Noise probing of topological band gaps in dispersionless quantum states

TL;DR

This paper establishes a theoretical link between current noise and topological band gaps in dispersionless quantum states, proposing a new experimental method to measure these gaps in flat band materials like moiré systems.

Contribution

It introduces a novel relationship connecting integrated current noise to the topological band gap and Chern number, enabling experimental probing of topological properties in flat band systems.

Findings

Derived a formula linking noise integral to topological gap and Chern number

Proposed noise measurement as a practical tool for gap detection in moiré materials

Applicable to challenging meV-scale gap measurements in flat band systems

Abstract

We uncover a useful connection between the integrated current noise $S(\omega)$ and the topological band gap in dispersionless quantum states, $\int d \omega [ \mathcal S^{\text{flat}}_{xx} + \mathcal S^{\text{flat}}_{yy} ] = C e^2 \Delta^2$ (in units $\hbar$$=$$1$), where $C$ is the Chern number, $e$ is electric charge, and $\Delta$ is the topological band gap. This relationship may serve as a working principle for a new experimental probe of topological band gaps in flat band materials. Possible applications include moir\'e systems, such as twisted bilayer graphene and twisted transition metal dichalcogenides, where a band gap measurement in meV regime presents an experimental challenge.