Hole Fermi surface inBi2Se3probed 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) Bi2Se3 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• and 90• , 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.

Determination of the energy band gap of Bi2Se3

“…These magneto-transport experiments also implied (via damping of Shubnikov-de Haas oscillations with temperature) the effective mass of bulk conduction band electrons, m e  ≈ 0.12 m 0 , which agrees well with values from previous studies 20, 22, 24–26 . Combining this electron mass with the hole mass from our recent magneto-transport studies performed on p -type Bi 2 Se 3 21 , m h  ≈ 0.24 m 0 , we obtain the reduced mass of μ  ≈ 0.08 m 0 , in perfect agreement with the value read directly from the separation of interband inter-Landau level resonances observed in our recent magneto-optical study 11 .…”

“…In a degenerate n -type semiconductor with a direct band gap, this shift reads: , where E F is the Fermi energy and m e ( h ) stands for the electron (hole) effective mass. The anisotropy of effective masses enters this expression only, when the ratio m e / m h becomes strongly anisotropic, which does not seem to be the case of Bi 2 Se 3 20, 21 . This formula is valid only for systems with well-defined effective masses, and therefore strictly parabolic bands.…”

Ultrahigh magnetic field spectroscopy reveals the band structure of the three-dimensional topological insulator Bi2Se3

“…2 (a). The reduced mass is consistent with recent results obtained by Shubnikov de Haas (SdH) measurements for n-type and p-type samples of Bi 2 Se 3 ; the range of effective masses of the electrons and holes respectively is 0.12-0.16 m 0 and 0.23-0.25 m 0 in the literature, 13,21,22 corresponding to a value for the reduced mass, µ, in the range 0.079-0.098 m 0 . It is also possible to estimate the effective masses from the Fermi velocity v D and the electron-hole asymmetry term C using m e = 2h 2 /(h 2 v 2 D /∆ + 4C) and m h = 2h 2 /(h 2 v 2 D /∆ − 4C), giving m e = 0.138 m 0 and m h = 0.176 m 0 , respectively.…”

Interband absorption edge in the topological insulators Bi2(Te1−xSex)3

“…The M (or camel-back) structure seen in ARPES data might be due to surface states or due to a deeper lying structure in the valence bands 41 . The latter scenario is confirmed by recent Shubnikov-de Haas (SdH) measurements 37 concluding that the top of the valence band is a downward oriented paraboloid with no signatures of an M shape of the top of the valence band. Note that the M-structure of the valence band seen in some LDA bandstructure calculations 45 is absent in the more realistic results of GW calculations 44,46,47 that exhibit a paraboloidal shape of the valence band.…”

“…Similarly, the valence band was reported 37 to have parabolic shape for the Fermi wavevector corresponding to our sample (k F,a ≈ 0.04Å −1 ). In the following we compare the obtained value of E direct g with literature values for the band gap determined by optical spectroscopy and corrected for the BM shift.…”