Multiphoton processes in microwave photoresistance of two-dimensional electron systems

We extend our studies of microwave photoresistance of ultrahigh mobility two-dimensional electron systems (2DES) into the high-intensity, nonlinear regime employing both monochromatic and bichromatic radiation. Under high-intensity monochromatic radiation $\omega$ we observe zero-resistance states (ZRSs) that correspond to the rational values of $\epsilon =\omega ∕{\omega }_C$ (${\omega }_C$ is the cyclotron frequency) and can be associated with multiphoton processes. Under bichromatic radiation ${\omega }_1,{\omega }_2$ we discover a resistance minimum, possibly a precursor of bichromatic ZRSs, which seems to originate from a frequency mixing process, ${\omega }_1+{\omega }_2$. These findings indicate that multiphoton processes play important roles in the physics of nonequilibrium transport of microwave-driven 2DES, and suggest new directions for theoretical and experimental studies.

Figure 1

(Color online) Magnetoresistance under microwave illumination of $f=\omega ∕2\pi =27\mathrm{GHz}$, for selected radiation intensities. Traces are vertically offset for clarity and are marked by attenuation. Vertical downward arrows mark the positions of oscillations minima corresponding to rational values of $\epsilon \approx 3∕2$, $2∕3$, and $1∕2$, from left to right, which develop into new ZRSs with increasing intensity. The insets illustrate virtual multiphoton processes responsible for these features at rational $\epsilon$. At $B>0.15\mathrm{T}$ nonresonant suppression of resistance is observed.

Figure 2

(Color online) Magnetoresistance under microwave illumination of $f=27\mathrm{GHz}$ as a function of $\epsilon$, at selected attenuations of $-8\mathrm{dB}$ [dotted (blue) line], $-4\mathrm{dB}$ [dashed (red) line], and $0\mathrm{dB}$ [solid (black) line], as marked. Panels (a) and (b) show evolution of photoresistance features at $\epsilon \approx 1∕2,2∕3,1$ and $\epsilon \approx 3∕2,2$, respectively.

Figure 3

(Color online) Magnetoresistance under monochromatic $f_1=31\mathrm{GHz}$ [dashed (red) line], $f_2=47\mathrm{GHz}$ [dotted (blue) line], and bichromatic $f_1=31\mathrm{Ghz}$ and $f_2=47\mathrm{GHz}$ [solid (black) line]. Vertical dashed (red) and dotted (blue) lines mark ${\epsilon }_{{\omega }_1}^{\left(2\right)}=1∕2$ and ${\epsilon }_{{\omega }_2}^{\left(1\right)}=1$, respectively. The vertical downward arrow at $\approx 0.16\mathrm{T}$ marks the position where a deep bichromatic minimum is formed. The inset illustrates three possible processes, from left to right, involving (a) two $f_1$ photons, (b) one $f_2$ photon, and (c) one $f_1$ and one $f_2$ photons. While (a) and (b) processes underpromote an electron and thus correspond to positive photoresistance, (c) results in overpromoting an electron, resulting in negative photoresistance.