trigonal warping. The satellite cones have opposite chirality to the central Dirac cone. Considering the overlap of the bands in energy, which lead to metallic states, we construct the experimentally observable phase diagram of the system in terms of the indirect bandgap and the anomalous valley Hall conductivity. We show that while most of the intermediate phase becomes metallic, there is a narrow parameter regime where the transition through three insulating phases with different quantized valley Hall conductivity can be seen. We systematically study the effects of variations in the model parameters on the phase diagram of the system to reveal the importance of particle-hole asymmetry and trigonal warping in constructing the phase diagram. We also study the effect of changes in interlayer tunneling on this phase diagram.