Nonlinear magnetotransport in microwave-illuminated two-dimensional electron systems

We study magnetoresistivity oscillations in a high-mobility two-dimensional electron system subject to both microwave and dc electric fields. First, we observe that the oscillation amplitude is a periodic function of the inverse magnetic field and is strongly suppressed at microwave frequencies near half-integers of the cyclotron frequency. Second, we obtain complete conditions for the differential resistivity extrema and saddle points. These findings indicate the importance of scattering without microwave absorption and a special role played by microwave-induced scattering events antiparallel to the electric field.

Figure 1

(Color online) Microwave magnetoresistance $r$ under dc excitations, from $I=0\mu \mathrm{A}$ (black curve) to $I=22\mu \mathrm{A}$ [dark blue (dark gray) curve], in $2\mu \mathrm{A}$ increments. Integers show the order of the MIRO peaks. The arrows mark zero-response nodes that largely remain immune to dc excitation.

Figure 2

(Color online) (a) Differential resistance $r$ vs ${ϵ}_{\mathrm{dc}}$ at fixed ${ϵ}_{\mathrm{ac}}$ from 2 to 3.5 in steps of 0.05. Traces are vertically offset in increments of $0.4\Omega$. (b) Amplitude of the oscillations vs ${ϵ}_{\mathrm{ac}}$. (c) Position of the resistance maximum extracted from (a) near $({ϵ}_{\mathrm{ac}},{ϵ}_{\mathrm{dc}})=(3,1)$. Solid line corresponds to Eq. (1).

Figure 3

(Color online) (a)[(b)] Grayscale plot of differential resistivity $r$ in the $({ϵ}_{\mathrm{ac}},{ϵ}_{\mathrm{dc}})$ plane around $({ϵ}_{\mathrm{ac}},{ϵ}_{\mathrm{dc}})=(3,1)$ $[({ϵ}_{\mathrm{ac}},{ϵ}_{\mathrm{dc}})=(7∕2,1∕2)]$. Dashed lines correspond to integer values of ${ϵ}_{\mathrm{ac}}+{ϵ}_{\mathrm{dc}}$ (negative slope) and ${ϵ}_{\mathrm{ac}}-{ϵ}_{\mathrm{dc}}$ (positive slope). Vertical lines drawn at the ${ϵ}_{\mathrm{ac}}={ϵ}_{\mathrm{ac}}^{\pm }$ pass through the extrema in $r$.

Figure 4

(Color online) Thick lines represent LLs tilted by dc electric field. Vertical (horizontal) arrows represent transitions due to microwave absorption (impurity scattering). Inclined arrows show combined transitions. Conditions for the maxima [minima] are satisfied in (a) and (d) [(b) and (c)], respectively.