Phonon-Mediated Nonequilibrium Interaction between Nanoscale Devices

Interactions between mesoscopic devices induced by interface acoustic phonons propagating in the plane of a two-dimensional electron system (2DES) are investigated by phonon spectroscopy. In our experiments, ballistic electrons injected from a biased quantum point contact emit phonons and a portion of them are reabsorbed exciting electrons in a nearby degenerate 2DES. We perform energy spectroscopy on these excited electrons employing a tunable electrostatic barrier in an electrically separate and unbiased detector circuit. The transferred energy is found to be bounded by a maximum value corresponding to Fermi-level electrons excited and backscattered by absorbing interface phonons. Our results imply that phonon-mediated interaction plays an important role for the decoherence of solid-state-based quantum circuits.

Figure 1

(a) Barrier calibration: Inset: calibration setup (for details see main text). Main figure: Current $I_a$ (gray scale for $I_{\mathrm{a}}<100\mathrm{fA}$, contour lines of constant current spaced by a factor of 3.3 for $I_{\mathrm{a}}>100\mathrm{fA}$) as a function of $V_{\mathrm{SD}}$ and the gate voltage $V_{{\mathrm{B}}_{\mathrm{a}}}$. The current onset ($I_{\mathrm{a}}\simeq 100\mathrm{fA}$), highlighted in purple, serves as calibration. The resulting energy scale is displayed on the top axis. (b) Sample geometry: A Hall-bar (dark gray) with eight Ohmic contacts ($1,2,\dots ,8$) is shaped from a $\mathrm{GaAs}/\mathrm{AlGaAs}$-heterostructure using electron-beam lithography (scanning electron micrograph). The Hall-bar is partly covered by metal gates (light gray) used to electrostatically define potential barriers (B1, B2, B3) and quantum point contacts (QPC1, QPC2).

Figure 2

Phonon-driven current: (a) Analyzer current $I_3=I_{\mathrm{a}}$ (gray scale, color for $I_3\ge 50\mathrm{fA}$) across B3 (as analyzer barrier ${\mathrm{B}}_{\mathrm{a}}$) as a function of its energetic height $E_{\mathrm{B}3}-E_{\mathrm{F}}$ in the bias range $0\ge V_{\mathrm{SD}}\ge -60\mathrm{mV}$ applied across QPC1 (as emitter). Barrier B1 is opaque for electrons and separates emitter and detector as sketched in the inset. B2 is left open ($E_{\mathrm{B}2}\ll E_{\mathrm{F}}$). Contour lines of constant current are spaced by a factor of 1.7. (b) $I_3-E_{\mathrm{B}3}$ traces along the horizontal lines in (a). The inset sketches relevant phonon absorption processes for an electron at the Fermi-level $E_{\mathrm{F}}$. (c) Analyzer current $I_3$ in the bias range $3\mathrm{mV}\ge V_{\mathrm{SD}}\ge -3\mathrm{mV}$. Currents comparable to those at larger bias are achieved by lowering the injector barrier resistance. For the detailed configuration see main text. (d) $I_3\mathrm{\text{−}}{V}_{\mathrm{SD}}$ traces along the vertical lines in (c). Also plotted is the injector current $I_{\mathrm{SD}}$ (right-hand side axis).

Figure 3

Mean-free path of interface acoustic phonons: Analyzer current $I_3$ as a function of the emitter bias $V_{\mathrm{SD}}$ for the two experimental setups sketched in the inset. In setup 1 B2 is left open [as for Fig. 2a] while in setup 2 both barriers B1 and B2 are opaque for electrons. The analyzer barrier is tuned to $E_{\mathrm{B}3}\simeq E_{\mathrm{F}}$. In setup 2 $I_3$ is reduced by about a factor of 10. Hence, the distance between B1 and B2 of about $1\mu \mathrm{m}$ roughly corresponds to the phonon mean-free path.