Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1204.2565 · Physical Review B

Transport and scattering in inhomogeneous quantum wires

Nicholas Sedlmayr, Jan Peter Ohst, Ian K. Affleck, Jesko Sirker, Sebastian Eggert

Published Sep 6, 2012• 20 citations
arXivHTMLPDF

Abstract

We consider scattering and transport in interacting quantum wires that are connected to leads. Such a setup can be represented by a minimal model of interacting fermions with sudden changes in interaction strength and/or velocity. The inhomogeneities generally cause relevant backscattering, so it is a priori unclear if perfect ballistic transport is possible in the low-temperature limit. We demonstrate that a conducting fixed point surprisingly exists even for large abrupt changes, which in the considered model corresponds to a velocity-matching condition. The general position-dependent Green's function is calculated in the presence of a sudden change, and is confirmed numerically with high accuracy. The exact form of the interference pattern in the form of density oscillations around inhomogeneities can be used to estimate the effective strength of local backscattering sources, offering a route to design experiments where the effects of the contacts are minimized.

DOI
10.1103/physrevb.86.121302

Related papers

Conducting fixed points for inhomogeneous quantum wires: A conformally invariant boundary theory

Nicholas Sedlmayr, Denis Morath, Jesko Sirker +2 more

Inhomogeneities and junctions in wires are natural sources of scattering, and hence resistance. A conducting fixed point usually requires an adiabatically smooth system. One notable exception is ``healing,'' which has been predicted in systems with special symmetries, where the system is driven to the homogeneous fixed point. Here we present theoretical results for a different type of conducting fixed point which occurs in inhomogeneous wires with an abrupt jump in hopping and interaction strength. We show that it is always possible to tune the system to an unstable conducting fixed point which does not correspond to translational invariance. We analyze the temperature scaling of correlation functions at and near this fixed point and show that two distinct boundary exponents appear, which correspond to different effective Luttinger liquid parameters. Even though the system consists of two separate interacting parts, the fixed point is described by a single conformally invariant boundary theory. We present details of the general effective bosonic field theory including the mode expansion and the finite size spectrum. The results are confirmed by numerical quantum Monte Carlo simulations on spinless fermions. We predict characteristic experimental signatures of the local density of states near junctions.

arXiv:1311.0007•Physical Review B•Jan 24, 2014•13 citations

Conductance in inhomogeneous quantum wires: Luttinger liquid predictions and quantum Monte Carlo results

Denis Morath, Nicholas Sedlmayr, Jesko Sirker +1 more

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.

arXiv:1606.07030•Physical review. B./Physical review. B•Sep 28, 2016•12 citations

Interaction-induced backscattering in short quantum wires

Maria-Theresa Rieder, Tobias Micklitz, Alex Levchenko +1 more

We study interaction-induced backscattering in clean quantum wires with adiabatic contacts exposed to a voltage bias. Particle backscattering relaxes such systems to a fully equilibrated steady state only on length scales exponentially large in the ratio of bandwidth of excitations and temperature. Here we focus on shorter wires in which full equilibration is not accomplished. Signatures of relaxation then are due to backscattering of hole excitations close to the band bottom which perform a diffusive motion in momentum space while scattering from excitations at the Fermi level. This is reminiscent to the first passage problem of a Brownian particle and, regardless of the interaction strength, can be described by an inhomogeneous Fokker-Planck equation. From general solutions of the latter we calculate the hole backscattering rate for different wire lengths and discuss the resulting length dependence of interaction-induced correction to the conductance of a clean single channel quantum wire.

arXiv:1407.1888•Physical Review B•Oct 6, 2014•11 citations

Conductance of quantum wires: A numerical study of effects of an impurity and interactions

Amit Agarwal, Diptiman Sen

We use the nonequilibrium Green's function formalism and a self-consistent Hartree-Fock approximation to numerically study the effects of a single impurity and interactions between the electrons (with and without spin) on the conductance of a quantum wire. We study how the conductance varies with the wire length, the temperature, and the strengths of the impurity and interactions. The numerical results for the dependence of the conductance on the wire length and temperature are compared with the results obtained from a renormalization group analysis based on the Hartree-Fock approximation. For the spin-$1∕2$ model with a repulsive on-site interaction or the spinless model with an attractive nearest neighbor interaction, we find that the conductance increases with increasing wire length or decreasing temperature. This can be explained using the Born approximation in scattering theory. For a strong impurity, the conductance is significantly different for a repulsive and an attractive impurity; this is due to the existence of a bound state in the latter case. In general, the large density deviations close to the impurity have an appreciable effect on the conductance at short distances which is not captured by the renormalization group equations.

arXiv:cond-mat/0507097•Physical Review B•Jan 30, 2006•15 citations

Transport properties of a quantum wire: Role of extended time-dependent impurities

