Non-equilibrium edge-channel spectroscopy in the integer quantum Hall regime

Abstract

The study of heat transport has the potential to reveal new insights into the physics of mesoscopic systems. This is especially true of those that show the integer quantum Hall effect1, in which the robust quantization of Hall currents limits the amount of information that can be obtained from charge transport alone2. As a consequence, our understanding of gapless edge excitations in these systems is incomplete. Effective edge-state theory describes them as prototypical one-dimensional chiral fermions3,4—a simple picture that explains a large body of observations5 and suggests the use of quantum point contacts as electronic beam splitters to explore a variety of quantum mechanical phenomena6,7,8. However, this picture is in apparent disagreement with the prevailing theoretical framework, which predicts in most situations9 extra gapless edge modes10. Here, we present a spectroscopic technique that addresses the question of whether some of the injected energy is captured by the predicted extra states, by probing the distribution function and energy flow in an edge channel operated out-of-equilibrium. Our results show it is not the case and therefore that regarding energy transport, quantum point contacts do indeed behave as optical beam splitters. This demonstrates a useful new tool for heat transport and out-of-equilibrium experiments.

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Figure 1: Experimental implementation of non-equilibrium edge-channel spectroscopy.
Figure 2: Equilibrium edge-channel spectroscopy and quantum-dot characterization.
Figure 3: Spectroscopy of an edge channel tuned out-of-equilibrium with the conductance of a QPC.
Figure 4: Spectroscopy of an edge channel tuned out-of-equilibrium with the voltage across a QPC.

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Acknowledgements

The authors gratefully acknowledge discussions with M. Buttiker, P. Degiovanni, C. Glattli, P. Joyez, A. H. MacDonald, F. Portier, H. Pothier, P. Roche and G. Vignale. This work was supported by the ANR (ANR-05-NANO-028-03).

Author information

Experimental work and data analysis: C.A., H.l.S. and F.P.; nanofabrication: C.A. and F.P. with input from D.M.; heterojunction growth: A.C. and U.G.; theoretical analysis and manuscript preparation: F.P. with input from coauthors; project planning and supervision: F.P.

Correspondence to F. Pierre.

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Altimiras, C., le Sueur, H., Gennser, U. et al. Non-equilibrium edge-channel spectroscopy in the integer quantum Hall regime. Nature Phys 6, 34–39 (2010). https://doi.org/10.1038/nphys1429

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