Phase Coherence in the Inelastic Cotunneling Regime

Two quantum dots with tunable mutual tunnel coupling have been embedded in a two-terminal Aharonov-Bohm geometry. Aharonov-Bohm oscillations investigated in the cotunneling regime demonstrate coherent tunneling through nonresonant states. Visibilities of more than 0.8 are measured indicating that phase-coherent processes are involved in the elastic and inelastic cotunneling. An oscillation-phase change of $\pi$ is detected as a function of bias voltage at the inelastic cotunneling onset.

Figure 1

(a) SFM micrograph of the structure. In-plane gates (white letters), Titanium oxide lines (black lines), and top gates (black letters) are indicated. The QDs are marked by white crosses. (b) Charge stability diagram of the double QD. (c) Conductance peak of dot 1 as a function of magnetic field and gate pg1 [corresponding to the horizontal line c in (b)]. Upper inset: the same peak with a line indicating its maximum. Lower inset: schematic of the double QD embedded in the AB ring. (d) Conductance peak maximum as a function of magnetic field. The AB period is about 50 mT. Inset: Fourier analysis.

Figure 2

(a) Differential conductance measured as a function of $V_{\mathrm{bias}}$ [in-plane gates fixed at black dot in Fig. 1b]. This curve is indicated in (b) and (c) and in Fig. 3a as a dashed line. (b) Differential conductance measured along lines b1 and b2 in Fig. 1b as a function of $V_{\mathrm{bias}}$ and $V_{\mathrm{pg}2}$. (c) Differential conductance measured along line c in Fig. 1b as a function of $V_{\mathrm{bias}}$ and $V_{\mathrm{pg}1}$.

Figure 3

(a) Differential conductance as a function of magnetic field and $V_{\mathrm{bias}}$ with both dots in the cotunneling regime. (b) Detail of (a) inside the black rectangle. The grayscale is linear. (c) Two traces for small (left axis) and high bias voltage (right axis) are extracted from Fig. 3b, as indicated by dashed lines.

Figure 4

(a) Example for a pair of possible interfering paths in the AB interferometer. (b) The same interfering paths in the energy-level diagram.