Energy Relaxation in the Integer Quantum Hall Regime

We investigate the energy exchanges along an electronic quantum channel realized in the integer quantum Hall regime at a filling factor of ${\nu }_L=2$. One of the two edge channels is driven out of equilibrium and the resulting electronic energy distribution is measured in the outer channel, after several propagation lengths $0.8\mu \mathrm{m}\le L\le 30\mu \mathrm{m}$. Whereas there are no discernible energy transfers toward thermalized states, we find efficient energy redistribution between the two channels without particle exchanges. At long distances $L\ge 10\mu \mathrm{m}$, 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.

Figure 1

Sample micrograph: metallic gates appear bright; the two widest gates (not colorized) are grounded. The current propagates counterclockwise along two edge channels (EC) depicted by lines. White dashed lines indicate intermediate EC transmissions. At the output of the voltage biased quantum point contact (left in figure), the electronic energy distribution is a double step (left inset) in the partly transmitted EC (dashed outer EC in figure). After an adjustable propagation distance ($L=4\mu \mathrm{m}$ in figure), the energy distribution $f_D$ in the outer EC is measured using a quantum dot (white circle, see right inset).

Figure 2

(a) The outer EC is driven out of equilibrium. (b) Raw data (symbols) at $\delta V_D=36\mu \mathrm{V}$, shifted vertically for several $L$. The nonequilibrium double dip relaxes over $L_{\mathrm{inel}}\approx 3\mu \mathrm{m}$ toward a dip broader than the equilibrium dip at $\delta V_D=0$ (dotted line). Solid lines are calculations with a Fermi distribution at 85 mK. (c) Excess temperatures extracted from the data (symbols) and prediction at the QPC output (dashed line). The outer EC cools down as $L$ is increased and saturates at a value below expectations for two interacting ECs (dotted line, see text).

Figure 3

(a) The inner EC is driven out of equilibrium. (b) Raw data at $\delta V_D=0$ (dotted line) and $\delta V_D=54\mu \mathrm{V}$ (symbols), shifted vertically for several $L$. The dip broadens as $L$ is increased. (c) Excess temperatures extracted from the data (full symbols) and prediction at the QPC output (dashed line). The outer EC heats up as $L$ is increased, up to an excess temperature close to that when driving the outer EC out of equilibrium [$T_{\mathrm{exc}}(L=10\mu \mathrm{m})$ in Fig. 2c are shown here as open symbols ($▿$)].