# Scaling of the Quantum Anomalous Hall Effect as an Indicator of Axion Electrodynamics

## TL;DR

This study investigates how the quantum anomalous Hall effect scales with sample thickness in V-doped topological insulators, revealing a dimensional crossover that links quantum Hall physics with axion electrodynamics.

## Contribution

It demonstrates a transition from 2D to 3D scaling behavior in the quantum anomalous Hall effect, highlighting the role of topological surface states and axion electrodynamics.

## Key findings

- Observation of 2D integer quantum Hall scaling in thin layers
- Detection of 3D surface state behavior with fractional Hall conductance
- Link between quantum Hall physics and axion electrodynamics

## Abstract

We report on the scaling behavior of V-doped (Bi,Sb)$_2$Te$_3$ samples in the quantum anomalous Hall regime for samples of various thickness. While previous quantum anomalous Hall measurements showed the same scaling as expected from a two-dimensional integer quantum Hall state, we observe a dimensional crossover to three spatial dimensions as a function of layer thickness. In the limit of a sufficiently thick layer, we find scaling behavior matching the flow diagram of two parallel conducting topological surface states of a three-dimensional topological insulator each featuring a fractional shift of $\frac{1}{2} e^2/h$ in the flow diagram Hall conductivity, while we recover the expected integer quantum Hall behavior for thinner layers. This constitutes the observation of a distinct type of quantum anomalous Hall effect, resulting from $\frac{1}{2} e^2/h$ Hall conductance quantization of three-dimensional topological insulator surface states, in an experiment which does not require decomposition of signal to separate the contribution of two surfaces. This provides a possible experimental link between quantum Hall physics and axion electrodynamics.