Anticrossings of spin-split Landau levels in an InAs two-dimensional electron gas with spin-orbit coupling

We report tilted-field transport measurements in the quantum Hall regime in an $\mathrm{In}\mathrm{As}∕{\mathrm{In}}_{0.75}{\mathrm{Ga}}_{0.25}\mathrm{As}∕{\mathrm{In}}_{0.75}{\mathrm{Al}}_{0.25}\mathrm{As}$ quantum well. We observe anticrossings of spin-split Landau levels, which suggest a mixing of spin states at Landau level coincidence. We propose that the level repulsion is due to the presence of spin-orbit and of band-nonparabolicity terms which are relevant in narrow-gap systems. Furthermore, electron-electron interaction is significant in our structure, as demonstrated by the large values of the interaction-induced enhancement of the electronic $g$ factor.

Figure 1

(Color online) (a) Conduction band (left axis) and density profile (right axis) for the $\mathrm{In}\mathrm{As}∕{\mathrm{In}}_{0.75}{\mathrm{Ga}}_{0.25}\mathrm{As}$ quantum well determined from 1D a Poisson-Schrödinger simulation with a constant background doping $N_{dd}=2.9\times {10}^{16}{\mathrm{cm}}^{-3}$. (b) Experimental and theroretical low-magnetic-field dependences of the longitudinal resistance (black and red curves, respectively) at $T=1.4\mathrm{K}$.

Figure 2

(Color online) Longitudinal resistance as a function of the perpendicular magnetic field for different tilt angles measured at $T=30\mathrm{mK}$. Curves have been shifted proportionally to $1∕\cos \left(\theta \right)$ for clarity. Vertical thin dotted lines indicate constant integer filling factors. Crossing at $\nu =6$ and anticrossings at $\nu =3$ and 5 are enlightened by the green and red lines to guide the eye, respectively. Upper inset: schematic diagram of the spin-split Landau levels vs $1∕\cos \left(\theta \right)$ (i.e., vs $E_z$ for fixed perpendicular magnetic field). Lower inset: sketch of the tilt-angle geometry.

Figure 3

(Color online) Perpendicular magnetic field position of the longitudinal resistance peaks as a function of the inverse cosine of the tilt angle at gate voltages (a) $V_g=0\mathrm{V}$ $(n_s=2.73\times {10}^{11}{\mathrm{cm}}^{-2})$ and (b) $V_g=0.5\mathrm{V}$ $(n_s=3.65\times {10}^{11}{\mathrm{cm}}^{-2})$. Thin red lines to guide the eye have been added to emphasize the anticrossings. The crossings and anticrossings have been labeled with the corresponding value of $r$.