Resonant Phonon Scattering in Quantum Hall Systems Driven by dc Electric Fields

Using dc excitation to spatially tilt Landau levels, we study resonant acoustic phonon scattering in two-dimensional electron systems. We observe that dc electric field strongly modifies phonon resonances, transforming resistance maxima into minima and back into maxima. Further, phonon resonances are enhanced dramatically in the nonlinear dc response and can be detected even at low temperatures. Most of our observations can be explained in terms of dc-induced (de)tuning of the resonant acoustic phonon scattering and its interplay with inter–Landau level impurity scattering. Finally, we observe a resistance maximum when the electron drift velocity approaches the speed of sound and a dc-induced zero-differential resistance state.

Figure 1

Solid lines are LLs at ${ϵ}^{\mathrm{ph}}=1$ and (a) ${ϵ}^{\mathrm{dc}}=0$, (b) ${ϵ}^{\mathrm{dc}}=1/2$, and (c) ${ϵ}^{\mathrm{dc}}=1$ as functions of $\Delta y$. Dashed lines represent phonon dispersion cone, $\hslash {\omega }_s=\pm \hslash s\Delta y/{\lambda }_B^2$. Arrows show $2k_F$ transitions due to acoustic phonon ($P$) and impurity ($I$) scattering. At ${ϵ}^{\mathrm{dc}}={ϵ}^{\mathrm{ph}}$ (c), intra–LL scattering ($S$) accompanied by phonon emission becomes possible.

Figure 2

(a) [(b)] $r/r_0$ vs $B$ at $I$ from 0 to $50\mu \mathrm{A}$ with step of $2\mu \mathrm{A}$ ($T\simeq 10\mathrm{K}$) [from $25\mu \mathrm{A}$ to $150\mu \mathrm{A}$ with step of $5\mu \mathrm{A}$ ($T\simeq 6\mathrm{K}$)]. Traces are vertically offset in increments of 2% [15%]. Vertical lines correspond to the PIRO peaks as marked at $I=0$. Numbers at the top traces mark HIRO peaks.

Figure 3

(a) $r$ vs ${ϵ}^{\mathrm{dc}}$ at $B$ from 1 to 4 kG in 0.1 kG steps ($T\simeq 5\mathrm{K}$). Traces are vertically offset by $0.5\Omega$. (b) $r$ vs $B$ at ${ϵ}^{\mathrm{dc}}=0$ (dotted line), ${ϵ}^{\mathrm{dc}}=1$ (circles), and ${ϵ}^{\mathrm{dc}}=3/2$ (squares) at $T\simeq 5\mathrm{K}$. (c) $r$ vs ${ϵ}^{\mathrm{dc}}$ at $B=2.7\mathrm{kG}$ and $T\simeq 1.5\mathrm{K}$.

Figure 4

(a) [(b)] $r$ in the ($B,I$) plane at $T\simeq 5\mathrm{K}$ [$T\simeq 1.5\mathrm{K}$]. Gray scale is in $\Omega$. (c) [(d)] $r$ maxima in ($B,v_H$) plane at $T\simeq 5\mathrm{K}$ [$T\simeq 1.5\mathrm{K}$]. Horizontal line is at $5.8\mathrm{km}/\mathrm{s}$.