Hinge mode dynamics of periodically driven higher-order Weyl semimetals

TL;DR

This paper investigates the dynamics of hinge modes in periodically driven higher-order Weyl semimetals, revealing special frequencies where the quasienergy spectrum becomes gapless and hinge modes merge with bulk states, supported by Floquet perturbation theory.

Contribution

It provides a perturbative analytic expression for the Floquet Hamiltonian and identifies special drive frequencies affecting hinge mode behavior in driven topological materials.

Findings

Quasienergy spectrum becomes gapless at specific drive frequencies.

Hinge modes penetrate into the bulk near these special frequencies.

Large drive amplitude regimes show distinct hinge mode dynamics.

Abstract

We study the stroboscopic dynamics of hinge modes of a second-order topological material modeled by a tight-binding free fermion Hamiltonian on a cubic lattice in the intermediate drive frequency regime for both discrete (square pulse) and continuous (cosine) periodic drive protocols. We analyze the Floquet phases of this system and show that its quasienergy spectrum becomes almost gapless in the large drive amplitude regime at special drive frequencies. Away from these frequencies, the gapped quasienergy spectrum supports weakly dispersing Floquet hinge modes. Near them, these hinge modes penetrate into the bulk and eventually become indistinguishable from the bulk modes. We provide an analytic, albeit perturbative, expression for the Floquet Hamiltonian using Floquet perturbation theory (FPT) which explains this phenomenon and leads to analytic expressions of these special frequencies. We also show that in the large drive amplitude regime, the zero energy hinge modes corresponding to the static tight-binding Hamiltonian display qualitatively different dynamics at these special frequencies. We discuss possible local density of state measurement using a scanning tunneling microscope which can test our theory.