Beating-free quantum oscillations in two-dimensional electron gases with strong spin-orbit and Zeeman interactions

Abstract

Shubnikov-de Haas (SdH) oscillations are the fingerprint of the Landau and Zeeman splitting level structure on the resistivity in presence of a moderate magnetic field before full quantization is manifest in the integer quantum Hall effect. These oscillations have served as a paradigmatic experimental probe and tool for extracting key semiconductor parameters such as carrier density, effective mass m^{*}, Zeeman splitting with g factor g^{*}, quantum scattering time, and Rashba α and Dresselhaus β spin-orbit (SO) coupling parameters. Analytical descriptions of the SdH oscillations are available for some special cases, but no analytical solution could be found for the vast majority of parameter space with all three terms present, usually relevant for experiments. Despite over 50 years of experiments and many theoretical models, which were put forth, this has seriously hampered the analysis and interpretation of experimental data. Here, we bridge this gap by providing an analytical formulation for the SdH oscillations of 2D electron gases (2DEGs) with simultaneous Rashba, Dresselhaus, and Zeeman interactions over a very broad range of parameter space. We use a Poisson summation formula for the density of states of the 2DEG, which affords a complete yet simple description of the oscillatory behavior of its magnetoresistivity. Our analytical and numerical calculations allow us to extract the beating frequencies, quantum lifetimes, and also to understand the role of higher harmonics in the SdH oscillations. More importantly, we derive a simple condition for beating-free SdH oscillations for all harmonics in 2DEGs α/β=[(1−Δ[over ̃])/(1+Δ[over ̃])]^{1/2}, where Δ[over ̃]∝g^{*}m^{*} is a material parameter given by the ratio of the Zeeman and Landau level splitting. This condition is notably different from that of the persistent spin helix at α/β=1 for materials with large g^{*}m^{*} such as InAs or InSb. We also predict beatings in the higher harmonics of the SdH oscillations and elucidate the inequivalence of the SdH response of Rashba-dominated (α>β) vs Dresselhaus-dominated (α<β) 2DEGs in semiconductors with substantial g^{*}. We find excellent agreement with recent available experimental data of Dettwiler et al. [Phys. Rev. X 7, 031010 (2017)2160-330810.1103/PhysRevX.7.031010], and Beukman et al. [Phys. Rev. B 96, 241401(R) (2017)2469-995010.1103/PhysRevB.96.241401]. The formalism builds the foundation for a generation of quantum transport experiments in quantum materials with unprecedented physical insight and material parameter extraction.