Floquet band structure of a semi-Dirac system

TL;DR

This paper investigates how circularly and linearly polarized light affect the band structure of semi-Dirac systems, revealing ways to induce topological phases and control electronic properties through optical means.

Contribution

It provides a detailed analysis of Floquet engineering in semi-Dirac systems, including gap opening, band inversion, and topological transitions induced by polarized light.

Findings

Circularly polarized light opens a topological gap with non-zero Chern number.

Linearly polarized light can split semi-Dirac points or open a gap depending on polarization direction.

The study connects Floquet theory with optical conductivity measurements and non-equilibrium spectral properties.

Abstract

In this work we use Floquet-Bloch theory to study the influence of circularly and linearly polarized light on two-dimensional band structures with semi-Dirac band touching points, taking the anisotropic nearest neighbor hopping model on the honeycomb lattice as an example. We find circularly polarized light opens a gap and induces a band inversion to create a finite Chern number in the two-band model. By contrast, linearly polarized light can either open up a gap (polarized in the quadratically dispersing direction) or split the semi-Dirac band touching point into two Dirac points (polarized in the linearly dispersing direction) by an amount that depends on the amplitude of the light. Motivated by recent pump-probe experiments, we investigated the non-equilibrium spectral properties and momentum-dependent spin-texture of our model in the Floquet state following a quench in absence of phonons, and in the presence of phonon dissipation that leads to a steady-state independent of the pump protocol. Finally, we make connections to optical measurements by computing the frequency dependence of the longitudinal and transverse optical conductivity for this two-band model. We analyze the various contributions from inter-band transitions and different Floquet modes. Our results suggest strategies for optically controlling band structures and experimentally measuring topological Floquet systems.