Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0910.3917 · Physical Review B

Tunneling into a nonequilibrium Luttinger liquid with impurity

Stéphane Ngo Dinh, Dmitry Bagrets, A. D. Mirlin

Published Feb 24, 2010• 31 citations
arXivHTMLPDF

Abstract

We evaluate tunneling rates into/from a voltage $(U)$ biased quantum wire containing a weak backscattering defect. Interacting electrons in such a wire form a true nonequilibrium state of the Luttinger liquid (LL). This state is created due to inelastic electron backscattering leading to the emission of nonequilibrium plasmons with typical frequency $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\le}U$. The tunneling rates are split in two edges. The tunneling exponent at the Fermi edge is positive and equals that of the equilibrium LL, while the exponent at the side edge ${E}_{F}\ensuremath{-}U$ is negative if Coulomb interaction is not too strong.

DOI
10.1103/physrevb.81.081306

Related papers

Bosonization of Nonequilibrium Quantum Wire Networks

Ngo Dinh, Stéphane

We develop a general approach to nonequilibrium nanostructures formed by one-dimensional channels coupled by tunnel junctions and/or by impurity scattering. As important applications of the formalism we consider tunneling into a voltage-biased quantum wire containing weak backscattering defects, electronic Fabry-Pérot and Mach-Zehnder interferometers realized in the integer quantum Hall systems, and the relaxation dynamics of a nonequilibrium Luttinger liquid after an interaction quench.

•Jan 1, 2013•0 citations

Nonequilibrium kinetics of a disordered Luttinger liquid

Д. А. Багрец, I. V. Gornyi, Dmitry G. Polyakov

We develop a kinetic theory for strongly correlated disordered one-dimensional electron systems out of equilibrium within the Luttinger liquid model. In the absence of inhomogeneities, the model exhibits no relaxation to equilibrium. We derive kinetic equations for electron and plasmon distribution functions in the presence of impurities and calculate the equilibration rate ${\ensuremath{\gamma}}_{E}$. Remarkably, for not too low temperature and bias voltage, ${\ensuremath{\gamma}}_{E}$ is given by the elastic backscattering rate $\ensuremath{\gamma}$: the ratio ${\ensuremath{\gamma}}_{E}/\ensuremath{\gamma}\ensuremath{\sim}1$ is independent of the strength of electron-electron interaction, temperature, and bias.

arXiv:0809.3166•Physical Review B•Sep 21, 2009•15 citations

Tunneling spectroscopy of Luttinger-liquid structures far from equilibrium

Dmitri B. Gutman, Yuval Gefen, A. D. Mirlin

We develop a theory of tunneling spectroscopy of interacting electrons in a nonequilibrium quantum wire coupled to reservoirs. The problem is modeled as an out-of-equilibrium Luttinger liquid with spatially dependent interaction. The interaction leads to the renormalization of the tunneling density of states, as well as to the redistribution of electrons over energies. Energy relaxation is controlled by plasmon scattering at the boundaries between regions with different interaction strengths and affects the distribution function of electrons in the wire as well as that of electrons emitted from the interacting regions into noninteracting electrodes.

arXiv:0903.3333•Physical Review B•Jul 8, 2009•43 citations

Relaxation processes in a disordered Luttinger liquid

Д. А. Багрец, I. V. Gornyi, A. D. Mirlin +1 more

The Luttinger liquid model, which describes interacting electrons in a single-channel quantum wire, is completely integrable in the absence of disorder and as such does not exhibit any relaxation to equilibrium. We consider relaxation processes induced by inelastic electron-electron interactions in a disordered Luttinger liquid, focusing on the equilibration rate and its essential differences from the electron-electron scattering rate as well as the rate of phase relaxation. In the first part of the paper, we review the basic concepts in a disordered Luttinger liquid at equilibrium. These include the elastic renormalization, dephasing, and interference-induced localization. In the second part, we formulate a conceptually important framework for systematically studying the nonequilibrium properties of a strongly correlated (non-Fermi) Luttinger liquid. We derive a coupled set of kinetic equations for the fermionic and bosonic distribution functions that describe the evolution of a nonequilibrium Luttinger liquid. Remarkably, the energy equilibration rate in the conducting disordered quantum wire (at sufficiently high temperature, when the localization effects are suppressed by dephasing) is shown to be on the order of the rate of elastic scattering off disorder, independent of the interaction constant and temperature.

arXiv:0804.4887•Semiconductors•Aug 1, 2008•16 citations

Quantum Wire Hybridized With a Single-Level Impurity

Igor V. Lerner, Vladimir I. Yudson, I. V. Yurkevich

We have studied low-temperature properties of interacting electrons in a one-dimensional quantum wire (Luttinger liquid) side-hybridized with a single-level impurity. The hybridization induces a backscattering of electrons in the wire which strongly affects its low-energy properties. Using a one-loop renormalization group approach valid for a weak electron-electron interaction, we have calculated a transmission coefficient through the wire, T(epsilon), and a local density of states, nu(epsilon) at low energies epsilon. In particular, we have found that the antiresonance in T(epsilon) has a generalized Breit-Wigner shape with the effective width Gamma(epsilon) which diverges at the Fermi level.

