Dirac materials under linear polarized light: quantum wave function evolution and topological Berry phases as classical charged particles trajectories under electromagnetic fields

TL;DR

This paper investigates the quantum wave function evolution and topological phases of Dirac materials like borophene and graphene under linearly polarized light, revealing anisotropic responses and classical particle analogies through advanced mathematical transformations.

Contribution

It introduces a novel approach using Whittaker-Hill and Ince equations to analyze wave function dynamics and topological phases in driven Dirac materials, providing new insights into their anisotropic and topological properties.

Findings

Strong anisotropic response in borophene under light

Wave functions follow classical charged particle trajectories

Topological phase diagram derived from dynamical and Berry phases

Abstract

The response of electrons under linearly polarized light in Dirac materials as borophene or graphene is analyzed in a continuous wave regime for an arbitrary intense field. Using a rotation and a time-dependent phase transformation, the wave function evolution is shown to be governed by a spinor-component decoupled Whittaker-Hill equation. The numerical solution of these equations enables to find the quasienergy spectrum. For borophene it reveals a strong anisotropic response. By applying an extra unitary transformation, the wave functions are proven to follow an Ince equation. The evolution of the real and imaginary parts of the wave function is interpreted as the trajectory of a classical charged particle under oscillating electric and magnetic field. The topological properties of this forced quantum system are studied using this analogy. In particular, in the adiabatic driving regime, the system is described with an effective Matthieu equation while in the non-adiabatic regime the full Whittaker-Hill equation is needed. From there, it is possible to separate the dynamical and Berry phase contributions to obtain the topological phase diagram due to the driving. Therefore, a different path to perturbation theory is developed to obtain time-driven topological phases.