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Physical review. B, Condensed matter

Interchannel electron transitions in a Luttinger liquid

Ilya V. Krive, S. I. Kulinich, L. Y. Gorelik, Robert I Shekhter, M. Jonson

Published Jul 6, 2001• 8 citations
Publisher

Abstract

Intermode electron transitions in a two-channel Luttinger liquid (LL) are considered. At first we study chiral LL and show that for a long-range Coulomb interaction even forward-scattering intermode electron transitions are strongly renormalized by interaction at low energies. For a short-range interaction the renormalization of the electron transition rates in a chiral LL do not depend on the energy (temperature, bias voltage) involved in the tunneling process. We show, however, that the interference effects are sensitive to the strength of electron interaction, and they are significantly enhanced for strongly correlated electrons. The analyses of the intermode electron transitions is generalized for a nonchiral two-channel LL. The forward- and the backward-scattering interchannel electron transition rates are calculated and their connection to the problem of x-ray singularity in a LL is elucidated.

DOI
10.1103/physrevb.64.045114

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Modern Physics Letters B•Feb 28, 1995•0 citations
Intermode electron transitions in a two-channel Luttinger liquid (LL) are considered. At first we study chiral LL and show that for a long-range Coulomb interaction even forward-scattering intermode electron transitions are strongly renormalized by interaction at low energies. For a short-range interaction the renormalization of the electron transition rates in a chiral LL do not depend on the energy (temperature, bias voltage) involved in the tunneling process. We show, however, that the interference effects are sensitive to the strength of electron interaction, and they are significantly enhanced for strongly correlated electrons. The analyses of the intermode electron transitions is generalized for a nonchiral two-channel LL. The forward- and the backward-scattering interchannel electron transition rates are calculated and their connection to the problem of x-ray singularity in a LL is elucidated.
Microwave-induced interchannel electron transitions in a Luttinger liquid irradiated by an ac electromagnetic field are considered. It is shown that oscillations in the power absorption caused by the interference of charge transport along the two channels are controlled by the effective coupling strength κ = V 0 /πℏ( v 1F − v 2F ), which strongly depends on the difference between the Fermi velocities v 1F ≠ v 2F in the channels. Interactions always enhance the interference effects induced by forward-scattering interchannel electron transitions. A novel regime of the statistical behavior of the fluctuations in power absorption is predicted.
The theoretical model of the short-range interacting Luttinger liquid predicts a power-law scaling of the density of states and the momentum distribution function around the Fermi surface, which can be readily tested through tunneling experiments. However, some physical systems have long-range interaction, most notably the Coulomb interaction, leading to significantly different behaviors from the short-range interacting system. In this paper, we revisit the tunneling theory for the one-dimensional electrons interacting via the long-range Coulomb force. We show that even though in a small dynamic range of temperature and bias voltage, the tunneling conductance may appear to have a power-law decay similar to short-range interacting systems, the effective exponent is scale-dependent and slowly increases with decreasing energy. This factor may lead to the sample-to-sample variation in the measured tunneling exponents. We also discuss the crossover to a free Fermi gas at high energy and the effect of the finite size. Our work demonstrates that experimental tunneling measurements in one-dimensional electron systems should be interpreted with great caution when the system is a Coulomb Luttinger liquid.
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.
The nonlinear charge transfer through a tunnel junction between two Luttinger systems is studied for repulsive, finite-range interaction between electrons on the same side, V11{\mathrm{V}}_{11}V11​, and on different sides, V12{\mathrm{V}}_{12}V12​, of a junction. Features of the Coulomb blockade effect are observed if V12{\mathrm{V}}_{12}V12​=0. We predict an interaction-induced enhancement of the current if V12{\mathrm{V}}_{12}V12​>0. When V12{\mathrm{V}}_{12}V12​=V11{\mathrm{V}}_{11}V11​, the current is suppressed at small bias, but the ``charging energy,'' obtained from the asymptotic behavior at high-bias voltage, vanishes.
We review some of our recent results on the potential scattering in a weakly interacting one-dimensional(1D) electron gas. The technique we developed is a poor man's renormalization group procedure in the scattered wave basis. This technique can treat the renormalizations of the scattering on the barrier and the scattering between the electrons in a coherent way, and it allows us to find the scattering amplitudes on a localized potential of arbitrary strength for electrons at any energy. The obtained phase shifts are used to study the Fermi-edge singularity in an interacting 1D electron system, where anomalous exponent of the power-law singularity in the vicinity of the edge is found. The transmission coefficient is directly related to the conductance of a 1D channel by the Landauer formula. Simple formulas that describe the conductance at any temperature are derived. In spin-[Formula: see text] systems, the electron–electron backscattering induces renormalizations of the interaction constants, which causes the low-temperature conductance to deviate from the results of the Luttinger liquid theory. In particular, the temperature dependence of the conductance may become nonmonotonic. In the presence of a magnetic field, backscattering gives rise to a peak in the differential conductance at bias equal to the Zeeman splitting.