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Europhysics Letters (EPL)

Interaction-enhanced interference effects in a Luttinger liquid

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

Published Feb 1, 2002• 3 citations
Publisher

Abstract

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.

DOI
10.1209/epl/i2002-00476-x

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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.
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Dynamics of one-dimensional electron transport between two reservoirs are studied based on the inhomogeneous Tomonaga-Luttinger-liquid model in the case when the effect of the electron backscattering on the impurities is negligible. The inhomogeneities of the interaction lead to a charge-wave reflection. This effect supposes a special behavior of the transport characteristics at the microwave frequencies. Different features are predicted in the current noise spectrum and in the ac frequency dependence. \textcopyright{} 1996 The American Physical Society.
We investigate the effects of the electron-electron interactions on the quantum transport through a charge Kondo circuit. The setup consists of a quantum dot sandwiched between two leads by two nearly transparent single mode quantum point contacts. The size of the interacting area LLL in the Luttinger liquid formed in the vicinities of the narrow constrictions is assumed to be much smaller compared to the size of the quantum dot aaa. We predict that the interplay between the electron-electron interactions in the Luttinger liquid and the fingerprints of the non-Fermi liquid behavior in the vicinity of the two channel Kondo intermediate coupling fixed point allows one to determine the interaction strength through the power-law temperature scaling of the electric conductance.
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 low-temperature AC conductance of a one-dimensional electron system with a strong interaction of finite range is calculated by using linear response theory. The conductance factorizes into parts which depend on the internal properties of the system, and the external probe. For short-range interaction, the result resembles that for non-interacting electrons, but with the zero-frequency limit and the Fermi velocity renormalized by the interaction strength. For strong and long-range interaction, the conductance shows a peak that is related to charge-wave excitations. In this limit, the AC conductance can be simulated by a quantum capacitance and a quantum inductance .
We study the transport properties of a Luttinger liquid in the presence of several time-dependent weak pointlike impurities. Our starting point is the bosonized form of the Luttinger liquid Hamiltonian with a potential introduced by the impurities. We find the correction to the total current due to the backscattering of the electrons by the impurities in first order of perturbation theory for a general time-dependent impurity potential. We then apply this result to a single time-dependent impurity, and show that it reproduces the result obtained by Feldman and Gefen [Phys. Rev. B 67, 115337 (2003)], in particular that the current enhancement occurs only for strong repulsive electron-electron interactions. For the case of two impurities oscillating with the same frequency, we find that the dc component of the backscattering current is positive even for weak repulsive interactions, due to the presence of the interference term induced by spatial correlations in the Luttinger liquid. We show that the impurity frequencies at which the enhancement takes place form a bandlike structure. In the case of several impurities, the bands become broader, because of interference effects.