arXiv:0711.4919•Physical Review Letters•Jun 27, 2008•42 citations

Nonequilibrium electron spectroscopy of Luttinger liquids

So Takei, Mirco Milletarì, Bernd Rosenow

We theoretically study a Luttinger liquid (LL) driven out of equilibrium by injection of high-energy electrons. The electrons are injected into the LL locally at a fixed energy and their spectral properties are detected at another spatial point some distance away by evaluating the average tunneling current from the LL into a resonant level with tunable energy. For energies slightly below the injection energy, the dependence of the detected current on the difference between injection, and detection energies is described by a power law whose exponent depends continuously on the Luttinger parameter. In contrast, for tunneling into a chiral LL edge of a fractional quantum-Hall state from the Laughlin sequence, we find that the detected current grows linearly with energy difference, despite a decreasing density of states.

arXiv:0912.3530•Physical Review B•Jul 22, 2010•29 citations
We evaluate tunneling rates into/from a voltage (U)(U)(U) biased quantum wire containing a weak backscattering defect. Interacting electrons in such a wire form a true nonequilibrium state of the Luttinger liquid (LL). This state is created due to inelastic electron backscattering leading to the emission of nonequilibrium plasmons with typical frequency \ensuremathℏ\ensuremathω\ensuremath≤U\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\le}U\ensuremathℏ\ensuremathω\ensuremath≤U. The tunneling rates are split in two edges. The tunneling exponent at the Fermi edge is positive and equals that of the equilibrium LL, while the exponent at the side edge EF\ensuremath−U{E}_{F}\ensuremath{-}UEF​\ensuremath−U is negative if Coulomb interaction is not too strong.
We develop a kinetic theory for strongly correlated disordered one-dimensional electron systems out of equilibrium within the Luttinger liquid model. In the absence of inhomogeneities, the model exhibits no relaxation to equilibrium. We derive kinetic equations for electron and plasmon distribution functions in the presence of impurities and calculate the equilibration rate ${\ensuremath{\gamma}}_{E}$. Remarkably, for not too low temperature and bias voltage, ${\ensuremath{\gamma}}_{E}$ is given by the elastic backscattering rate $\ensuremath{\gamma}$: the ratio ${\ensuremath{\gamma}}_{E}/\ensuremath{\gamma}\ensuremath{\sim}1$ is independent of the strength of electron-electron interaction, temperature, and bias.
We develop a theory of tunneling spectroscopy of interacting electrons in a nonequilibrium quantum wire coupled to reservoirs. The problem is modeled as an out-of-equilibrium Luttinger liquid with spatially dependent interaction. The interaction leads to the renormalization of the tunneling density of states, as well as to the redistribution of electrons over energies. Energy relaxation is controlled by plasmon scattering at the boundaries between regions with different interaction strengths and affects the distribution function of electrons in the wire as well as that of electrons emitted from the interacting regions into noninteracting electrodes.
The Luttinger liquid model, which describes interacting electrons in a single-channel quantum wire, is completely integrable in the absence of disorder and as such does not exhibit any relaxation to equilibrium. We consider relaxation processes induced by inelastic electron-electron interactions in a disordered Luttinger liquid, focusing on the equilibration rate and its essential differences from the electron-electron scattering rate as well as the rate of phase relaxation. In the first part of the paper, we review the basic concepts in a disordered Luttinger liquid at equilibrium. These include the elastic renormalization, dephasing, and interference-induced localization. In the second part, we formulate a conceptually important framework for systematically studying the nonequilibrium properties of a strongly correlated (non-Fermi) Luttinger liquid. We derive a coupled set of kinetic equations for the fermionic and bosonic distribution functions that describe the evolution of a nonequilibrium Luttinger liquid. Remarkably, the energy equilibration rate in the conducting disordered quantum wire (at sufficiently high temperature, when the localization effects are suppressed by dephasing) is shown to be on the order of the rate of elastic scattering off disorder, independent of the interaction constant and temperature.
We have studied low-temperature properties of interacting electrons in a one-dimensional quantum wire (Luttinger liquid) side-hybridized with a single-level impurity. The hybridization induces a backscattering of electrons in the wire which strongly affects its low-energy properties. Using a one-loop renormalization group approach valid for a weak electron-electron interaction, we have calculated a transmission coefficient through the wire, T(epsilon), and a local density of states, nu(epsilon) at low energies epsilon. In particular, we have found that the antiresonance in T(epsilon) has a generalized Breit-Wigner shape with the effective width Gamma(epsilon) which diverges at the Fermi level.
We theoretically study a Luttinger liquid (LL) driven out of equilibrium by injection of high-energy electrons. The electrons are injected into the LL locally at a fixed energy and their spectral properties are detected at another spatial point some distance away by evaluating the average tunneling current from the LL into a resonant level with tunable energy. For energies slightly below the injection energy, the dependence of the detected current on the difference between injection, and detection energies is described by a power law whose exponent depends continuously on the Luttinger parameter. In contrast, for tunneling into a chiral LL edge of a fractional quantum-Hall state from the Laughlin sequence, we find that the detected current grows linearly with energy difference, despite a decreasing density of states.