Effect of dc and ac excitations on the longitudinal resistance of a two-dimensional electron gas in highly doped GaAs quantum wells

Linear ac $\left(888\mathrm{Hz}\right)$ resistance of highly mobile two-dimensional electrons in GaAs heavily doped quantum wells is studied at different magnitudes of dc and ac $\left(10\mathrm{KHz}\text{to}20\mathrm{GHz}\right)$ excitations. In the dc excitation regime the differential resistance oscillates with the dc current and external magnetic field similar to that observed earlier in $\mathrm{Al}\mathrm{Ga}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ heterostructures [C. L. Yang et al., Phys. Rev. Lett. 89, 076801 (2002)]. At external ac excitations the resistance is also found to be oscillating with the magnetic field. However the form of the oscillations is considerably different from the dc case. We show that at frequency below $100\mathrm{KHz}$ the difference is the result of a specific average of the dc differential resistance during the period of the external ac excitations.

Figure 1

Dependence of differential resistance $r_{xx}$ on magnetic field at different dc current from $0\text{to}0.4\mathrm{mA}$ in steps of $0.05\mathrm{mA}$. For clarity, the curves are shifted vertically by $n\times 8\text{Ohm}$, where $n=0,1,\dots ,8$. The experimental setup is shown on the top. Sample No. 1 before light illumination.

Figure 2

(a) Dependence of the derivative $d{r}_{xx}∕dB$ on magnetic field at $I_{\mathrm{dc}}=0.4\mathrm{mA}$. The inset demonstrates the $1∕B$ periodicity extracted from the $d{r}_{xx}∕dB$ trace. (b) Positions of oscillation maximums $B_l$ $(l=1,2,3)$ versus dc current density $J_{\mathrm{dc}}$. A linear fit reveals the relation $B_l\sim J_{\mathrm{dc}}∕l$. Sample No. 1 before light illumination.

Figure 3

(a) Magnetoresistance $R_{xx}$ at different amplitudes of ac excitation. Maximums of the resistance oscillations are marked by arrows. Positions of the maximums are approximately periodic in $1∕B$. A diagram for the electrical measurement is presented at the bottom of the figure. (b) The oscillation maximums $B_N$ $(N=1,2,3)$ versus current density $J_F$. Linear fit reveals the relation $B_N\sim J_F∕N$. Sample No. 1 before light illumination.

Figure 4

(a) Magnetoresistance $R_{xx}$ at different levels of microwave power as labeled. (b) Dependence of the longitudinal resistance on inverse magnetic field $1∕B$ at microwave excitation $P=0\mathrm{dBm}$. Insert demonstrates the $1∕B$ periodicity of the oscillations. (c) Position of the oscillation maximums vs square root of input microwave power. (b) and (c) are obtained with the same conditions as (a). Sample No. 1 after light illumination.

Figure 5

(a) Dependence of differential resistance $r_{xx}$ on dc bias at different magnetic field $B$ as labeled. (b) Measured magnetoresistance $R_{xx}$ at two different levels of ac excitations as labeled (solid lines). Calculated magnetoresistance obtained from the dc biased measurements in (a) (open dots). The procedure is described in text. No adjusting parameters are used for the comparison. Sample No. 1 before light illumination.