Density dependence of microwave induced magnetoresistance oscillations in a two-dimensional electron gas

We have measured the magnetoresistance of a two-dimensional electron gas (2DEG) under continuous microwave irradiation as a function of electron density and mobility tuned with a metallic top-gate. In the entire range of density and mobility we have investigated, we observe microwave induced oscillations of large amplitude that are $B$-periodic. These $B$-periodic oscillations are reminiscent of the ones reported by Kukushkin et al. [Phys. Rev. Lett. 92, 236803 (2004)] and which were attributed to the presence of edge-magneto-plasmons. We have found that the $B$-periodicity does not increase linearly with the density in our sample but shows a plateau in the range $\left(2.4\text{–}3\right)\times {10}^{11}{\mathrm{cm}}^{-2}$. In this regime, the phase of the $B$-periodic oscillations is found to shift continuously by two periods.

Figure 1

Magnetoresistance measured under continuous microwave irradiation for different powers is compared for three different illumination conditions. The microwave power $P$ lies in the range $\left(1\mu \mathrm{W}\text{–}1\mathrm{mW}\right)$. $N_s=5\times {10}^{11}{\mathrm{cm}}^{-2}$ and $\mu =7.50\times {10}^6{\mathrm{cm}}^2∕\mathrm{V}\mathrm{s}$ for (a) and (b) while $N_s=4\times {10}^{11}{\mathrm{cm}}^{-2}$ and $\mu =5.3\times {10}^6{\mathrm{cm}}^2∕\mathrm{V}\mathrm{s}$ for (c).

Figure 2

Experiment No. 1: illumination at $T_{\mathrm{Illu}}=2.2\mathrm{K}$. Magnetoresistance measured for three different densities versus the microwave power $P$ in the range $\left(1\mu \mathrm{W}\text{–}1\mathrm{mW}\right)$. The value of the $B$-field at which ${\omega }_c=\omega$ is marked with an arrow.

Figure 3

Experiment No. 3. (a) Position of the maxima vs oscillation index for various density ranging between 2.4 and $3.6\times {10}^{11}{\mathrm{cm}}^{-2}$. The period $\Delta B$ is deduced from a linear fit with a reliability factor fluctuating between 99.7% and 99.9%. Inset: magnetoresistance (continuous line) and photovoltage (dotted line) measured for $N_s=2.4\times {10}^{11}{\mathrm{cm}}^{-2}$. The current through the Hall bar is 200 nA and $P\sim 300\mu \mathrm{W}$. (b) Period of the photoresistance vs $N_s$. (c) Period of the photovoltage vs $N_s$.

Figure 4

Experiment No. 3. (a) Microwave-induced oscillations in the low field range measured for various $N_s$ ranging between 2.4 and $2.9\times {10}^{11}{\mathrm{cm}}^{-2}$. The curves are offset for clarity and correspond to a step upward in density of $0.1\times {10}^{11}{\mathrm{cm}}^{-2}$ from the lowest one. (b) shows the phase $\varphi$ of the $B$-periodic oscillations vs $N_s$. The phase was determined from the maxima denoted by 1 and 2 in (a) with respect to the $B$-field at which ${\omega }_c=\omega$, i.e., 0.09 T for $\omega =35.5\mathrm{GHz}$. The continuous line is a guide to the eyes. Inset: picture of the Hall-bar sample with its TiAu top-gate (circle). The distance between the voltage probes is $200\mu \mathrm{m}$.