Phonon-Mediated versus Coulombic Backaction in Quantum Dot Circuits

Quantum point contacts (QPCs) are commonly employed to detect capacitively the charge state of coupled quantum dots (QDs). An indirect backaction of a biased QPC onto a double QD laterally defined in a $\mathrm{GaAs}/\mathrm{AlGaAs}$ heterostructure is observed. Energy is emitted by nonequilibrium charge carriers in the leads of the biased QPC. Part of this energy is absorbed by the double QD where it causes charge fluctuations that can be observed under certain conditions in its stability diagram. By investigating the spectrum of the absorbed energy, we find that both acoustic phonons and Coulomb interaction can be involved in the backaction, depending on the geometry and coupling constants.

Figure 1

(a) Scanning electron micrograph of an identical device. Metal gates (light gray) are negatively biased, darker gates are grounded. QDs ($B,C$), current paths (arrows), and Ohmic contacts (roman numbers) are indicated. (b) Sketch of a double QD charge stability diagram. Numbers in brackets indicate stable charge configurations ($N_B$, $N_C$). The gray triangle features backaction [compare (d)]. (c) Level diagram of the double QD. Dotted lines depict the electron excitation spectrum of QD $C$. (d) Measured transconductance $d{I}_{\mathrm{QPC}}/d{V}_{\beta }$ (gray scale) as a function of voltages applied to gates $\beta$ and $\gamma$ for $V_{\mathrm{QPC}}=-1.6\mathrm{mV}$ and $P_{\mathrm{QPC}}=0.64\mathrm{pW}$.

Figure 2

(a),(b) Transconductance $d{I}_{\mathrm{QPC}}/d{V}_{\beta }$ (gray scale) as a function of $V_{\beta }$ and $V_{\gamma }$. (c) Observed maximum of absorbed energy $E_{\max }$ [compare Fig. 1d] as a function of $P_{\mathrm{QPC}}$ and $V_{\mathrm{QPC}}$. Arrows show where (a) and (b) are located in this graph. See main text for details.

Figure 3

(a),(b) $\delta I_{\mathrm{QPC}}$ (gray scale) as a function of $V_{\beta }$ and $V_{\gamma }$. A plane fit is subtracted from $I_{\mathrm{QPC}}$ (resulting in $\delta I_{\mathrm{QPC}}$) to correct for capacitances between gates and the QPC. In (a) only QPC-I is biased with $V_{\mathrm{QPC}}=-0.8\mathrm{mV}$ and $P_{\mathrm{QPC}}=2.5\mathrm{pW}$; for (b) the values are $V_{\mathrm{QPC}}=-0.1\mathrm{mV}$ and $P_{\mathrm{QPC}}=0.01\mathrm{pW}$. QPC-II is additionally biased in with $V_{\mathrm{QPC}}=-2.0\mathrm{mV}$ and $P_{\mathrm{QPC}}=72\mathrm{pW}$ in (b). (c)–(e) Normalized current change $\Delta I_{\mathrm{QPC}}$ versus asymmetry energy $\Delta$ [compare Fig. 1c] along the white line in (a). $\Delta I_{\mathrm{QPC}}$ corresponding to configurations (2,0), (1,1) and (0,1) are highlighted in gray.