Coherent Probing of Excited Quantum Dot States in an Interferometer

Measurements of elastic and inelastic cotunneling currents are presented on a two-terminal Aharonov-Bohm interferometer with a Coulomb-blockaded quantum dot embedded in each arm. Coherent current contributions, even in a magnetic field, are found in the nonlinear regime of inelastic cotunneling at a finite-bias voltage. The phase of the Aharonov-Bohm oscillations in the current exhibits phase jumps of $\pi$ at the onsets of inelastic processes. We suggest that additional coherent elastic processes occur via the excited state. Our measurement technique allows the detection of such processes on a background of other inelastic current contributions and contains qualitative information about the ratio of transport and inelastic relaxation rates.

Figure 1

(a) SFM micrograph of the structure (details in the main text). (b) $G_{\mathrm{sd}}$ as a function of $V_{\mathrm{pg}1}$ and $V_{\mathrm{pg}2}$ representing the charge stability diagram of the two QDs. The finite-bias measurements in Fig. 2 were taken along the dashed lines.

Figure 2

(a) Differential conductance is measured as a function of dc source-drain voltage along trace $a$ in Fig. 1b. An inelastic onset independent of the electron number of dot 1 is superposed on the Coulomb diamonds. (b) Differential conductance is measured as a function of bias voltage along trace $b$ in Fig. 1b. The inelastic onset can be linked to an excited state of dot 2.

Figure 3

(a) $B$ dependence of the differential conductance for gate voltages set to the center of the hexagon in Fig. 1b. Bottom trace: low dc bias voltage (square, c.f. Fig. 2); top trace: high dc bias voltage (dot). (b) Normalized AB conductance $g_{\mathrm{AB}}(B,V_{\mathrm{bias}})$.

Figure 4

(a) Differential conductance and its derivative averaged over one AB period around zero magnetic field as a function of dc source-drain voltage. (b) Normalized amplitude of the AB oscillation at $B=0$ as a function of source-drain bias. (c) AB phase at $B=0$. (d) Schematic of elastic cotunneling transport through dot 2 triggered at the inelastic onset.