Bichromatic Microwave Photoresistance of a Two-Dimensional Electron System

We explore experimentally bichromatic (frequencies ${\omega }_1$ and ${\omega }_2$) photoresistance of a two-dimensional electron system in the regimes of microwave-induced resistance oscillations and zero-resistance states. We find bichromatic resistance to be well described by a superposition of ${\omega }_1$ and ${\omega }_2$ components, provided that both monochromatic resistances are positive. This relation holds even when the oscillation amplitudes are small and one could expect additive contributions from monochromatic photoresistances. In contrast, whenever a zero-resistance state is formed by one of the frequencies, such superposition relation breaks down and the bichromatic resistance is strongly suppressed.

Figure 1

Panels (a) and (b) show magnetoresistance data $R^{{\omega }_1}$ and $R^{{\omega }_2}$ under monochromatic radiation of frequencies $f_1=31\mathrm{GHz}$ and $f_2=47\mathrm{GHz}$, respectively. Numbers label harmonics of cyclotron resonance. In panel (c) solid line represents experimental bichromatic magnetoresistance ($f_1$ and $f_2$). Maximum-maximum, minimum-minimum, and maximum-minimum overlaps are marked by $\uparrow$, $\downarrow$, and $\updownarrow$, respectively. The upper boundary of the shaded area represents the average of monochromatic resistances $R^{{\omega }_1}$ and $R^{{\omega }_2}$ presented in (a) and (b) (see text). Dotted lines in (a) and (b) represent reconstructed negative resistance as described in the text.

Figure 2

Monochromaric $R^{{\omega }_1}$ (dashed line), $R^{{\omega }_2}$ (dotted line), and bichromatic $R^{{\omega }_1{\omega }_2}$ (solid line) resistance vs inverse magnetic field. Upper (lower) set of numbers labels ${\omega }_2$ (${\omega }_1$) CR harmonics.

Figure 3

Top two traces are monochromatic magnetoresistances $R^{{\omega }_1}$ and $R^{{\omega }_2}$. Vertical arrows mark the positions of $B_2^{{\omega }_2+}\approx B_1^{{\omega }_1-}$ ($\uparrow$) and $B_4^{{\omega }_2-}\approx B_3^{{\omega }_1+}$ ($\downarrow$). Bottom three traces show bichromatic magnetoresistance at various intensities of the ${\omega }_2$ source as marked by attenuation. In the inset solid lines duplicate the magnetoresistance in the MIRO regime ($100\mathrm{G}<B<200\mathrm{G}$) and dotted lines are calculated as described in the text.