The hole Fermi surface in Bi${}_2$Se${}_3$ probed by quantum oscillations

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.

A supplemental material file giving a more detailed description of our work is available upon request