Demonstration of gate control of spin splitting in a high-mobility InAs/AlSb two-dimensional electron gas

Control of zero-field spin splitting is realized in a dual-gated high-quality InAs-AlSb two-dimensional electron gas. Magnetotransport experiments showed clean Shubnikov–de Haas oscillations down to low magnetic fields, and the gate-tuned electron mobility exceeded $700000\mathrm{c}{\mathrm{m}}^2/\mathrm{V}\mathrm{s}$. A clear beating effect was observed in magnetoresistance oscillations at large potential asymmetry between gates. Beat patterns due to zero-field spin splitting and other classes of transverse magnetoresistance oscillations were distinguished by temperature-dependent magnetoresistance measurements. Analysis of the magnetoresistance oscillations indicated that the zero-field spin splitting could be tuned via the Rashba effect while keeping the two-dimensional electron gas charge density constant.

Figure 1

(a) A schematic of the InAs quantum well heterostructure with $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ gate dielectric and Ti/Au front gate. (b) A $5\times 5\mu {\mathrm{m}}^2$ atomic force microscope image of the heterostructure taken at the surface of the GaSb capping layer. (c) An optical micrograph of the Hall bar used in this study. The scale bar at the lower right represents 20 μm. (d) A self-consistent calculation of the conduction band profile and carrier density distribution in the vicinity of the InAs quantum well when $V_{\mathrm{fg}}=1\mathrm{V}$ and $V_{\mathrm{bg}}=0\mathrm{V}$ (blue lines), and when $V_{\mathrm{fg}}=1.6\mathrm{V}$ and $V_{\mathrm{bg}}=-1\mathrm{V}$ (black lines). See text for details of the calculation.

Figure 2

(a) Magnetoresistivity at $V_{\mathrm{fg}}=0$, 0.4, 0.8, 1.2, and 1.6 V while $V_{\mathrm{bg}}=0\mathrm{V}$ (upper plot), and at $V_{\mathrm{bg}}=-0.2$, −0.4, −0.6, −0.8 and −1 V while $V_{\mathrm{fg}}=1\mathrm{V}$ (lower plot). (b) Fourier amplitude versus magnetoresistance oscillation frequency determined from a Fourier analysis of the corresponding magnetoresistance in (a) as a function of inverse magnetic field. The data in (a) and (b) are offset for clarity. (c) Hall resistance at $V_{\mathrm{fg}}=0$, 0.4, 0.8, 1.2, and 1.6 V while $V_{\mathrm{bg}}=0\mathrm{V}$. (d) Hall resistance at $V_{\mathrm{bg}}=-0.2$, −0.4, −0.6, −0.8, and −1 V while $V_{\mathrm{fg}}=1\mathrm{V}$. Measurements were performed at a sample temperature of 2 K.

Figure 3

(a) The dependence of mobility on carrier density at a sample temperature of 2 K and at constant back gate voltages $V_{\mathrm{bg}}=-1$, 0, and +1 V. The carrier density was varied using the front gate, where in each case an increase in the front gate voltage corresponds to an increase in carrier density. (b) Dingle analysis of the SdH oscillations at a sample temperature of 2 K and at four carrier densities near zero gate bias. The carrier density was modulated using the back gate. Linear fits are shown as dotted lines. (c) The dependence of quantum lifetime on carrier density determined from the data in (b).

Figure 4

(a) Magnetoresistivity at sample temperatures 2, 5, and 10 K for $V_{\mathrm{fg}}=1.0\mathrm{V}$ (upper plot) and 2.0 V (lower plot). (b) Fourier amplitude versus magnetoresistance oscillation frequency determined from a Fourier analysis of the corresponding magnetoresistance in (a) as a function of inverse magnetic field. The data in (a) and (b) are offset for clarity. (c) The temperature dependence of the Fourier amplitudes denoted by $\mathrm{SdH}{n}_{+},\mathrm{SdH}{n}_{-}$, 1, 2, and 3 in the Fourier analysis shown in (b) for the front gate voltage $V_{\mathrm{fg}}=2\mathrm{V}$. The solid line depicts the theoretical temperature dependence of SdH Fourier amplitudes, $\sim \left(2{\pi }^2{k}_{\mathrm{B}}T/\hslash {\omega }_{\mathrm{c}}\right)/\sinh \left(2{\pi }^2{k}_{\mathrm{B}}T/\hslash {\omega }_{\mathrm{c}}\right)$.

Figure 5

Experimentally determined Rashba spin-orbit coupling parameter versus carrier density. The data are grouped by common fixed front gate voltage. For a given front gate voltage the back gate voltage was varied from 0 to −1.0 V in 0.2 V increments.