Weak antilocalization in gate-controlled ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ two-dimensional electron gases

Weak antilocalization and the Shubnikov–de Haas effect were investigated in ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ two-dimensional electron gases. The weak antilocalization measurements on a gated sample revealed a constant spin-orbit scattering length, which does not change if the Al content or the thickness of the ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ barrier layer is varied. The occurrence of spin-orbit coupling is assigned to the lack of crystal inversion symmetry. Although for some of the samples a beating pattern was observed in the Shubnikov–de Haas oscillations, its presence was not attributed to spin-orbit coupling but rather to inhomogeneities in the ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ barrier.

Figure 1

(Color online) (a) Magnetoresistance $R_{xx}$ of sample 1 for different gate voltages in the range from $0\text{to}-2.5\mathrm{V}$ at $1.0\mathrm{K}$. The node positions are indicated by circles. For $V_G=0$ and $-2.5\mathrm{V}$ the filling factors $\nu$ are given. (b) Amplitude of the corresponding $1∕B$ fast Fourier transform of the magnetoresistance in arbitrary units as a function of the oscillation frequency $B_f$ in units of T. The corresponding electron concentration $n$ is given by the upper scale.

Figure 2

(Color online) Experimental values (●) of the quantum correction to the conductivity $\sigma \left(B\right)-\sigma \left(0\right)$ in units of $e^2∕2\pi h$ vs $B$ of sample 1 at $T=1\mathrm{K}$. The gate voltage $V_G$ was varied from $0\text{to}-2.5$ V in steps of $0.25\mathrm{V}$. The curves are offset by 0.2 $e^2∕2\pi h$ for clarity. Full lines show the fit to the experimental data using the ILP model (Ref. 25).

Figure 3

(Color online) (a) Phase coherence length $l_{\varphi }$ and phase coherence time ${\tau }_{\varphi }$ vs electron concentration $n$. (b) Spin-relaxation length $l_{\mathit{so}}$ and spin-relaxation time ${\tau }_{\mathit{so}}$ vs $n$. The corresponding effective spin-orbit coupling parameter ${\alpha }^{*}$ is shown in (c).

Figure 4

(Color online) (a) Experimental values (●) of $\sigma \left(B\right)-\sigma \left(0\right)$ in units of $e^2∕2\pi h$ vs $B$ of sample 1 at $V_G=0$. From the top to the bottom, the curves correspond to $T=4.8,3.7,3.1,2.6,2.0,1.4,0.5\mathrm{K}$. Full lines (green) show the fit to the experimental data using the ILP model (Ref. 25). (b) Inverse phase coherence time $1∕{\tau }_{\varphi }$ as a function of temperature at $V_G=0$. The gray line shows the corresponding linear fit.

Figure 5

(Color online) (a) Shubnikov–de Haas oscillations of samples 2 and 3. The filling factors $\nu$ are given for higher magnetic fields. Because of the beating pattern, $\nu$ has to be assigned to the maxima of the oscillations for sample 2. (b) Sample 2: Experimental values (●) of $\sigma \left(B\right)-\sigma \left(0\right)$ in units of $e^2∕2\pi h$ vs $B$ and fit to the ILP model (full line). (c) Corresponding data for sample 3.