Topological Floquet states on a M\"obius band irradiated by circularly polarised light

TL;DR

This paper explores how circularly polarized light induces topological Floquet states in a graphene M"obius band, revealing a competition between quantum anomalous Hall and quantum spin Hall effects influenced by geometry and light parameters.

Contribution

It introduces a novel analysis of Floquet topological states on a non-orientable M"obius band under light irradiation, highlighting the interplay of geometry, light, and spin-orbit coupling.

Findings

Homogeneous quantum Hall effect cannot exist on a M"obius band.

Periodic driving tends to generate quantum anomalous Hall states.

Strong spin-orbit coupling may lead to quantum spin Hall-like states.

Abstract

Topological states of matter in equilibrium, as well as out of equilibrium, have been thoroughly investigated during the last years in condensed-matter and cold-atom systems. However, the geometric topology of the studied samples is usually trivial, such as a ribbon or a cylinder. In this paper, we consider a graphene M\"obius band irradiated with circularly polarised light. Interestingly, due to the non-orientability of the M\"obius band, a homogeneous quantum Hall effect cannot exist in this system, but the quantum spin Hall effect can. To avoid this restriction, the irradiation is applied in a longitudinal-domain-wall configuration. In this way, the periodic time-dependent driving term tends to generate the quantum anomalous Hall effect. On the other hand, due to the bent geometry of the M\"obius band, we expect a strong spin-orbit coupling, which may lead to quantum spin Hall-like topological states. Here, we investigate the competition between these two phenomena upon varying the amplitude and the frequency of the light, for a fixed value of the spin-orbit coupling strength. The topological properties are analysed by identifying the edge states in the Floquet spectrum at intermediate frequencies, when there are resonances between the light frequency and the energy difference between the conduction and valence bands of the graphene system.