Higher Order Topological Insulator via Periodic Driving

TL;DR

This paper demonstrates how periodic driving can induce higher order topological insulator phases with corner modes in a semimetal, using Floquet theory and symmetry breaking, revealing new topological phenomena.

Contribution

It introduces a method to realize Floquet higher order topological insulators with corner modes through symmetry breaking and Floquet engineering in a driven semimetal.

Findings

Bulk topological phase transition with changing drive amplitude

Quantized Floquet quadrupolar moment indicating HOTI phase

Emergence of dressed corner modes at quasi-energy ω/2

Abstract

We theoretically investigate a periodically driven semimetal based on a square lattice. The possibility of engineering both Floquet Topological Insulator featuring Floquet edge states and Floquet higher order topological insulating phase, accommodating topological corner modes has been demonstrated starting from the semimetal phase, based on Floquet Hamiltonian picture. Topological phase transition takes place in the bulk quasi-energy spectrum with the variation of the drive amplitude where Chern number changes sign from $+1$ to $-1$. This can be attributed to broken time-reversal invariance ($\mathcal{T}$) due to circularly polarized light. When the discrete four-fold rotational symmetry ($\mathcal{C}_4$) is also broken by adding a Wilson mass term along with broken $\mathcal{T}$, higher order topological insulator (HOTI), hosting in-gap modes at all the corners, can be realized. The Floquet quadrupolar moment, calculated with the Floquet states, exhibits a quantized value of $ 0.5$ (modulo 1) identifying the HOTI phase. We also show the emergence of the {\it{dressed corner modes}} at quasi-energy $\omega/2$ (remnants of zero modes in the quasi-static high frequency limit), where $\omega$ is the driving frequency, in the intermediate frequency regime.