The hole Fermi surface in Bi$_{2}$Se$_{3}$ probed by quantum oscillations

TL;DR

This study uses quantum oscillations to map the bulk hole Fermi surface in p-type Bi$_{2}$Se$_{3}$, revealing a bag-shaped surface without camel-back features, consistent with theoretical predictions.

Contribution

It provides the first detailed characterization of the bulk hole Fermi surface in p-type Bi$_{2}$Se$_{3}$ using quantum oscillation techniques.

Findings

Identified a bag-shaped hole Fermi surface at low carrier density.

No evidence of a camel-back structure in the valence band.

Fermi surface remains consistent across tilt angles, indicating a single extremal cross-section.

Abstract

Transport and torque magnetometry measurements are performed at high magnetic fields and low temperatures in a series of p-type (Ca-doped) Bi$_{2}$Se$_{3}$ crystals. The angular dependence of the Shubnikov-de Haas and de Haas-van Alphen quantum oscillations enables us to determine the Fermi surface of the bulk valence band states as a function of the carrier density. At low density, the angular dependence exhibits a downturn in the oscillations frequency between $0^\circ$ and $90^\circ$, reflecting a bag-shaped hole Fermi surface. The detection of a single frequency for all tilt angles rules out the existence of a Fermi surface with different extremal cross-sections down to $24$~meV. There is therefore no signature of a camel-back in the valence band of our bulk samples, in accordance with the direct band gap predicted by $GW$ calculations.