Quantum oscillation in narrow-gap topological insulators

TL;DR

This paper explains quantum oscillations observed in narrow-gap topological insulators like SmB6 by showing that magnetic fields cause hybridization gap oscillations, revealing nontrivial band topology through Berry phase changes.

Contribution

It introduces a two-band model demonstrating how magnetic fields induce bulk density of states oscillations in narrow-gap topological insulators, linking them to nontrivial band topology.

Findings

Oscillations arise from periodically narrowing hybridization gaps in magnetic fields.

The temperature dependence deviates from Lifshitz-Kosevich theory.

Berry phase transitions from nonzero to trivial with temperature or field increase.

Abstract

The canonical understanding of quantum oscillation in metals is challenged by the observation of de Haas-van Alphen effect in an insulator, SmB$_{6}$ [Tan \emph{et al}, Science {\bf349}, 287 (2015)]. Based on a two-band model with inverted band structure, we show that the periodically narrowing hybridization gap in magnetic fields can induce the oscillation of low-energy density of states in the bulk, which is observable provided that the hybridization gap is narrow and comparable to the Landau level spacing. Its temperature dependence strongly deviates from the Lifshitz-Kosevich theory. The nontrivial band topology manifests itself as a nonzero Berry phase in the oscillation pattern, which crosses over to a trivial Berry phase by increasing the temperature or the magnetic field. Further predictions to experiments are also proposed.