D. Makogon, Vladimir Juričić, C. Morais Smith

We study the transport properties of a quantum wire, described by the Tomonaga-Luttinger model, in the presence of a backscattering potential provided by several extended time-dependent impurities (barriers). Employing the B\"uttiker-Landauer approach, we first consider the scattering of noninteracting electrons $(g=1)$ by a rectangularlike barrier and find an exact solution for the backscattering current, as well as a perturbative solution for a weak static potential with an arbitrary shape. We then include electron-electron interactions and use the Keldysh formalism combined with the bosonization technique to study oscillating extended barriers. We show that the backscattering current off time-dependent impurities can be expressed in terms of the current for the corresponding static barrier. Then we determine the backscattering current for a static extended potential, which, in the limit of noninteracting electrons $(g=1)$, coincides with the result obtained using the B\"uttiker-Landauer formalism. In particular, we find that the conductance can be increased beyond its quantized value in the whole range of repulsive interactions $0<g<1$ already in the case of a single oscillating extended impurity, in contrast to the case of a pointlike impurity, where this phenomenon occurs only for $0<g<1∕2$.

arXiv:cond-mat/0609372•Physical Review B•Jan 30, 2007•9 citations

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

Inès Safi A, Heinz J. Schulz

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.

arXiv:cond-mat/9711082•Nov 10, 1997•0 citations
We consider scattering and transport in interacting quantum wires that are connected to leads. Such a setup can be represented by a minimal model of interacting fermions with sudden changes in interaction strength and/or velocity. The inhomogeneities generally cause relevant backscattering, so it is a priori unclear if perfect ballistic transport is possible in the low-temperature limit. We demonstrate that a conducting fixed point surprisingly exists even for large abrupt changes, which in the considered model corresponds to a velocity-matching condition. The general position-dependent Green's function is calculated in the presence of a sudden change, and is confirmed numerically with high accuracy. The exact form of the interference pattern in the form of density oscillations around inhomogeneities can be used to estimate the effective strength of local backscattering sources, offering a route to design experiments where the effects of the contacts are minimized.
Inhomogeneities and junctions in wires are natural sources of scattering, and hence resistance. A conducting fixed point usually requires an adiabatically smooth system. One notable exception is ``healing,'' which has been predicted in systems with special symmetries, where the system is driven to the homogeneous fixed point. Here we present theoretical results for a different type of conducting fixed point which occurs in inhomogeneous wires with an abrupt jump in hopping and interaction strength. We show that it is always possible to tune the system to an unstable conducting fixed point which does not correspond to translational invariance. We analyze the temperature scaling of correlation functions at and near this fixed point and show that two distinct boundary exponents appear, which correspond to different effective Luttinger liquid parameters. Even though the system consists of two separate interacting parts, the fixed point is described by a single conformally invariant boundary theory. We present details of the general effective bosonic field theory including the mode expansion and the finite size spectrum. The results are confirmed by numerical quantum Monte Carlo simulations on spinless fermions. We predict characteristic experimental signatures of the local density of states near junctions.
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.
We study interaction-induced backscattering in clean quantum wires with adiabatic contacts exposed to a voltage bias. Particle backscattering relaxes such systems to a fully equilibrated steady state only on length scales exponentially large in the ratio of bandwidth of excitations and temperature. Here we focus on shorter wires in which full equilibration is not accomplished. Signatures of relaxation then are due to backscattering of hole excitations close to the band bottom which perform a diffusive motion in momentum space while scattering from excitations at the Fermi level. This is reminiscent to the first passage problem of a Brownian particle and, regardless of the interaction strength, can be described by an inhomogeneous Fokker-Planck equation. From general solutions of the latter we calculate the hole backscattering rate for different wire lengths and discuss the resulting length dependence of interaction-induced correction to the conductance of a clean single channel quantum wire.
We use the nonequilibrium Green's function formalism and a self-consistent Hartree-Fock approximation to numerically study the effects of a single impurity and interactions between the electrons (with and without spin) on the conductance of a quantum wire. We study how the conductance varies with the wire length, the temperature, and the strengths of the impurity and interactions. The numerical results for the dependence of the conductance on the wire length and temperature are compared with the results obtained from a renormalization group analysis based on the Hartree-Fock approximation. For the spin-1∕21∕21∕2 model with a repulsive on-site interaction or the spinless model with an attractive nearest neighbor interaction, we find that the conductance increases with increasing wire length or decreasing temperature. This can be explained using the Born approximation in scattering theory. For a strong impurity, the conductance is significantly different for a repulsive and an attractive impurity; this is due to the existence of a bound state in the latter case. In general, the large density deviations close to the impurity have an appreciable effect on the conductance at short distances which is not captured by the renormalization group equations.
We study the transport properties of a quantum wire, described by the Tomonaga-Luttinger model, in the presence of a backscattering potential provided by several extended time-dependent impurities (barriers). Employing the B\"uttiker-Landauer approach, we first consider the scattering of noninteracting electrons (g=1)(g=1)(g=1) by a rectangularlike barrier and find an exact solution for the backscattering current, as well as a perturbative solution for a weak static potential with an arbitrary shape. We then include electron-electron interactions and use the Keldysh formalism combined with the bosonization technique to study oscillating extended barriers. We show that the backscattering current off time-dependent impurities can be expressed in terms of the current for the corresponding static barrier. Then we determine the backscattering current for a static extended potential, which, in the limit of noninteracting electrons (g=1)(g=1)(g=1), coincides with the result obtained using the B\"uttiker-Landauer formalism. In particular, we find that the conductance can be increased beyond its quantized value in the whole range of repulsive interactions 0<g<10<g<10<g<1 already in the case of a single oscillating extended impurity, in contrast to the case of a pointlike impurity, where this phenomenon occurs only for 0<g<1∕20<g<1∕20<g<1∕2.
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.