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arXiv:1804.02523

Signatures of a non-thermal metastable state in copropagating quantum Hall edge channels

Kosuke Itoh, Ryo Nakazawa, Tomoaki Ota, Masayuki Hashisaka, Koji Muraki, T. Fujisawa

Published Apr 7, 2018• 4 citations
arXivHTMLPDF

Abstract

A Tomonaga-Luttinger (TL) liquid is known as an integrable system, in which a non-equilibrium many-body state survives without relaxing to a thermalized state. This intriguing characteristic is tested experimentally in copropagating quantum Hall edge channels at bulk filling factor nu = 2. The unidirectional transport allows us to investigate the time evolution by measuring the spatial evolution of the electronic states. The initial state is prepared with a biased quantum point contact, and its spatial evolution is measured with a quantum-dot energy spectrometer. We find strong evidences for a non-thermal metastable state in agreement with the TL theory before the system relaxes to thermal equilibrium with coupling to the environment.

DOI
10.48550/arxiv.1804.02523

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A Tomonaga-Luttinger (TL) liquid is known as an integrable system, in which a non-equilibrium many-body state survives without relaxing to a thermalized state. This intriguing characteristic is tested experimentally in copropagating quantum Hall edge channels at bulk filling factor nu = 2. The unidirectional transport allows us to investigate the time evolution by measuring the spatial evolution of the electronic states. The initial state is prepared with a biased quantum point contact, and its spatial evolution is measured with a quantum-dot energy spectrometer. We find strong evidences for a non-thermal metastable state in agreement with the TL theory before the system relaxes to thermal equilibrium with coupling to the environment.
A Tomonaga-Luttinger (TL) liquid is known as an integrable system, in which a non-equilibrium many-body state survives without relaxing to a thermalized state.This intriguing characteristic is tested experimentally in copropagating quantum Hall edge channels at bulk filling factor ν = 2.The unidirectional transport allows us to investigate the time evolution by measuring the spatial evolution of the electronic states.The initial state is prepared with a biased quantum point contact, and its spatial evolution is measured with a quantum-dot energy spectrometer.We find strong evidences for a non-thermal metastable state in agreement with the TL theory before the system relaxes to thermal equilibrium with coupling to the environment.
A Tomonaga-Luttinger (TL) liquid is known as an integrable system, in which a nonequilibrium many-body state survives without relaxing to a thermalized state. This intriguing characteristic is tested experimentally in copropagating quantum Hall edge channels at bulk filling factor ν=2. The unidirectional transport allows us to investigate the time evolution by measuring the spatial evolution of the electronic states. The initial state is prepared with a biased quantum point contact, and its spatial evolution is measured with a quantum-dot energy spectrometer. We find strong evidence for a nonthermal metastable state in agreement with the TL theory before the system relaxes to thermal equilibrium with coupling to the environment.
Abstract Dynamics of integrable systems, such as Tomonaga-Luttinger (TL) liquids, is deterministic, and the absence of stochastic thermalization processes provides unique characteristics, such as long-lived non-thermal metastable states with many conserved quantities. Here, we show such non-thermal states can emerge even when the TL liquid is excited with extremely high-energy hot electrons in chiral quantum-Hall edge channels. This demonstrates the robustness of the integrable model against the excitation energy. Crossover from the single-particle hot electrons to the many-body TL liquid is investigated by using on-chip detectors with a quantum point contact and a quantum dot. The charge dynamics can be understood with a single-particle picture only for hot electrons. The resulting electron-hole plasma in the TL liquid shows a non-thermal metastable state, in which warm and cold electrons coexist without further thermalization. The multi-temperature constituents are attractive for transporting information with conserved quantities along the channels.
The existence of long-lived nonequilibrium states without showing thermalization, which has previously been demonstrated in time evolution of ultracold atoms, suggests the possibility of their spatial analog in transport behavior of interacting electrons in solid-state systems. Here we report long-lived nonequilibrium states in one-dimensional edge channels in the integer quantum Hall regime. An indirect heating scheme in a counterpropagating configuration is employed to generate a nontrivial binary spectrum consisting of high- and low-temperature components. This unusual spectrum is sustained even after traveling 5--$10\ensuremath{\mu}\mathrm{m}$, much longer than the length for electronic relaxation (about 0.$1\ensuremath{\mu}\mathrm{m})$, without showing significant thermalization. This observation is consistent with the integrable model of Tomonaga-Luttinger liquid. The long-lived spectrum implies that the system is well described by noninteracting plasmons, which are attractive for carrying information for a long distance.
This thesis deals with the study of transport properties of integer and fractional QH edge states and it is based on the work I performed during my Ph.D. studies. The focus of this thesis is on Luttinger liquids far from equilibrium and their relaxation dynamics. Since Boltzmann, a fundamental aspect of statistical mechanics has been the understanding of the emergence of an equilibrium state. Interactions play a crucial role in the thermalization process that drives a system through states described by the Gibbs equilibrium ensemble. Therefore, it seems counterintuitive that a strongly interacting system, such as the Luttinger liquid, should not present any relaxation dynamics. This peculiar fact is due to the integrability of the Luttinger model, i.e. the existence of an infinite number of conserved quantities that precludes the equilibration process. However, in the past few years it has become clear that integrable systems can present some kind of relaxation, even though not towards the Gibbs equilibrium ensemble. Remarkably, the necessity of correctly taking into account some particular non-equilibrium configurations, also revealed the necessity of modifying bosonization, a technique widely used to study strongly interacting systems in one dimension. In this work we focus on three different cases: • Relaxation of high energy electrons injected in a ν = 1/3 chiral Luttinger liquid and in a standard Luttinger liquid. • Heating and the emergence of effective temperatures in a Quantum Hall system at fractional filling fraction ν = 2/3 partitioned by a Quantum Point Contact. • Effect of relaxation on shot-noise measurement of the quasi-particle charge in a ν = 2 QH state.
Abstract Tomonaga–Luttinger liquids exhibit unique features that cannot be seen in ordinary Fermi liquids. Recent advancement in measurement techniques on 1D quantum Hall edge channels allows to reveal unique characteristics, such as spin‐charge separation and nonthermal metastable states. In this review, an overview of nonequilibrium dynamics in quantum‐Hall Tomonaga–Luttinger liquids is presented. After the introduction of a circuit model for collective excitations (bosons) in the system, transport eigenmodes in interaction‐ and disorder‐dominated regimes are discussed with time‐resolved charge measurements for the integer and fractional quantum Hall systems. Moreover, nonthermal steady states associated with the integrable model are studied with energy distribution functions obtained with a quantum dot spectrometer. These nontrivial dynamics can be extended to other 1D systems, including 2D topological insulators.