Shift current response in twisted double bilayer graphene

We present our numerical results on the shift current response in AB-AB and AB-BA stacked twisted double bilayer graphene (TDBG).

The shift current is a second-order nonlinear optical (NLO) response with a striking feature is that the output current is dc despite the input electric field being ac. The shift current is characterized by the shift vector, expressed in terms of the Berry connection [1]. From this, the shift current is utilized to probe the topology of various materials [2]. Yet, NLO responses tend to generate small contributions, making experimental measurements a challenge.

Moiré materials are a desirable platform to study NLO responses due to their large density of states. TDBG is an example of a moiré system that can be prepared by stacking two sheets of untwisted AB stacked bilayer graphene and introducing a relative twist angle. It is known that the two stacking configurations (AB-AB/BA) of TDBG have similar band structures, yet, contrasting valley Chern numbers [3].

Here, we are motivated to investigate the effect of the contrasting topology of AB-AB and AB-BA stacked TDBG on the shift current response. Using the effective continuum Hamiltonian for TDBG [3], we have shown that the difference in the topology between the two variants manifests as the relative sign of the signal. We further show that topological transitions are detectable through the sign flip of the shift current.

[1] J. E. Sipe, et al., PRB 61, 5337 (2000).

[2] J.-X. Hu, et al., PRB 107, 075424 (2023).

[3] M. Koshino, PRB 99, 235406 (2019).