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arXiv:0710.4585 · Physical Review Letters

Resistivity of Inhomogeneous Quantum Wires

Jérôme Rech, К. А. Матвеев

Published Feb 15, 2008• 32 citations
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Abstract

We study the effect of electron-electron interactions on the transport in an inhomogeneous quantum wire. We show that contrary to the well-known Luttinger liquid result, nonuniform interactions contribute substantially to the resistance of the wire. In the regime of weakly interacting electrons and moderately low temperatures we find a linear in T resistivity induced by the interactions. We then use the bosonization technique to generalize this result to the case of arbitrarily strong interactions.

DOI
10.1103/physrevlett.100.066407

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We study the effect of electron-electron interactions on the transport in an inhomogeneous quantum wire. We show that contrary to the well-known Luttinger liquid result, nonuniform interactions contribute substantially to the resistance of the wire. In the regime of weakly interacting electrons and moderately low temperatures we find a linear in T resistivity induced by the interactions. We then use the bosonization technique to generalize this result to the case of arbitrarily strong interactions.
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We study the transport properties of long quantum wires by generalizing the Luttinger liquid approach to allow for the finite lifetime of the bosonic excitations. Our theory accounts for long-range disorder and strong electron interactions, both of which are common features of experiments with quantum wires. We obtain the electrical and thermal resistances and thermoelectric properties of such quantum wires and find a strong deviation from perfect conductance quantization. We cast our results in terms of the thermal conductivity and bulk viscosity of the electron liquid and give the temperature scale above which the transport can be described by classical hydrodynamics.
We study the effect that resistive regions have on the conductance of a quantum wire with interacting electrons which is connected to Fermi liquid leads. Using the bosonization formalism and a Rayleigh dissipation function to model the power dissipation, we use both scattering theory and Green's function techniques to derive the DC conductance. The resistive regions are generally found to lead to incoherent transport. For a single wire, we find that the resistance adds in series to the contact resistance of h / e 2 for spinless electrons, and the total resistance is independent of the Luttinger parameter K W of the wire. We numerically solve the bosonic equations to illustrate what happens when a charge density pulse is incident on the wire; the results depend on the parameters of the resistive and interacting regions in interesting ways. For a junction of Tomonaga-Luttinger liquid wires, we use a dissipationless current splitting matrix to model the junction. For a junction of three wires connected to Fermi liquid leads, there are two families of such matrices; we find that the conductance matrix generally depends on K W for one family but is independent of K W for the other family, regardless of the resistances present in the system.
We study the effect that resistive regions have on the conductance of a quantum wire with interacting electrons which is connected to Fermi liquid leads. Using the bosonization formalism and a Rayleigh dissipation function to model the power dissipation, we use both scattering theory and Green's function techniques to derive the DC conductance. The resistive regions are generally found to lead to incoherent transport. For a single wire, we find that the resistance adds in series to the contact resistance of h/e(2) for spinless electrons, and the total resistance is independent of the Luttinger parameter K-W of the wire. We numerically solve the bosonic equations to illustrate what happens when a charge density pulse is incident on the wire; the results depend on the parameters of the resistive and interacting regions in interesting ways. For a junction of Tomonaga-Luttinger liquid wires, we use a dissipationless current splitting matrix to model the junction. For a junction of three wires connected to Fermi liquid leads, there are two families of such matrices; we find that the conductance matrix generally depends on K-W for one family but is independent of K-W for the other family, regardless of the resistances present in the system. Copyright (c) EPLA, 2011
We use the technique of bosonization to understand a variety of recent experimental results on the conductivity of a quantum wire. The quantum wire is taken to be a finite-length Luttinger liquid connected on two sides to semi-infinite Fermi liquids through contacts. The contacts are modeled as (short) Luttinger liquids bounded by localized one-body potentials. We use effective actions and the renormalization group to study the effects of electronic interactions within the wire, the length of the wire, finite temperature, and a magnetic field, on the conductivity. We explain the deviations of the conductivity from 2Ne2/h{2Ne}^{2}/h2Ne2/h in wires that are not too short as arising from renormalization effects caused by the repulsive interactions. We also explain the universal conductance corrections observed in different channels at higher temperatures. We study the effects of an external magnetic field on electronic transport through this system and explain why odd and even spin-split bands show different renormalizations from the universal conductance values. We discuss the case of resonant transmission and of the possibility of producing a spin valve that only allows electrons of one value of the spin to go through. We compare our results for the conductance corrections with experimental observations. We also propose an experimental test of our model of the contact regions.
We study electron and spin transport in interacting quantum wires contacted by noninteracting leads. We theoretically model the wire and junctions as an inhomogeneous chain where the parameters at the junction change on the scale of the lattice spacing. We study such systems analytically in the appropriate limits based on Luttinger liquid theory and compare the results to quantum Monte Carlo calculations of the conductances and local densities near the junction. We first consider an inhomogeneous spinless fermion model with a nearest-neighbor interaction and then generalize our results to a spinful model with an on-site Hubbard interaction.