### Fano effect in few-electron quantum dots

**Introduction**

With the recent progress in microfarication techniques, it becomes possible to make devices in which quantum effects appear. This opens new approach to understand quantum effects with preparing artificially controlled systems.

One example of such a device is a quantum dot. A quantum dot is a small box in which electrons are confined. The confined electrons show quantum effects like formation of the discrete energy level.

We are studying combined systems of this quantum dots with other quantum structures. In this page, we would like to introduce an experiment with a system consists of a quantum dot and a quantum wire (A very narrow wire which shows quantum effects).

**Experiment**

Right figures show a schematic and a scanning electron micrograph of the device. A quantum dot couples to the upper side of a quantum wire.

The quantum wire and the quantum dot are formed by controlling electrons which are confined in a heterostructure of GaAs and AlGaAs.

The right figure shows the conductance through the quantum wire with changing the number of electrons in the dot and the width of the wire. The horizontal axis corresponds to the voltage of the gate that controls the number of electrons. The vertical axis shows the voltage of the gate that controls the width of the wire.

Sudden changes of the conductance are observed when the number of electron changes. These are results of the charge detection effect and the interference effect that called Fano effect.

The electrons in the quantum dot modulate the surrounding electrostatic potential. The potential affects the conductance of the wire and causes the charge detection effect.

Fano effect is caused by the interference with a direct path that go through the wire and indirect paths with bounces to the dot. We focused on this Fano effect in this experiment.

A close-up of the region at which the Fano effect is dominant is shown right. With the change of the wire state, the modulation of the conductance also changes.

The cross sections along with a orange line and a green line are shown. We can see the change of the waveform.

This result implies the wave shape of Fano effect is modulated by the state of the wire.

To explain the change in the waveform, we construct a model in the right figure. The quantum dot couples to some sites in the quantum wire, and we treat finite coupling width between the dot and the wire.

The calculated conductance is shown in the graph. The horizontal axis shows the energy at the dot site. The vertical axis corresponds to the transmission probability. The traces show the results with changing the energy of the wire sites.

With the change of wire state, the waveform changes like the experimental result.

The physical meaning of this calculation is "The change of the wire state introduce the change of the phase relation between the sites which couple to the dot. This affects the interference and the resulting Fano wave shape changes."

**Conclusion**

We measured the conductance through the combined system with a quantum dot and a quantum wire. Changes of the Fano waveform are observed with the change of the wire state.

We explained this experimental result with constructing a model with finite coupling width between the dot and the wire.

**Reference**

"Fano Effect in a Few-Electron Quantum Dot", Tomohiro Otsuka, Eisuke Abe, Shingo Katsumoto, Yasuhiro Iye, Gyong L. Khym, and Kicheon Kang, J. Phys. Soc. Jpn. 76 084706 (2007).