Microwave Photoresistance in dc-Driven 2D Systems at Cyclotron Resonance Subharmonics

We study microwave photoresistivity oscillations in a high-mobility two-dimensional electron system subject to strong dc electric fields. We find that near the second subharmonic of the cyclotron resonance the frequency of the resistivity oscillations with a dc electric field is twice the frequency of the oscillations at the cyclotron resonance, its harmonics, or in the absence of microwave radiation. This observation is discussed in terms of the microwave-induced sidebands in the density of states and the interplay between different scattering processes in the separated Landau level regime.

Figure 1

Differential magnetoresistivity $r_{xx}(B)$ under microwave illumination of $f=27\mathrm{GHz}$ measured at $T=1.5\mathrm{K}$ for $I$ from 0 to $40\mu \mathrm{A}$ in steps of $2\mu \mathrm{A}$. The traces are vertically offset by $0.5\Omega$. Vertical dotted (dashed) lines are drawn at ${ϵ}_{\mathrm{ac}}=2,3$ (${ϵ}_{\mathrm{ac}}=1/2,1/3$) marking harmonics (subharmonics) of the cyclotron resonance (solid line).

Figure 2

(a) [(b)] Differential resistivity $r_{xx}$ vs ${ϵ}_{\mathrm{dc}}$ (bottom axis) and $I$ (top axis) at ${ϵ}_{\mathrm{ac}}\simeq 1$ [${ϵ}_{\mathrm{ac}}\simeq 1/2$].

Figure 3

(a) [(b)] Gray scale plot of $r_{xx}$ in the (${ϵ}_{\mathrm{ac}},{ϵ}_{\mathrm{dc}}$) plane, near $({ϵ}_{\mathrm{ac}},{ϵ}_{\mathrm{dc}})=(1,1)$ [$({ϵ}_{\mathrm{ac}},{ϵ}_{\mathrm{dc}})=(1/2,1/2)$]. Light (dark) corresponds to high (low) $r_{xx}$ values.

Figure 4

Combined transitions (dotted arrows) between Landau levels (dark lines) and theoretically predicted microwave-induced sidebands [17] (light lines) consist of microwave absorption (vertical arrows) and impurity scattering (horizontal arrows) for (a) a maximum at $({ϵ}_{\mathrm{ac}},{ϵ}_{\mathrm{dc}})=(5/8,3/8)$ and (b) a minimum at $({ϵ}_{\mathrm{ac}},{ϵ}_{\mathrm{dc}})=(5/8,5/8)$.