Equilibration of integer quantum Hall edge states

Abstract

We study equilibration of quantum Hall edge states at integer filling factors, motivated by experiments involving point contacts at finite bias. Idealising the experimental situation and extending the notion of a quantum quench, we consider time evolution from an initial non-equilibrium state in a translationally invariant system. We show that electron interactions bring the system into a steady state at long times. Strikingly, this state is not a thermal one: its properties depend on the full functional form of the initial electron distribution, and not simply on the initial energy density. Further, we demonstrate that measurements of the tunneling density of states at long times can yield either an over-estimate or an under-estimate of the energy density, depending on details of the analysis, and discuss this finding in connection with an apparent energy loss observed experimentally. More specifically, we treat several separate cases: for filling factor ν=1 we discuss relaxation due to finite-range or Coulomb interactions between electrons in the same channel, and for filling factor ν=2 we examine relaxation due to contact interactions between electrons in different channels. In both instances we calculate analytically the long-time asymptotics of the single-particle correlation function. These results are supported by an exact solution at arbitrary time for the problem of relaxation at ν=2 from an initial state in which the two channels have electron distributions that are both thermal but with unequal temperatures, for which we also examine the tunneling density of states.

12 pages, 5 figures, final version as published

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• Interaction Quench in Nonequilibrium Luttinger Liquids
• Auger-spectroscopy in quantum Hall edge channels: a possible resolution to the missing energy problem
• Unified time-dependent perturbative relations applied to spectroscopy through photo-drag current
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• Solution of a model for the two-channel electronic Mach-Zehnder interferometer
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• Suppressed compressibility of quantum Hall effect edge states in epitaxial graphene on SiC
• Interaction-induced charge transfer in a mesoscopic electron spectrometer
• Nonlocal thermoelectric detection of interaction and correlations in edge states
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• Transient Features in Charge Fractionalization, Local Equilibration and Non-equilibrium Bosonization
• Spin-Selective Equilibration among Integer Quantum Hall Edge Channels
• Decoherence of high-energy electrons in weakly disordered quantum Hall edge states
• Efficient heat-energy conversion from a non-thermal Tomonaga-Luttinger liquid
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• Equilibration and Filtering of Quantum Hall Edge States in Few-Layer Black Phosphorus
• Fractional charges in emergent neutral modes at the integer quantum Hall effect
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