Uncover band topology via quantized drift in two-dimensional Bloch oscillations

TL;DR

This paper introduces a method to measure band topology in 2D lattices by observing quantized displacements in Bloch oscillations, enabling detection of Chern numbers even in complex bands.

Contribution

It presents a novel approach to determine Chern numbers through quantized drift in Bloch oscillations, applicable to both energy-separable and inseparable bands.

Findings

Quantized displacement relates to a reduced Chern number.

Method works for energy-inseparable bands.

Enables detection of topological phase transitions.

Abstract

We propose to measure band topology via quantized drift of Bloch oscillations in a two-dimensional Harper-Hofstadter lattice subjected to tilted fields in both directions. When the difference between the two tilted fields is large, Bloch oscillations uniformly sample all momenta, and hence the displacement in each direction tends to be quantized at multiples of the overall period, regardless of any momentum of initial state. The quantized displacement is related to a reduced Chern number defined as a line integral of Berry curvature in each direction, providing an almost perfect measurement of Chern number. Our scheme can apply to detect Chern number and topological phase transitions not only for the energy-separable band, but also for energy-inseparable bands which cannot be achieved by conventional Thouless pumping or integer quantum Hall effect.