The 6D quantum Hall effect and 3D topological pumps

TL;DR

This paper derives the bulk response of a six-dimensional Chern insulator, revealing a quantized response linked to the 3rd Chern number, and proposes realization via 3D topological charge pumps in cold atoms.

Contribution

It provides the first derivation of the 6D quantum Hall effect from first principles and connects it to lower-dimensional responses and experimental realizations.

Findings

Quantized bulk response from 6D topological index (3rd Chern number)

Description of lower even-dimensional Chern-like responses

Proposal for experimental realization using 3D topological charge pumps

Abstract

Modern technological advances allow for the study of systems with additional synthetic dimensions. Using such approaches, higher-dimensional physics that was previously deemed to be of purely theoretical interest has now become an active field of research. In this work, we derive from first principles using a semiclassical equation of motions approach, the bulk response of a six-dimensional Chern insulator. We find that in such a system a quantized bulk response appears with a quantization originating from a six-dimensional topological index -- the 3rd Chern number. Alongside this novel six-dimensional response, we rigorously describe the lower even-dimensional Chern-like responses that can occur due to nonvanishing 1st and 2nd Chern numbers in sub-spaces of the six-dimensional space. Last, we propose how to realize such a bulk response using three-dimensional topological charge pumps in cold atomic systems.