# Generating surface states in a Weyl semi-metal by applying electromagnetic radiation

## TL;DR

Applying circularly polarized electromagnetic radiation to Weyl semi-metals can generate and manipulate surface states, revealing new bulk-boundary relations and extending to topological and trivial insulators.

## Contribution

This paper demonstrates that electromagnetic radiation can induce and control surface states in Weyl semi-metals, topological insulators, and trivial insulators, revealing novel bulk-boundary phenomena.

## Key findings

- Surface states are generated by radiation with complex Floquet eigenvalues.
- Surface Floquet eigenvalues relate to bulk eigenvalue extrema.
- Radiation increases decay lengths of surface states in topological insulators.

## Abstract

We show that the application of circularly polarized electromagnetic radiation on the surface of a Weyl semi-metal can generate states at that surface. These states can be characterized by their surface momentum. The Floquet eigenvalues of these states come in complex conjugate pairs rather than being equal to $\pm 1$. If the amplitude of the radiation is small, we find some unusual bulk-boundary relations: the Floquet eigenvalues of the surface states lie at the extrema of the Floquet eigenvalues of the bulk system, and the peaks of the Fourier transforms of the surface state wave functions lie at the momenta where the bulk Floquet eigenvalues have extrema. For the case of zero surface momentum, we can analytically derive scaling relations between the decay length of the surface states and the amplitude and penetration length of the radiation. For topological insulators, we again find that circularly polarized radiation can generate states on the surfaces; these states have much larger decay lengths than the surface states which are present even in the absence of radiation. Finally, we show that radiation can generate surface states for trivial insulators also.