Non-Abelian Bloch oscillations in higher-order topological insulators

TL;DR

This paper reveals a novel topological effect in Bloch oscillations of higher-order topological insulators, linking non-Abelian Berry curvature with quantized Wilson loops, and suggests experimental detection methods.

Contribution

It uncovers a unique non-Abelian topological phenomenon in BOs of higher-order topological insulators, highlighting the role of Wannier centers and proposing experimental detection strategies.

Findings

Oscillating Hall drift synchronized with inter-band beating

Multiplied Bloch period observed in BOs

Topologically-protected quantum dynamics of Wannier centers

Abstract

Bloch oscillations (BOs) are a fundamental phenomenon by which a wave packet undergoes a periodic motion in a lattice when subjected to an external force. Observed in a wide range of synthetic lattice systems, BOs are intrinsically related to the geometric and topological properties of the underlying band structure. This has established BOs as a prominent tool for the detection of Berry phase effects, including those described by non-Abelian gauge fields. In this work, we unveil a unique topological effect that manifests in the BOs of higher-order topological insulators through the interplay of non-Abelian Berry curvature and quantized Wilson loops. It is characterized by an oscillating Hall drift that is synchronized with a topologically-protected inter-band beating and a multiplied Bloch period. We elucidate that the origin of this synchronization mechanism relies on the periodic quantum dynamics of Wannier centers. Our work paves the way to the experimental detection of non-Abelian topological properties in synthetic matter through the measurement of Berry phases and center-of-mass displacements.