Warped Fermi Surface in GaSb from Shubnikov-de Haas Measurements

The frequencies of Shubnikov-de Haas oscillations in $n$-type tellurium-doped GaSb have been obtained as a function of magnetic field direction in samples with electron concentrations $n\approx {10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Field-modulation and phase-sensitive detection techniques were employed in the measurements. A frequency anisotropy of ∼1% has been unambiguously determined. These results are explained by the warping contribution to the $k=0\mathrm{}$ conduction-band energy expression derived by Kane using k·p perturbation theory. By fitting the frequency anisotropy to the theoretical prediction, it is found that the warping parameter $L-M-N=(11\mathrm{}\pm 2)\frac{{\hslash }^2}{2m_0}$. A small (∼2%) effective-mass anisotropy has been observed; the symmetry of the result is predicted from the warping model, i.e., $m^{*}\mathrm{}\left(111\right)>m^{*}\mathrm{}\left(110\right)>m^{*}\mathrm{}\left(100\right)\mathrm{}$.