Nonequilibrium kinetics of a disordered Luttinger liquid

Bagrets, Dmitry; Gornyi, I. V.; Polyakov, D. G.

doi:10.1103/physrevb.80.113403

Cited by 14 publications

(4 citation statements)

References 33 publications

(50 reference statements)

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“…In long samples the conductance is not observed to be quantized [7] indicating that backscattering processes occur between the counterpropagating edge channels. It was found that in the limit eV k B T the resistance is independent on temperature between 20 mK -4.2 K and it increases linearly with the edge length L. These observations are not surprising once the elastic backscattering processes are allowed and large voltage is applied, because under these conditions the inelastic scattering rate is expected to be approximately equal to the elastic one [33], and therefore the localization effects can be neglected and the resistance is expected to be temperature independent. In the QSH phase the elastic backscattering is forbidden in the presence of time-reversal symmetry due to the topological protection, so these observations are not consistent with the system being in the QSH phase without additional assumption about the existence of charge puddles that may lead to enhanced backscattering rate [34].…”

Section: Length Temperature and Voltage Dependence Of The Conductancementioning

confidence: 95%

Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers I: Transport properties

Paul¹,

Becerra²,

Hyart³

2022

Preprint

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The band-inverted electron-hole bilayers, such as InAs/GaSb, are an interesting playground for the interplay of quantum spin Hall effect and correlation effects because of the small density of electrons and holes and the relatively small hybridization between the electron and hole bands. It has been proposed that Coulomb interactions lead to a time-reversal symmetry broken phase when the electron and hole densities are tuned from the trivial to the quantum spin Hall insulator regime. We show that the transport properties of the system in the time-reversal symmetry broken phase are consistent with the recent experimental observations in InAs/GaSb. Moreover, we carry out a quantum transport study on a Corbino disc where the bulk and edge contributions to the conductance can be separated. We show that the edge becomes smoothly conducting and the bulk is always insulating when one tunes the system from the trivial to the quantum spin Hall insulator phase, providing unambiguous transport signatures of the time-reversal symmetry broken phase.

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Section: Length Temperature and Voltage Dependence Of The Conductancementioning

confidence: 95%

Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers I: Transport properties

Paul¹,

Becerra²,

Hyart³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Defining signatures of a LL such as spin-charge separation [6,7], charge fractionalization [8,9], and the power-law suppression of the local electron tunneling density of states [10,11,12,13,14] have been experimentally verified. Recently, LLs driven far from equilibrium have begun to receive attention [15,16,17,18]. Studying these systems offers the possibility to characterize novel aspects of electron-electron interactions and to understand energy relaxation processes that have not been apparent in the above-mentioned equilibrium experiments.…”

mentioning

confidence: 99%

Nonequilibrium electron spectroscopy of Luttinger liquids

2010

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Understanding the effects of nonequilibrium on strongly interacting quantum systems is a challenging problem in condensed matter physics. In dimensions greater than one, interacting electrons can often be understood within Fermi-liquid theory where low-energy excitations are weakly interacting quasiparticles. On the contrary, electrons in one dimension are known to form a strongly-correlated phase of matter called a Luttinger liquid (LL), whose low-energy excitations are collective density waves, or plasmons, of the electron gas. Here we show that spectroscopy of locally injected high-energy electrons can be used to probe energy relaxation in the presence of such strong correlations. For detection energies near the injection energy, the electron distribution is described by a power law whose exponent depends in a continuous way on the Luttinger parameter, and energy relaxation can be attributed to plasmon emission. For a chiral LL as realized at the edge of a fractional quantum Hall state, the distribution function grows linearly with the distance to the injection energy, independent of filling fraction.Over the last decade, experimental advances in nanostructure fabrication have brought a resurgence of interest in the LL model because of the possibility to test its peculiar predictions [1,2,3,4,5]. Defining signatures of a LL such as spin-charge separation [6,7], charge fractionalization [8,9], and the power-law suppression of the local electron tunneling density of states [10,11,12,13,14] have been experimentally verified. Recently, LLs driven far from equilibrium have begun to receive attention [15,16,17,18]. Studying these systems offers the possibility to characterize novel aspects of electron-electron interactions and to understand energy relaxation processes that have not been apparent in the above-mentioned equilibrium experiments.Here we consider a LL driven out of equilibrium by local injection of high-energy electrons, far away from any contacts, at a fixed energy. Their spectral properties are extracted at another spatial point some distance away by evaluating the average tunneling current from the LL into an empty resonant level with tunable energy. In this work, we consider both standard (non-chiral) and chiral LLs, which are realized at the edge of fractional quantum Hall systems [3,4,12,13,14].For the standard LL and for probe energies slightly below the injection energy, we find that the inelastic component of the current shows a power law behavior as a function of the difference between injection and detection energy, with an exponent that continuously evolves as the interaction parameter is varied. We develop a perturbative approach which shows how injected electrons can relax by emitting plasmons inside the wire.For a chiral LL at the edge of a fractional quantum Hall state from the Laughlin sequence, an essentially exact calculation of the tunneling current is possible. Here, the inelastic part of the electron current increases in a linear fashion as the probe energy is lowered from the inje...

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“…In long samples, the conductance is not observed to be quantized [7], indicating that backscattering processes occur between the counterpropagating edge channels. It was found that in the limit eV k B T , the resistance is independent on temperature between 20 mK-4.2 K and it increases linearly with the edge length L. These observations are not surprising once the elastic backscattering processes are allowed and large voltage is applied, because under these conditions the inelastic scattering rate is expected to be approximately equal to the elastic one [35] and therefore the localization effects can be neglected and the resistance is expected to be temperature independent. In the QSH phase, the elastic backscattering is forbidden in the presence of TRS due to the topological protection, so these observations are not consistent with the system being in the QSH phase without additional assumptions about the existence of charge puddles that may lead to enhanced backscattering rate [36].…”

Section: Length Temperature and Voltage Dependence Of The Conductancementioning

confidence: 96%

Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers. I. Transport properties

2022

View full text Add to dashboard Cite

The band-inverted electron-hole bilayers, such as InAs/GaSb, are an interesting playground for the interplay of quantum spin Hall effect and correlation effects because of the small density of electrons and holes and the relatively small hybridization between the electron and hole bands. It has been proposed that Coulomb interactions lead to a time-reversal symmetry broken phase when the electron and hole densities are tuned from the trivial to the quantum spin Hall insulator regime. We show that the transport properties of the system in the time-reversal symmetry broken phase are consistent with recent experimental observations in InAs/GaSb. Moreover, we carry out a quantum transport study on a Corbino disk where the bulk and edge contributions to the conductance can be separated. We show that the edge becomes smoothly conducting and the bulk is always insulating when one tunes the system from the trivial to the quantum spin Hall insulator phase, providing unambiguous transport signatures of the time-reversal symmetry broken phase.

show abstract

Nonequilibrium kinetics of a disordered Luttinger liquid

Cited by 14 publications

References 33 publications

Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers I: Transport properties

Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers I: Transport properties

Nonequilibrium electron spectroscopy of Luttinger liquids

Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers. I. Transport properties

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