Inversion-Asymmetry Splitting of the Conduction Band in GaSb from Shubnikov-de Haas Measurements

A detailed experimental investigation has been carried out on the beating patterns seen in the Shubnikov-de Haas (SdH) oscillations in Te-doped $n$-GaSb. Samples with Hall coefficients $R_{4.2°\mathrm{K}}=-5.5\mathrm{}$ ${\mathrm{cm}}^3$/C to $R_{4.2°\mathrm{K}}=-3.2\mathrm{}$ ${\mathrm{cm}}^3$/C were studied. Typical behavior is seen in a sample with $R_{4.2°\mathrm{K}}=-3.2\mathrm{}$ ${\mathrm{cm}}^3$/C, where nodes or minima in the oscillatory amplitude occur at ∼11 kG and ∼4.8 kG for $\mathrm{B}\parallel 〈111〉$, and at ∼6.5 kG for $\mathrm{B}\parallel 〈001〉$; no minima are observed for $\mathrm{B}\parallel 〈110〉$. The low-field results are in contrast to high-field behavior in which only approximately exponential field dependence of the oscillatory amplitude is obtained. These patterns are similar to those observed by Whitsett in the SdH effect in $n$-HgSe. We analyze the results in GaSb initially in terms of a classical model of two Fermi surfaces split by inversion asymmetry. This model qualitatively predicts some features of the data, including the concentration dependence of the highest-field nodal point seen with $\mathrm{B}\parallel 〈111〉$. Finally, we compare the data with predictions of a nonclassical model involving interaction between electron spin and external magnetic fields. The nonclassical model correctly predicts the nodal positions in GaSb, using a value of the splitting parameter $C_2=0.05\mathrm{}$, where $C_2{E}_F$ is the maximum energy splitting at the Fermi surface. For a sample $R_{4.2°\mathrm{K}}=-3.2\mathrm{}$ ${\mathrm{cm}}^3$/C ($E_F\simeq 0.096$ eV), the maximum splitting is 0.005 eV. The analysis further yields a value for the higher-band matrix element sum $B^{\prime }$ (Kane's $B$) $\approx \frac{9.6{\hslash }^2}{2m_0}$.