Dynamical Fragile Topology in Floquet Crystals

TL;DR

This paper extends the concept of fragile topology to noninteracting Floquet crystals, defining dynamical fragile topology based on obstructions to static limits, and provides a concrete 2+1D example with anomalous edge modes.

Contribution

It introduces the notion of dynamical fragile topology for Floquet systems and demonstrates it with a specific 2+1D model exhibiting anomalous edge modes.

Findings

Dynamical fragile topology is characterized by obstructions to static limits in Floquet crystals.

A concrete 2+1D example exhibits anomalous chiral edge modes without crystalline symmetries.

Dynamical fragile topology can be removed by adding symmetry-preserving static Hamiltonians.

Abstract

Although fragile topology has been intensely studied in static crystals in terms of Wannier obstruction, it is not clear how to generalize the concept to dynamical systems. In this work, we generalize the concept of fragile topology, and provide a definition of fragile topology for noninteracting Floquet crystals, which we refer to as dynamical fragile topology. In contrast to the static fragile topology defined by Wannier obstruction, dynamical fragile topology is defined for the nontrivial quantum dynamics characterized by the obstruction to static limits (OTSL). Specifically, the OTSL of a Floquet crystal is fragile if and only if it disappears after adding a symmetry-preserving static Hamiltonian in a direct-sum way preserving the relevant gaps (RGs). We further present a concrete 2+1D example for dynamical fragile topology, based on a model that is qualitatively the same as the dynamical model with anomalous chiral edge modes in [Rudner et al., Phys. Rev. X 3, 031005 (2013)]. The fragile OTSL in the 2+1D example exhibits anomalous chiral edge modes for a natural open boundary condition, and does not require any crystalline symmetries besides lattice translations. Our work paves the way to study fragile topology for general quantum dynamics.