Floquet second-order topological Anderson insulator hosting corner localized modes

TL;DR

This paper theoretically demonstrates how disorder and periodic driving can induce a higher-order topological insulator phase with localized corner modes, characterized by a new real-space topological invariant.

Contribution

It introduces the concept of Floquet higher-order topological Anderson insulator and develops a chiral winding number to characterize its topological phases.

Findings

Disorder and periodic drive generate FHOTAI with corner modes.

FHOTAI hosts both 0- and π-modes.

A new real-space topological invariant characterizes the phase transition.

Abstract

The presence of random disorder in a metallic system accounts for the localization of extended states in general. On the contrary, the presence of disorder can induce topological phases hosting metallic boundary states out of a non-topological system, giving birth to the topological Anderson insulator phase. In this context, we theoretically investigate the generation of an out of equilibrium higher-order topological Anderson phase in the presence of disorder potential in a time-periodic dynamical background. In particular, the time-dependent drive and the disorder potential concomitantly render the generation of Floquet higher-order topological Anderson insulator~(FHOTAI) phase, while the clean, undriven system is topologically trivial. We showcase the generation of FHOTAI hosting both $0$- and $\pi$-modes. Most importantly, we develop the real space topological invariant -- a winding number based on chiral symmetry to characterize the Floquet $0$- and $\pi$-modes distinctly. This chiral winding number serves the purpose of the indicator for the topological phase transition in the presence of drive as well as disorder and appropriately characterizes the FHOTAI.