^{a)}

^{a)}This paper is based on a talk presented by the authors at the 28th International Conference on the Physics of Semiconductors, which was held 24–28 July 2006, in Vienna, Austria. Contributed papers for that conference may be found in “Physics of Semiconductors: 28th International Conference on the Physics of Semiconductors,” AIP Conference Proceedings No. 893 (AIP, Melville, NY, 2007); see http://proceedings.aip.org/proceedings/confproceed/893.jsp

^{1}, T. Ihn

^{1}, K. Ensslin

^{1,b)}, M. Reinwald

^{2}and W. Wegscheider

^{2}

### Abstract

For low biases the linear conductance of quantum dots is based on elastic transport processes. At finite bias in the Coulomb blockade regime, inelastic cotunneling sets in once the applied bias exceeds the energy between ground and excited state in the dot. Here we report on transport experiments through an Aharonov-Bohm ring containing a quantum dot in each arm of the ring. The tunnel coupling between the two dots can be tuned by electrostatic gates. For strong tunnel coupling and low bias we observe pronounced Aharonov-Bohm oscillations in the ring with visibilities exceeding 80%. For quantum dots which are purely capacitively coupled, the Aharonov-Bohm amplitude is reduced to a more standard 10%. For finite bias, where transport through excited states becomes possible and a conductance onset is observed, the visibility of the Aharonov-Bohm oscillations remains basically unchanged, while the phase typically undergoes a change of . We discuss these observations in view of the possible elastic and inelastic transport processes and their contributions to coherent transport.

The authors thank D. Loss, Y. Meir, and D. Sanchez for valuable discussions. Financial support from the Swiss Science Foundation (Schweizerischer Nationalfonds) is gratefully acknowledged.

I. INTRODUCTION

II. TRANSPORT THROUGH THE OPEN RING

III. ANALYSIS OF THE FEATURES IN MAGNETIC FIELD

IV. TUNABLE DOUBLE DOT

V. WEAK INTERDOT COUPLING

VI. STRONG INTERDOT COUPLING

VII. DISCUSSION

VIII. CONCLUSIONS

### Key Topics

- Excited states
- 21.0
- Quantum dots
- 20.0
- Magnetic fields
- 11.0
- Visibility
- 11.0
- Elasticity
- 10.0

## Figures

(Color online) (a) SFM micrograph of the structure. In-plane gates (white letters), titanium oxide lines (black lines), and top gates (black letters) are indicated. The ring–double-dot system is illustrated by the quantum dots (full circles) and the AB loop (bright lines through QDs). (b) The conductance from source to drain through the open ring as a function of magnetic field is plotted. For the upper curve the top plunger gate was adjusted to . This allows significant tunneling between the two branches of the ring. For the lower curve the coupling point contact between the branches was closed by applying a more negative voltage of to the top plunger gate. AB oscillations are observed for both curves. (c) The Fourier transform as a function of period is plotted for both top plunger gate settings. An additional AB period for a small orbit is found for the case of coupled branches corresponding to interference around one oxide dot in the structure.

(Color online) (a) SFM micrograph of the structure. In-plane gates (white letters), titanium oxide lines (black lines), and top gates (black letters) are indicated. The ring–double-dot system is illustrated by the quantum dots (full circles) and the AB loop (bright lines through QDs). (b) The conductance from source to drain through the open ring as a function of magnetic field is plotted. For the upper curve the top plunger gate was adjusted to . This allows significant tunneling between the two branches of the ring. For the lower curve the coupling point contact between the branches was closed by applying a more negative voltage of to the top plunger gate. AB oscillations are observed for both curves. (c) The Fourier transform as a function of period is plotted for both top plunger gate settings. An additional AB period for a small orbit is found for the case of coupled branches corresponding to interference around one oxide dot in the structure.

