Magnetotransport in high-$g$-factor low-density two-dimensional electron systems confined in ${\text{In}}_{0.75}{\text{Ga}}_{0.25}\text{As}∕{\text{In}}_{0.75}{\text{Al}}_{0.25}\text{As}$ quantum wells

We report magnetotransport measurements on high-mobility two-dimensional electron systems (2DESs) confined in ${\text{In}}_{0.75}{\text{Ga}}_{0.25}\text{As}∕{\text{In}}_{0.75}{\text{Al}}_{0.25}\text{As}$ single quantum wells. Several quantum Hall states are observed in a wide range of temperatures and electron densities, the latter controlled by a gate voltage down to values of $1\times {10}^{11}{\text{cm}}^{-2}$. A tilted-field configuration is used to induce Landau level crossings and magnetic transitions between quantum Hall states with different spin polarizations. A large filling factor dependent effective electronic $g$-factor is determined by the coincidence method and cyclotron resonance measurements. From these measurements the change in exchange-correlation energy at the magnetic transition is deduced. These results demonstrate the impact of many-body effects in tilted-field magnetotransport of high-mobility 2DESs confined in ${\text{In}}_{0.75}{\text{Ga}}_{0.25}\text{As}∕{\text{In}}_{0.75}{\text{Al}}_{0.25}\text{As}$ quantum wells. The large tunability of electron density and effective $g$-factor, in addition, make this material system a promising candidate for the observation of a large variety of spin-related phenomena.

Figure 1

Longitudinal resistance $R_{xx}$ (solid curve, vertical left axis) and resistance change $d{R}_{xx}$ (dotted curve) after far-infrared radiation at $2.542\text{THz}$ as a function of magnetic field at $T=4.2\mathrm{K}$. The inset shows the conduction-band diagram of the heterostructure and charge distribution obtained from 1D Poisson-Schrödinger simulation assuming a uniform distribution of deep donor states in the barriers.

Figure 2

(a) Longitudinal resistance $R_{xx}$ vs magnetic field $B$ as a function of temperature. Data correspond to sample with electron density $n_s=3.1\times {10}^{11}{\text{cm}}^{-2}$ and mobility $\mu =2.1\times {10}^5{\text{cm}}^2∕\mathrm{V}\mathrm{s}$. (b) $R_{xx}$ vs magnetic field for different values of the gate voltage $V_{\text{gate}}$ at $T=360\text{mK}$. (c) Gate voltage dependence of electron density (left vertical axis) and mobility (right vertical axis) for two different samples at $T=360\text{mK}$. The sketch of the sample with gate is shown in the upper part of the panel.

Figure 3

(a) Perpendicular magnetic field dependence of the longitudinal resistance for different tilt angles $\theta$. The latter were accurately obtained from the Hall voltage. The carrier density is $n_s=3.1\times {10}^{11}{\text{cm}}^{-2}$. The curves are shifted for clarity; the inset shows a sketch of the tilted-field geometry. (b) Perpendicular magnetic field position of the $R_{xx}$ peaks vs $1∕\cos \left(\theta \right)$. The thin lines are guides for the eye; the arrows indicate the angles ($\theta =79.68°$, $80.89°$, and $81.67°$) at which the first coincidence of Landau levels occurs at even-integer filling factors ($\nu =4,6$, and 8, respectively).

Figure 4

Perpendicular magnetic field position of the $R_{xx}$ peaks as a function of $1∕\cos \left(\theta \right)$ for a ${\text{In}}_{0.75}{\text{Ga}}_{0.25}\text{As}∕{\text{In}}_{0.75}{\text{Al}}_{0.25}\text{As}$ quantum well with a density of $n_s=3.7\times {10}^{11}{\text{cm}}^{-2}$ and a mobility of $\mu =7.5\times {10}^4{\text{cm}}^2∕\mathrm{V}\mathrm{s}$. The graphs (from left to right) have been obtained at three different gate voltages: $V_g=-0.5\mathrm{V}$ $\left(n_s=2.55\times {10}^{11}{\text{cm}}^{-2}\right)$, $0\mathrm{V}$, and $+0.5\mathrm{V}$ $\left(n_s=4.9\times {10}^{11}{\text{cm}}^{-2}\right)$, respectively. Here data are presented for filling factors $\nu =4$ (up triangles), 6 (squares), 8 (disks), 10 (diamonds), and 12 (down triangles). The thin lines are guides for the eye.

Figure 5

Enhanced electronic $g$-factor [defined as $2m_0\cos \left({\theta }_c\right)∕m^{*}$] as a function of perpendicular magnetic field for both samples presented in Fig. 3b (solid squares) and Fig. 4 (open symbols). The latter provides three sets of values obtained at different gate voltages: $V_g=-0.5\mathrm{V}$ (open circles), $V_g=0\mathrm{V}$ (open squares), and $V_g=+0.5\mathrm{V}$ (open triangles). The dashed line shows a linear dependence of $g^{*}$ vs $B_{\perp }$ with a zero field value equal to 5.5. Inset: energy difference, $\hslash {\omega }_c-g_0{\mu }_{B}B$ at coincidence, as a function of $B_{\perp }$.