Extrinsic topology of Floquet anomalous boundary states in quantum walks

TL;DR

This paper explores how Floquet anomalous boundary states in quantum walks exhibit extrinsic topological properties, revealing new insights into boundary phenomena beyond bulk topological invariants.

Contribution

It uncovers the extrinsic topological nature of Floquet boundary states in quantum walks, even in first-order phases, and provides a topological classification and concrete examples.

Findings

Floquet boundary states have extrinsic topological origins.

Extrinsic topology is present even in first-order topological phases.

A topological table for extrinsic topology in quantum walks is established.

Abstract

Bulk-boundary correspondence is a fundamental principle for topological phases where bulk topology determines gapless boundary states. On the other hand, it has been known that corner or hinge modes in higher order topological insulators may appear due to "extrinsic" topology of the boundaries even when the bulk topological numbers are trivial. In this paper, we find that Floquet anomalous boundary states in quantum walks have similar extrinsic topological natures. In contrast to higher order topological insulators, the extrinsic topology in quantum walks is manifest even for first-order topological phases. We present the topological table for extrinsic topology in quantum walks and illustrate extrinsic natures of Floquet anomalous boundary states in concrete examples.