Material and size dependent corrections to conductance quantization in anomalous Hall effect from anomaly inflow

TL;DR

This paper investigates how finite edge mode localization length affects conductance quantization in quantum anomalous Hall systems, revealing material-dependent corrections that limit measurement precision and are explained via anomaly inflow theory.

Contribution

It introduces a correction to conductance quantization accounting for finite edge mode width using anomaly inflow, highlighting non-universal material-dependent effects.

Findings

Conductance quantum is corrected by a material-dependent factor due to finite edge localization.

Corrections depend on ratios involving bulk gap, Fermi velocity, and sample size.

Precision limits in quantized conductance measurements are linked to anomaly inflow physics.

Abstract

In quantum anomalous Hall (QAH) systems, the Hall conductance is quantized and the corresponding effective topological theory of the system is the Chern-Simons theory. The conductance quantum is given by the universal constant $e^2/h$ -- the inverse von Klitzing constant -- that is independent of the bulk gap, as well as the size of the system. This picture relies on the assumption that the edge modes are sharply localized at the edge, i.e. they have zero width. We show that considering the physical case where the edge modes have finite localization length $b$, the effective action would not be topological in bulk direction anymore. Due to non-zero $b$ the conductance quantum will be corrected as $(1-\varepsilon)e^2/h$ where $\varepsilon$ encompasses the non-universal (i.e. material/sample dependent) part that is determined by the dimensionless ratios $\frac{gb}{\hbar v_F}$ and $\frac{b}{L}$ where $g,v_F,L$ are the bulk gap, Fermi velocity and sample length. To compute the non-universal correction $\varepsilon$ we use anomaly inflow framework according to which the bulk action produces the correct amount of anomaly inflow that would cancel the anomaly of the chiral edge modes. These corrections place limits on the precision of measurable quantization in units of the inverse von Klitzing constant for QAH systems with smaller sizes and/or smaller bulk gaps. Our result suggests that the failure of precision measurements to reproduce the exact conductance quantum $e^2/h$ is not an annoying sample quality issue, but it contains the quantitative physics of anomaly inflow that can be inferred by the systematic study of such corrections.