Energy Relaxation in the Integer Quantum Hall Regime

Abstract

We investigate the energy exchanges along an electronic quantum channel realized in the integer quantum Hall regime at filling factor νL = 2. One of the two edge channels is driven out-ofequilibrium and the resulting electronic energy distribution is measured in the outer channel, after several propagation lengths 0.8 µm≤ L ≤ 30 µm. Whereas there are no discernable energy transfers toward thermalized states, we find efficient energy redistribution between the two channels without particle exchanges. At long distances L ≥ 10 µm, the measured energy distribution is a hot Fermi function whose temperature is lower than expected for two interacting channels, which suggests the contribution of extra degrees of freedom. The observed short energy relaxation length challenges the usual description of quantum Hall excitations as quasiparticles localized in one edge channel.PACS numbers: 73.43. Fj, 72.15.Lh, 73.23.Ad, 73.43.Lp The basic manifestation of the quantum Hall effect is a quantized Hall resistance R H = h/e 2 ν L , accompanied by a vanishing longitudinal resistance. In this regime, quantization of the two-dimensional cyclotron motion opens a large gap separating Landau levels in the bulk of the sample from the Fermi energy. The only available low energy excitations propagate along the edges, where the Landau levels cross the Fermi energy. The effective edge state theory suggests these excitations are prototypal one-dimensional chiral fermions (1DCF) [1], each of the ν L edge channels (EC) being identified with a onedimensional conductor. Because back-scattering is forbidden by chirality, ECs are considered to be ideal ballistic quantum channels. Their similitude with light beams has inspired electronic analogues of quantum optics experiments [2-5] and proposals for quantum information applications [6]. However, the nature and decoherence of edge excitations are poorly understood, as highlighted by unexpected results obtained with electronic MachZehnder interferometers: an unusual energy dependence of the interference fringes' visibility [2, 7], a non-gaussian noise [8] and a short coherence length [9, 10]. Interactions between ECs and with their environment are seen as the key ingredient to explain these results (see e.g. [11, 12]).In the present experimental work, we investigate the interaction mechanisms taking place along an EC through the energy exchanges they induce. A similar approach was previously used on mesoscopic metal wires [13] and on carbon nanotubes [14]. Here we focus on the filling factor ν L = 2, where two co-propagating ECs are present, and at which the above unexpected results were observed. Our experiment relies on the techniques we recently demonstrated to drive out-of-equilibrium an EC and to measure the resulting energy distribution f (E) of 1DCF quasiparticles [15]. There, we drove out-ofequilibrium only the outer EC, and f (E) was measured in the same EC after a short 0.8 µm propagation distance, for which the energy redistribution is negligible. Here, we drive out-of-equilibrium sel...

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