[Paper Review] Floquet engineering and non-equilibrium topological maps in twisted trilayer graphene

I. A. Assi, J. P. F. LeBlanc+3 more|arXiv (Cornell University)|Jun 23, 2021

Graphene research and applicationsMaterials Science98 references23 citations

TL;DR

This paper investigates Floquet engineering in twisted trilayer graphene (TTG) under circularly polarized light and waveguide-incident longitudinal light, deriving effective time-independent Hamiltonians to analyze light-induced band flattening, gap openings, and topological phase transitions. The key contribution is the discovery of distinct Chern number maps and tunable magic angles, with ABC-stacked TTG showing chiral-dependent topological phases under circularly polarized light, proposing optical conductivity measurements to probe these differences experimentally.

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.

Motivation & Objective

• To explore non-equilibrium topological phases in twisted trilayer graphene (TTG) under periodic light irradiation.
• To investigate how different stacking configurations (ABC, AAA, ABA, etc.) respond to circularly polarized light and waveguide-incident longitudinal light.
• To derive effective time-independent Floquet Hamiltonians for computationally efficient analysis of light-driven band structure modifications.
• To map the Chern numbers of the six central bands across parameter space and identify topological phase transitions.
• To propose an experimental test using optical conductivity to distinguish between topological phases induced by left- and right-handed circularly polarized light in ABC-stacked TTG.

Proposed method

• Formalism of time-dependent Floquet theory is applied to derive effective time-independent Hamiltonians for TTG under periodic light irradiation.
• The model uses a bounded tight-binding Hamiltonian with interlayer hopping parameters tuned by twist angles and layer stacking configurations.
• Circularly polarized light is introduced via a Peierls substitution with vector potential, while longitudinal light from a waveguide is modeled as a spatially varying electric field.
• Chern numbers are computed numerically using the Fukui-Hatsugai-Suzuki method on discretized Brillouin zones to characterize band topology.
• Effective Hamiltonians are derived using Floquet perturbation theory to capture light-induced band flattening and gap openings.
• Band structures and topological invariants are analyzed across multiple stacking configurations and light polarization states.

Experimental results

Research questions

• RQ1 How does circularly polarized light modify the band structure and topology of twisted trilayer graphene across different stacking configurations?
• RQ2 What are the distinct Chern number maps for the six central bands in TTG under circularly polarized light, and how do they depend on stacking and light handedness?
• RQ3 Can longitudinal light from a waveguide tune the magic angles at which flat bands emerge in TTG?
• RQ4 What is the mechanism behind light-induced band flattening and gap opening in TTG under circularly polarized light?
• RQ5 How can optical conductivity measurements distinguish between topological phases induced by left- and right-handed circularly polarized light in ABC-stacked TTG?

Key findings

• Circularly polarized light induces band flattening and gap openings in all four TTG stacking configurations, with the most complex topological response observed in ABC-stacked TTG with top-layer twist.
• The Chern number maps for the six central bands in ABC-stacked TTG with top-layer twist exhibit distinct phase diagrams depending on the handedness of the circularly polarized light.
• For ABC-stacked TTG, left- and right-handed circularly polarized light produce topologically distinct phases, which can be probed via optical conductivity measurements.
• Longitudinal light from a waveguide preserves the equilibrium band structure topology but enables in-situ tuning of magic angles by varying light intensity.
• Effective time-independent Floquet Hamiltonians accurately capture light-induced band modifications, enabling efficient computation of topological invariants and band structure evolution.
• The study reveals that light-induced topology in TTG is highly sensitive to stacking order and polarization handedness, suggesting new avenues for topological control in moiré materials.