Floquet engineering and non-equilibrium topological maps in twisted trilayer graphene

TL;DR

This paper explores how different types of light influence the electronic band structure and topology of twisted trilayer graphene, revealing tunable flat bands, band gaps, and topological phases through Floquet engineering.

Contribution

It introduces effective Floquet Hamiltonians for various stacking configurations of twisted trilayer graphene under light, highlighting tunable topological properties and proposing experimental detection methods.

Findings

Circularly polarized light induces band flattening and gap openings.

Distinct topological phases are mapped via Chern numbers for different stackings.

Longitudinal light allows in-situ tuning of magic angles in the band structure.

Abstract

Motivated by the recent experimental realization of twisted trilayer graphene and the observed superconductivity that is associated with its flat bands at specific angles, we study trilayer graphene under the influence of different forms of light in the non-interacting limit. Specifically, we study four different types of stacking configurations with a single twisted layer. In all four cases, we study the impact of circularly polarized light and longitudinal light coming from a waveguide. We derive effective time-independent Floquet Hamiltonians and review light-induced changes to the band structure. For circularly polarized light, we find band flattening effects as well as band gap openings. We emphasize that there is a rich band topology, which we summarize in Chern number maps that are different for all four studied lattice configurations. The case of a so-called ABC stacking with top layer twist is especially rich and shows a different phase diagram depending on the handedness of the circularly polarized light. Consequently, we propose an experiment where this difference in typologies could be captured via optical conductivity measurements. In contrast for the case of longitudinal light that is coming from a waveguide, we find that the band structure is very closely related to the equilibrium one but the magic angles can be tuned in-situ by varying the intensity of the incident beam of light.