# Floquet engineering of Dirac cones on the surface of a topological insulator

## TL;DR

This paper demonstrates how external periodic driving fields can be used to engineer and control Dirac cones on the surface of topological insulators, revealing tunable properties and robustness of surface states.

## Contribution

It introduces a full Hamiltonian approach to Floquet engineering of topological insulator surfaces, showing enhanced control and validation of effective surface Hamiltonians.

## Key findings

- Fermi velocity can be tuned via polarization, direction, and amplitude of the driving field.
- Dirac cones can become elliptic or massive under external driving.
- Surface Dirac cones remain robust despite bulk states presence.

## Abstract

We propose to Floquet-engineer Dirac cones at the surface of a three-dimensional topological insulator. We show that a large tunability of the Fermi velocity can be achieved as a function of the polarization, direction and amplitude of the driving field. Using this external control, the Dirac cones in the quasienergy spectrum may become elliptic or massive, in accordance to experimental evidences. These results help us to understand the interplay of surface states and external ac driving fields in topological insulators. In our work we use the full Hamiltonian for the three-dimensional system instead of effective surface Hamiltonians, which are usually considered in the literature. Our findings show that the Dirac cones in the quasienergy spectrum remain robust even in the presence of bulk states and, therefore, they validate the usage of effective surface Hamiltonians to explore the properties of Floquet-driven topological boundaries. Furthermore, our model allows us to introduce new out-of-plane field configurations, which cannot be accounted for by effective surface Hamiltonians.