Signature of non-trivial band topology in Shubnikov--de Haas oscillations

TL;DR

This paper demonstrates that non-trivial topological properties in 2D topological insulators produce unique beating patterns in Shubnikov-de Haas oscillations, enabling bulk measurement-based detection of topological phases.

Contribution

The authors derive analytical expressions linking SdH oscillations to topological features, revealing a robust, topology-specific beating pattern in magneto-oscillations.

Findings

Non-trivial topology causes anomalous beating in SdH oscillations.

Beatings are distinct from those caused by spin-orbit interactions.

Fourier analysis of oscillations can extract topological gap information.

Abstract

We investigate the Shubnikov-de Haas (SdH) magneto-oscillations in the resistivity of two-dimensional topological insulators (TIs). Within the Bernevig-Hughes-Zhang (BHZ) model for TIs in the presence of a quantizing magnetic field, we obtain analytical expressions for the SdH oscillations by combining a semiclassical approach for the resistivity and a trace formula for the density of states. We show that when the non-trivial topology is produced by inverted bands with ''Mexican-hat'' shape, SdH oscillations show an anomalous beating pattern that is {\it solely} due to the non-trivial topology of the system. These beatings are robust against, and distinct from beatings originating from spin-orbit interactions. This provides a direct way to experimentally probe the non-trivial topology of 2D TIs entirely from a bulk measurement. Furthermore, the Fourier transform of the SdH oscillations as a function of the Fermi energy and quantum capacitance models allows for extracting both the topological gap and gap at zero momentum.