Surface-Acoustic-Wave-Induced Transport in a Double Quantum Dot

We report on nonadiabatic transport through a double quantum dot under irradiation of surface acoustic waves generated on chip. At low excitation powers, absorption and emission of single and multiple phonons are observed. At higher power, sequential phonon assisted tunneling processes excite the double dot in a highly nonequilibrium state. The present system is attractive for studying electron-phonon interaction with piezoelectric coupling.

Figure 1

(a) Picture of the device with an IDT (left) and a DQD (right). The source (S) and drain (D) reservoirs are indicated. The IDT-DQD distance is $227.5\mu \mathrm{m}$. In the SEM of the IDT, the electrodes, separated by $\lambda =1.4\mu \mathrm{m}$, are visible. In the hatched regions of the DQD SEM, the 2DEG is depleted by shallow dry etching. The position of the dots is indicated by white dots. (b) Transmission $T$ (blue curve) and reflection $R$ (red and green curves) at room temperature of two IDTs similar to the one used in the experiments, separated by a distance of $455\mu \mathrm{m}$. A clear peak in $T$ and a dip in $R$ are visible at 1.92 GHz. (c) Color scale plot of the DQD current as a function of gate voltages $V_{\mathrm{gl}}$ and $V_{\mathrm{gr}}$ at source drain voltage $V_{\mathrm{SD}}=500\mu \mathrm{V}$ without SAW generation. The conductance triangles are accentuated by dotted lines. Resonant tunneling lines are clearly visible. The dual gate sweep direction for the SAW experiments is indicated by the red arrow.

Figure 2

(a) Color scale plot of the DQD current versus ground state level spacing $\Delta E$ and microwave frequency $f$ applied to the IDT ($-40\mathrm{dBm}$ microwave power). $V_{\mathrm{gl}}$ and $V_{\mathrm{gr}}$ are swept along the red arrow indicated in Fig. 1c. The current at $\Delta E=0$ and $150\mu \mathrm{eV}$ corresponds to resonant tunneling through the ground states (GG) and through the left ground state and an excited state in the right dot (GE1), respectively. A clear resonance is observed at 1.9446 GHz ($\Delta f=1.4\mathrm{MHz}$), corresponding to the IDT resonance frequency. The inelastic current is due to absorption and emission of SAW phonons, as schematically depicted in the energy diagrams (b) and (d), respectively. The energy diagram for elastic resonant tunneling is shown in (c).

Figure 3

(a) Color scale plot of the DQD current versus $\Delta E$ and microwave power $P$, at $f_{\mathrm{SAW}}=1.9446\mathrm{GHz}$, for the same transitions as in Fig. 2. (b) Experimental (black dots) and calculated (red curves) current spectra for different microwave powers, extracted from (a) and (c), respectively. The experimental microwave power incident on the IDT is converted to normalized potential amplitude $\alpha$ using (d). The current height of the calculated spectra is fitted to the experimental data. (c) Calculated DQD current versus $\Delta E$ and $\alpha$ in the nonadiabatic limit, as explained in the text. Inset: Squared Bessel functions $J_n^2(\alpha )$ for $n=0$, 1, 2, and 3. (d) Splitting of the current peaks as a function of the amplitude of the microwave voltage $V_{\mathrm{IDT}}$ applied to the IDT for the experimental data (black data points and axes) and current peak splitting derived from the calculated spectra in (c) as a function of $\alpha$ (red curve and axes). By matching the experimental and calculated curves, the conversion between $P$ and $\alpha$ is found. (e) Schematic energy level diagrams for positions 1 and 2 indicated in (a). The transitions (i)–(iv) are discussed in the text.