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arXiv:cond-mat/9711082

Transport in a one-dimensional wire connected to leads and proximity effects

Inès Safi A, Heinz J. Schulz

Published Nov 10, 1997• 0 citations
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Abstract

We investigate transport through a finite interacting wire connected to noninteracting leads. The conductance of the pure wire is not renormalized by the interactions for any spatial variation of the interaction parameters $u,K$, and not even for Coulomb interactions restricted to the wire. We rigorously relate the conductance to the transmission, that turns out to be perfect. If $K$ varies abruptly at the contacts, an electron incident on the wire is reflected into a series of partial spatially separated charges which sum up to unity. For attractive interactions, the reflection at the contact is similar to Andreev reflection on a gapless superconductor. This process affects the density-density or pairing correlation functions: they are enhanced on the bulk of the wire as in an infinite Luttinger liquid, then extend to the external noninteracting leads in a way reminiscent of the proximity effect. The effect of impurities is governed by the wire parameter but is affected by the leads close to the contacts. Our results give a possible explanation to recent experiments on quantum wires by Tarucha et al.

DOI
10.48550/arxiv.cond-mat/9711082

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We investigate transport through a finite interacting wire connected to noninteracting leads. The conductance of the pure wire is not renormalized by the interactions for any spatial variation of the interaction parameters u,Ku,Ku,K, and not even for Coulomb interactions restricted to the wire. We rigorously relate the conductance to the transmission, that turns out to be perfect. If KKK varies abruptly at the contacts, an electron incident on the wire is reflected into a series of partial spatially separated charges which sum up to unity. For attractive interactions, the reflection at the contact is similar to Andreev reflection on a gapless superconductor. This process affects the density-density or pairing correlation functions: they are enhanced on the bulk of the wire as in an infinite Luttinger liquid, then extend to the external noninteracting leads in a way reminiscent of the proximity effect. The effect of impurities is governed by the wire parameter but is affected by the leads close to the contacts. Our results give a possible explanation to recent experiments on quantum wires by Tarucha et al.
Transport through a one-dimensional wire of interacting electrons connected to semi infinite leads is investigated using a bosonization approach. The dynamic nonlocal conductivity is rigorously expressed in terms of the transmission. For abrupt variations of the interaction parameters at the junctions, an incident electron is transmitted as a sequence of partial charges: the central wire acts as a Fabry-Perot resonator. The dc conductance is shown to be given by the total transmission which turns out to be perfect. When the wire has a tendency towards superconducting order, partial Andreev reflection of an incident electron occurs. Finally, we study the role of a weak barrier at one contact or inside the wire by a renormalization group method at finite temperature. We compute the conductance in the presence of localized or extended disorder, and compare our results to recent experiments on quantum wires.
We investigate how the conductance GGG through a clean interacting quantum wire is affected by the presence of contacts and noninteracting leads. The contacts are defined by a vanishing two-particle interaction to the left and a finite repulsive interaction to the right or vice versa. No additional single-particle scattering terms (impurities) are added. We first use Bosonization and the local Luttinger liquid picture and show that within this approach GGG is determined by the properties of the leads regardless of the details of the spatial variation of the Luttinger liquid parameters. This generalizes earlier results obtained for steplike variations. In particular, no single-particle backscattering is generated at the contacts. We then study a microscopic model applying the functional renormalization group and show that the spatial variation of the interaction produces single-particle backscattering, which in turn leads to a reduced conductance. We investigate how the smoothness of the contacts affects GGG and show that for decreasing energy scale its deviation from the unitary limit follows a power law with the same exponent as obtained for a system with a weak single-particle impurity placed in the contact region of the interacting wire and the leads.
Transport through a clean one-dimensional wire of interacting electrons connected to semi-infinite leads is investigated using a bosonization approach. An incident electron is transmitted as a sequence of partial charges. The dc conductance is found to be entirely determined by the properties of the leads. The dynamic nonlocal conductivity is rigorously expressed in terms of the transmission. For abrupt variations of the interaction parameters at the junctions, the central wire acts as a Fabry-P\'erot resonator. When one of the connected wires has a tendencey towards superconducting order, partial Andreev reflection of an incident electron occurs.
We investigate a one-dimensional wire of interacting electrons connected to one-dimensional noninteracting leads in the absence and in the presence of a backscattering potential. The ballistic wire separates the charge and spin parts of an incident electron even in the noninteracting leads. The Fourier transform of nonlocal correlation functions is computed for $T\ensuremath{\gg}\ensuremath{\omega}$. In particular, this allows to study the proximity effect, related to the Andreev reflection. In addition, a new type of proximity effect emerges when the wire has normally a tendency towards Wigner crystal formation. The latter is suppressed by the leads below a space-dependent crossover temperature; it gets dominated everywhere by the 2kF{2k}_{F}2kF​ charge-density wave at $T<{L}^{(3/2)(K\ensuremath{-}1)}$ for short-range interactions with parameter K<1/3K<1/3K<1/3. The lowest-order renormalization equations of a weak backscattering potential are derived explicitly at finite temperature. A perturbative expression for the conductance in the presence of a potential with arbitrary spatial extension is given. It depends on the interactions, but is also affected by the noninteracting leads, especially for very repulsive interactions, K<1/3K<1/3K<1/3. This leads to various regimes, depending on temperature and on KKK. For randomly distributed weak impurities, the conductance fluctuations, equal to that of $\mathcal{R}=g\ensuremath{-}{2e}^{2}/h$, are computed. They depend on the interaction parameters, and are different for electrons with or without spin. But the ratio Var(R)/R2\mathrm{Var}(\mathcal{R})/{\mathcal{R}}^{2}Var(R)/R2 stays always of the same order: it is equal to ${L}_{T}/L\ensuremath{\ll}1$ in the high-temperature limit, then saturates at 1/21/21/2 in the low-temperature limit, indicating that the relative fluctuations of R\mathcal{R}R are universal.
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.
The conductance G of an interacting nano-wire containing an impurity and coupled to non-interacting semi-infinite leads is studied using a functional renormalization group method. We obtain results for microscopic lattice models without any further idealizations. For an interaction which is turned on smoothly at the contacts we show that one-parameter scaling of G holds. If abrupt contacts are included, we find power law suppression of G with an exponent which is twice as large as the one obtained for smooth contacts and no one-parameter scaling. Our results show excellent agreement with the analytically known scaling function at Luttinger liquid parameter K = 1/2 and numerical density matrix renormalization group data.