Observation of Hybrid-Order Topological Pump in a Kekule-Textured Graphene Lattice

TL;DR

This paper demonstrates a hybrid-order topological pump in a Kekulé-textured graphene lattice, showing simultaneous transitions of bulk, edge, and corner states through acoustic experiments, expanding understanding of topological phases.

Contribution

It introduces the concept of a hybrid-order topological pump involving bulk, edge, and corner state transitions, verified through acoustic experiments in a Kekulé-textured graphene lattice.

Findings

Verified boundary landmarks using acoustic experiments

Demonstrated simultaneous bulk, edge, and corner state transitions

Broadened understanding of higher-order topological phases

Abstract

Thouless charge pumping protocol provides an effective route for realizing topological particle transport. To date, the first-order and higher-order topological pumps, exhibiting transitions of edge-bulk-edge and corner-bulk-corner states, respectively, are observed in a variety of experimental platforms. Here, we propose a concept of hybrid-order topological pump, which involves a transition of bulk, edge, and corner states simultaneously. More specifically, we consider a Kekul\'e-textured graphene lattice that features a tunable phase parameter. The finite sample of zigzag boundaries, where the corner configuration is abnormal and inaccessible by repeating unit cells, hosts topological responses at both the edges and corners. The former is protected by a nonzero winding number, while the latter can be explained by a nontrivial vector Chern number. Using our skillful acoustic experiments, we verify those nontrivial boundary landmarks and visualize the consequent hybrid-order topological pump process directly. This work deepens our understanding to higher-order topological phases and broadens the scope of topological pumps.