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arXiv:cond-mat/9804124 · Journal of the Physical Society of Japan

Landauer Conductance and Nonequilibrium Noise of One-Dimensional Interacting Electron Systems

Akira Shimizu

Published May 15, 1996• 33 citations
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Abstract

The conductance of one-dimensional interacting electron systems is calculated in a manner similar to Landauer's argument for non-interacting systems. Unlike in previous studies in which the Kubo formula was used, the conductance is directly evaluated as the ratio of current $J$ to the chemical potential difference $Δμ$ between right-going and left-going particles. It is shown that both $J$ and $Δμ$ are renormalized by electron-electron (e-e) interactions, but their ratio, the conductance, is not renormalized at all if the e-e interactions are the only scattering mechanism. It is also shown that nonequilibrium current fluctuation at low frequency is absent in such a case. These conclusions are drawn for both Fermi liquids (in which quasi-particles are accompanied with the backflow) and Tomonaga-Luttinger liquids.

DOI
10.1143/jpsj.65.1162

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Journal of the Physical Society of Japan•Jan 15, 1996•83 citations
The conductance of one-dimensional interacting electron systems is calculated in a manner similar to Landauer's argument for non-interacting systems. Unlike in previous studies in which the Kubo formula was used, the conductance is directly evaluated as the ratio of current JJJ to the chemical potential difference ΔμΔμΔμ between right-going and left-going particles. It is shown that both JJJ and ΔμΔμΔμ are renormalized by electron-electron (e-e) interactions, but their ratio, the conductance, is not renormalized at all if the e-e interactions are the only scattering mechanism. It is also shown that nonequilibrium current fluctuation at low frequency is absent in such a case. These conclusions are drawn for both Fermi liquids (in which quasi-particles are accompanied with the backflow) and Tomonaga-Luttinger liquids.
The conductance of one-dimensional interacting electron systems is calculated in a manner similar to Landauer's argument for non-interacting systems.Unlike in previous studies in which the Kubo formula was used, the conductance is directly evaluated as the ratio of current J to the chemical potential difference ∆µ between right-going and left-going particles.It is shown that both J and ∆µ are renormalized by electron-electron (e-e) interactions, but their ratio, the conductance, is not renormalized at all if the e-e interactions are the only scattering mechanism.It is also shown that nonequilibrium current fluctuation at low frequency is absent in such a case.These conclusions are drawn for both Fermi liquids (in which quasi-particles are accompanied with the backflow) and Tomonaga-Luttinger liquids.
Electron conduction in one-dimensional system is investigated explicitly taking into account the reservoirs to which 1D channel is connected at its ends. We calculate the current driven by the chemical potential difference of two reservoirs, using the linear response theory by Kubo. At 0K, the conductance of 1D channel is expressed in terms of one-electron Green's functions even in the presence of the interaction, in contrast to the theory based on Kubo formula, in which two-electron Green's functions are essentially involved. The formalism in this paper provides a new interpretation of Landauer formula. As regards the interaction effects, the conductance of Fermi liquid without potential scattering is 2 e 2 / h , while that of Tomonaga-Luttinger liquid deceases with power low as the length of 1D channel increases.
The transport in a pure one-dimensional quantum wire is investigated for any range of interactions. First, the wire is connected to measuring leads. The transmission of an incident electron is found to be perfect, i.e., the conductance is not renormalized by the interactions. Either Landauer's approach or the Kubo formula can be used as long as the reservoirs impose the boundary conditions. Second, the Kubo formula as a response to the local field is reconsidered in a generic Luttinger liquid: the ``intrinsic'' conductance thus obtained is determined by the same combination of interaction parameters as that which renormalizes the current.
We investigate the effect of electron-electron interactions on the conductance of quasi one-dimensional systems without potential scattering. For a finite temperature or system length, the short-range interaction is not renormalized to 0, and it gives rise to a finite correction to the conductance if we calculate it using Kubo formula. We show that this correction can be absorbed into the renormalization of the chemical potential and that the properly defined conductance to be observed in the experiments is equal to that of non-interacting electrons.
Current quantum noise can be pictured as a sum over transitions through which the electronic system exchanges energy with its environment. We formulate this picture and use it to show which type of current correlators are measurable, and in what measurement the zero point fluctuations will play a role (the answer to the latter is as expected: only if the detector excites the system.) Using the above picture, we calculate and give physical interpretation of the finite-frequency finite-temperature current noise in a noninteracting Landauer-type system, where the chemical potentials of terminals 1 and 2 are μ+eV/2μ+eV/2μ+eV/2 and μ−eV/2μ-eV/2μ−eV/2 respectively, and derive a detailed-balance condition for this nonequilibrium system. Finally, we derive a generalized form of the Kubo formula for a wide class of interacting nonequilibrium systems, relating the differential conductivity to the current noise.