Multiphoton processes at cyclotron resonance subharmonics in a two-dimensional electron system under dc and microwave excitation

We investigate a two-dimensional electron system (2DES) under microwave illumination at cyclotron resonance subharmonics. The 2DES carries sufficient direct current, $I$, that the differential resistivity oscillates as $I$ is swept. At magnetic fields sufficient to resolve individual Landau levels, we find the number of oscillations within an $I$ range systematically changes with increasing microwave power. Microwave absorption and emission of $N$ photons, where $N$ is controlled by the microwave power, describes our observations in the framework of the displacement mechanism of impurity scattering between Hall-field tilted Landau levels.

Figure 1

(a) Schematic of the microwave setup for a top view, not to scale. (b) $r$ vs $B$ with microwave radiation of $f=30.5$ GHz at different applied currents from $I=0$ to $24\mu \mathrm{A}$ in steps of $4\mu \mathrm{A}$ for microwave power $+3$ dB. Vertical dashed lines denote the cyclotron resonance and its second harmonic and the dotted lines mark its second and third subharmonic. Traces are vertically offset for clarity.

Figure 2

$r$ vs ${\epsilon }_{\text{dc}}$ at $f=31$ GHz and ${\epsilon }_{\text{ac}}=1/2$ for a baseline weak power, dotted trace in each panel, and increasing power of $+3$ dB (a), $+6$ dB (b), and $+10$ dB (c).

Figure 3

$r$ vs ${\epsilon }_{\text{dc}}$ at $f=31$ GHz and ${\epsilon }_{\text{ac}}=1/3$ for a baseline weak power, dotted trace in each panel, and increasing power of $+3$ dB (a), $+6$ dB (b), and $+10$ dB (c).

Figure 4

Energy vs distance Landau level diagrams for ${\epsilon }_{\text{ac}}=1/3$ for maxima at (a) ${\epsilon }_{\text{dc}}=2/3$, $N=1$; (b) ${\epsilon }_{\text{dc}}=4/3$, $N=-1$; (c) ${\epsilon }_{\text{dc}}=1/3$, $N=2$; and (d) ${\epsilon }_{\text{dc}}=4/3$, $N=2$. Thick lines denote Hall-field tilted Landau levels, vertical dotted arrows represent energy change due to absorption (up arrows) or emission (down arrows) of a photon, horizontal dashed arrows for spatial change of an electron backscattering by the cyclotron diameter $\left(2R_{\text{C}}\right)$, and inclined solid arrows for a combined transition.