Giant Spin-Orbit Splitting in Inverted $\mathrm{InAs}/\mathrm{GaSb}$ Double Quantum Wells

Transport measurements in inverted $\mathrm{InAs}/\mathrm{GaSb}$ quantum wells reveal a giant spin-orbit splitting of the energy bands close to the hybridization gap. The splitting results from the interplay of electron-hole mixing and spin-orbit coupling, and can exceed the hybridization gap. We experimentally investigate the band splitting as a function of top gate voltage for both electronlike and holelike states. Unlike conventional, noninverted two-dimensional electron gases, the Fermi energy in $\mathrm{InAs}/\mathrm{GaSb}$ can cross a single spin-resolved band, resulting in full spin-orbit polarization. In the fully polarized regime we observe exotic transport phenomena such as quantum Hall plateaus evolving in $e^2/h$ steps and a nontrivial Berry phase.

Figure 1

(a) Expected electron and hole densities dependence on $V_{\mathrm{TG}}$. (b) Numerical band structure calculation for $V_{\mathrm{TG}}=-0.4\mathrm{V}$. The color indicates the wave function main character, solid and dotted lines distinguish two spin-orbit split subbands. (c) Fermi contours and spin texture of electronlike states for the Fermi energies II and III indicated in (b). The axis divisions are $0.2{\mathrm{nm}}^{-1}$, with the black dot indicating the origin. Fermi pockets at large $k$ vector are ignored, but discussed further in the Supplemental Material [23].

Figure 2

(a) Longitudinal resistivity ${\rho }_{xx}$ as a function of top gate voltage for $B_{\perp }=0$, with the position of the charge neutrality point indicated. (b) Transverse resistivity ${\rho }_{xy}$ as a function of $B_{\perp }$ for different values of $V_{\mathrm{TG}}$, as also indicated by the markers in (a) and (c). (c) ${\rho }_{xx}$ as a function of $V_{\mathrm{TG}}$ and $B_{\perp }$, with positive (negative) numbering indicating electronlike (holelike) LLs. Pink dots denote holelike filling factors and are used to extract the hole density shown in Fig. 3.

Figure 3

(a) Longitudinal resistivity ${\rho }_{xx}$ as in Fig. 2 for $V_{\mathrm{TG}}\ge -0.5\mathrm{V}$ as a function of $1/B_{\perp }$. The arrows indicate a beating in the SdH oscillations, visible as a $\pi$ phase shift. (b) Normalized power spectrum of ${\rho }_{xx}(1/B_{\perp })$ for various gate voltages (data offset for clarity). The frequency axis has been multiplied by $e/h$ to directly show the subband densities. (c) Color map of the power spectrum as in (b) as a function of $V_{\mathrm{TG}}$. The amplitude of the power spectrum has been normalized, column by column, to the $n_1$ peak. The solid blue line indicates the density obtained from the Hall slope, the dashed line marks the $n_1$ peak, and the dotted line gives the difference between the two. Dots indicate the hole density obtained from holelike LLs in Fig. 2, with the dash-dotted line being a guide to the eye.

Figure 4

(a) Spin-orbit polarization of electronlike states as a function of $V_{\mathrm{TG}}$, with markers defined as in (b). (b) Inverse transverse resistivity ${\rho }_{xy}^{-1}$ for different top gate voltages $V_{\mathrm{TG}}$. Inset: Inverse magnetic field positions of the filling factors $\nu$ for different $V_{\mathrm{TG}}$ values. Solid lines are linear fits to the data. (c) Phase offset $\gamma$ of the data in the inset of (b) extrapolated for $1/B\to 0$.