Effect of Spin-Orbit Coupling on Anomalous Quantum Oscillations in InAs/GaSb Quantum Wells

TL;DR

The paper investigates how spin-orbit coupling (SOC) influences anomalous quantum oscillations in InAs/GaSb quantum wells, using a four-band Bernevig–Hughes–Zhang framework with Rashba SOC and disorder treated via the self-consistent Born approximation. Landau quantization is implemented with the Knolle–Cooper method, and LEDOS serves as a proxy for dHvA/SdH signals. The key findings are that SOC suppresses anomalous oscillations in the clean limit by widening the bandgap, but in the presence of disorder SOC enhances these oscillations by redistributing in-gap spectral weight and can induce a π phase shift. A practical temperature–disorder window (roughly T<0.1Δ with 0.6Δ<Γ_h<0.9Δ) is identified where SOC-assisted anomalous oscillations are most pronounced, offering guidance for experimental observation and deeper understanding of SOC effects on anomalous quantum oscillations.

Abstract

We theoretically study the effect of spin-orbit coupling (SOC) on anomalous quantum oscillations in InAs/GaSb quantum wells. By comparing different cases, we show that SOC induces two opposing effects on anomalous quantum oscillations: it suppresses the oscillations in the clean case, while enhancing them in the disordered case. Using an effective model, we analyze in detail the origins of anomalous oscillations in both clean and disordered cases. Based on these origins, we explain why SOC suppresses or enhances the anomalous oscillations in different cases, thereby extending the understanding of the conventional theory. Moreover, in the disordered case, SOC can induce a phase shift of the anomalous oscillations. We further identify a parameter window where the anomalous oscillations are significantly enhanced in the presence of both disorder and SOC. These results provide a theoretical basis for understanding the role of SOC in anomalous quantum oscillations.

Figures (8)

• Figure 1: (Color online) Band structure of InAs/GaSb quantum wells with a direct bandgap $\Delta$. The black dashed curves represent the bands without SOC, and the red and blue solid curves correspond to the spin-split bands with SOC. (a) Clean case. Black arrows indicate the direction of SOC-induced band splitting. (b) Disordered case. The purple-shaded region schematically indicates the presence of disorder. The chemical potential $\mu$ is denoted by the horizontal black dashed line.
• Figure 2: (Color online) LL spectra and LEDOS in the absence of SOC. (a,b) Clean case ($\beta = 5$ meV$\cdot$nm) at temperature $T = 0.3\Delta$. (c,d) Clean (gray dash-dotted curves) and Disordered (blue solid curves) cases at $\beta = 20$ meV$\cdot$nm, calculated at an extremely low temperature $T = 0.003\Delta$ to emphasize disorder effects. The red dashed line marks the critical magnetic field $B_c$ separating the metallic and insulating regimes. The insets in (b) and (d) highlight the emergence of anomalous quantum oscillations in the insulating regime.
• Figure 3: (Color online) LL spectra and LEDOS in the presence of SOC. (a,b) Clean case with $\beta=5$: SOC ($\alpha=4$ meV$\cdot$nm) induces bandgap expansion, suppressing the anomalous LEDOS oscillations. (c,d) Disordered case with $\beta=20$: SOC ($\alpha=16$ meV$\cdot$nm) enlarges the bandgap, while enhancing anomalous LEDOS oscillations compared to the case without SOC. Red arrows indicate the direction of bandgap widening. The inset highlights the anomalous quantum oscillations in the insulating regime.
• Figure 4: (Color online) Spectral functions of the disordered case with $\Gamma_h = 0.8 \Delta$ in the absence of a magnetic field. (a) Without SOC ($\alpha=0$) and (c) with SOC ($\alpha=16$ meV$\cdot$nm), showing the overall spectral features. (b,d) Enlarged views of the white dashed rectangles in (a) and (c), respectively, display detailed gap structures.
• Figure 5: (Color online) Spectral functions with $\Gamma_h = 0.8 \Delta$ in the presence of magnetic field: (a) without SOC and (b) with SOC. The blue dashed curves indicate Landau levels; the white dashed contours outline the high-density regions.