(Color online) (a) A conductance trace as a function of magnetic field containing weak AB oscillations is plotted (black). The step size of the magnetic field provides about 20 data points per AB period. The superposed curve is composed of the filtered AB signal and the background conductance without the high-frequency part. (b) The filtered AB signal is plotted as a function of magnetic field. It still contains a small varying background due to the finite width of the Gauss window in Fourier space. (c) Subtracting the two curves in (a) yields the high-frequency fluctuations plotted here. Many features are symmetric in magnetic field and therefore reproducible. They mostly originate from interference effects in the contacts of the structure.

(Color online) (a) A conductance trace as a function of magnetic field containing weak AB oscillations is plotted (black). The step size of the magnetic field provides about 20 data points per AB period. The superposed curve is composed of the filtered AB signal and the background conductance without the high-frequency part. (b) The filtered AB signal is plotted as a function of magnetic field. It still contains a small varying background due to the finite width of the Gauss window in Fourier space. (c) Subtracting the two curves in (a) yields the high-frequency fluctuations plotted here. Many features are symmetric in magnetic field and therefore reproducible. They mostly originate from interference effects in the contacts of the structure.

(a) The charge stability diagram of double-dot system as a function of both in-plane plunger gates is shown in the regime of only capacitive coupling between the dots. The dot marks the gate settings for further finite-bias cotunneling measurements. (b) The charge stability diagram of double-dot system as a function of both in-plane plunger gates is shown in the regime of finite tunnel coupling between the dots.

(a) The charge stability diagram of double-dot system as a function of both in-plane plunger gates is shown in the regime of only capacitive coupling between the dots. The dot marks the gate settings for further finite-bias cotunneling measurements. (b) The charge stability diagram of double-dot system as a function of both in-plane plunger gates is shown in the regime of finite tunnel coupling between the dots.

(Color online) Experiments are performed for only capacitive coupling between the two dots in the cotunneling regime indicated by the black dot in Fig. 3(a). (a) In the upper curve, differential conductance is plotted as a function of DC source-drain voltage averaged over one AB period around zero magnetic field. The inelastic onsets are highlighted. The lower curve shows the phase of the AB oscillations as a function of dc source-drain bias voltage around zero magnetic field. We do not observe a phase jump for every inelastic onset. (b) The filtered AB oscillations with a period of about 22 mT are illustrated as a function of magnetic field and dc bias voltage. Slight shifts of the AB maxima as a function of bias voltage indicate a change in AB period.

(Color online) Experiments are performed for only capacitive coupling between the two dots in the cotunneling regime indicated by the black dot in Fig. 3(a). (a) In the upper curve, differential conductance is plotted as a function of DC source-drain voltage averaged over one AB period around zero magnetic field. The inelastic onsets are highlighted. The lower curve shows the phase of the AB oscillations as a function of dc source-drain bias voltage around zero magnetic field. We do not observe a phase jump for every inelastic onset. (b) The filtered AB oscillations with a period of about 22 mT are illustrated as a function of magnetic field and dc bias voltage. Slight shifts of the AB maxima as a function of bias voltage indicate a change in AB period.

(Color online) Experiments are performed for finite tunnel coupling between the two dots in the cotunneling regime indicated by the black dot in Fig. 3(b). (a) Differential conductance is plotted as a function of magnetic field and dc bias voltage on a nonlinear scale. AB oscillations with a period of about 47 mT are observed corresponding to interference around an oxide dot in the structure. (b) The normalized AB signal is illustrated as a function of magnetic field and dc bias voltage. A phase jump in the AB oscillations is observed across the inelastic onset.

(Color online) Experiments are performed for finite tunnel coupling between the two dots in the cotunneling regime indicated by the black dot in Fig. 3(b). (a) Differential conductance is plotted as a function of magnetic field and dc bias voltage on a nonlinear scale. AB oscillations with a period of about 47 mT are observed corresponding to interference around an oxide dot in the structure. (b) The normalized AB signal is illustrated as a function of magnetic field and dc bias voltage. A phase jump in the AB oscillations is observed across the inelastic onset.

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