### Measurement of energy relaxation in quantum Hall edge states utilizing quantum point contacts

**Introduction**

Quantum Hall edge states are formed when we apply magnetic fields to two dimensional electron gas. The states have long coherence length and chirality in solids, and can be applied to interesting electronic devices and quantum information processing.

For such application, understanding of the local electronic states and the energy relaxation in the edge states are important. So far, experiments utilizing quantum dots have been reported. In this work, we demonstrated easier method utilizing quantum point contacts to probe the local electronic states and the energy relaxation. Also, we applied the method to examine the energy relaxation around a hot spot in the quantum Hall regime.

**Experiment**

The right figures show the pictures and the schematics of the device.

QPC1 is used to create non-equilibrium electronic states in the quantum Hall edge states. QPC2-5 are used to probe the local electrochemical potential and the change of the local electronic states by the energy relaxation.

First, we did a measurement in the case with electron tunneling between the edge states. To induce the tunneling, we created a difference in the electrochemical potentials between the edge states.

The observed local voltages show no change up to 30 micro meters. This shows that the energy relaxation length is over 30 micro meters. This result is consistent with the previous experiment with macroscopic voltage probes.

Second, we measured in the case only with energy exchange between the edge states. To induce such energy relaxation, we created non-equilibrium energy distribution in the outer edge channel.

The observed local voltage decreases with the increase of the propagation length. From the decay, the energy relaxation length is estimated as 3 micro meters and this value is consistent with the previous experiments.

These results show that we can detect the local electronic states and the energy relaxation utilizing QPCs.

(About the mechanism of the detection, we have not understood the detail. As a possible mechanism, we might detect the voltage created by the temperature gradient, which is caused by the non-equilibrium energy distribution.)

Third, we applied this technique to explore the energy relaxation around a hot spot in the quantum Hall regime, at which the relaxation happens specifically.

A decrease of the local voltage is observed and the obtained energy relaxation is 2 micro meters.

This relaxation length is comparable with the value in the case only with energy exchange between the edge states. This implies that the energy exchange will contribute the energy relaxation around the hot spot in this length scale.

**Conclusion**

We demonstrated that we can detect the local electronic states and the energy relaxation in the quantum Hall edge states utilizing quantum point contacts.

We applied this method to examine the energy relaxation around the hot spot in the quantum Hall regime.

This method and the results will be useful to develop interesting devices utilizing the quantum Hall edge states.

**Reference**

“Measurement of Energy Relaxation in Quantum Hall Edge States Utilizing Quantum Point Contacts”,

__Tomohiro Otsuka__*, Yuuki Sugihara*, Jun Yoneda, Takashi Nakajima, and Seigo Tarucha,

Journal of the Physical Society of Japan 83, 014710 (2014) (*equal contribution).