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:1108.0319 · Physical Review B

Transient and finite-size effects in transport properties of a quantum wire

Mariano J. Salvay, Anı́bal Iucci, Carlos Naón

Published Aug 16, 2011• 2 citations
arXivHTMLPDF

Abstract

We study the time-dependent backscattered current produced in a quantum wire when a local barrier is suddenly switched on. Previous investigations are improved by taking into account the finite length of the device. We establish two different regimes in terms of the relationship between the energy scales associated with the voltage and the length of the system. We show how previous results, valid for wires of infinite length, are modified by the finite size of the system. In particular, our study reveals a rich pattern of temporal steps within which the current suffers an initial relaxation followed by temporary revivals. By employing both analytical and numerical methods we describe peculiar features of this structure. From this analysis one concludes that our results render a recently proposed approach to the determination of the Luttinger parameter, $K$, more realistic.

DOI
10.1103/physrevb.84.075482

Related papers

Transient effects in the backscattered current of a Luttinger liquid

Mariano J. Salvay, Hugo Aita, Carlos Naón

We study the backscattered current in a Luttinger liquid in the presence of a pointlike weak impurity switched on at finite time, taking into account finite-temperature effects. We show how the well-known results for a static impurity are distorted. We derive a dimensionless parameter ${\ensuremath{\tau}}_{R}$ as a function of the electron-electron interaction and the temperature, such that for ${\ensuremath{\tau}}_{R}<1$ $(>1)$ the switching process is relevant (irrelevant). Our results suggest the possibility of determining the value of the Luttinger parameter $K$ through time measurements in transport experiments at fixed voltage.

arXiv:1002.3121•Physical Review B•Mar 5, 2010•7 citations

Transport properties for a Luttinger liquid wire in the presence of a time-dependent impurity

Fang Cheng, Guanghui Zhou

We study theoretically the transport properties of an interacting quantum wire in the presence of a time-dependent point impurity. Using the Keldysh formalism within the framework of Luttinger liquid model, we calculate and analyze the dc contribution of the backscattered current and the shot noise of the system with arbitrary Luttinger interaction strength and impurity position. From some numerical examples, we find that the time-dependent point impurity in the wire can enhance the total current in the strongly interaction regime, and the total current enhancement is dependent on both the impurity potential frequency and the equivalent frequency in relation to the drain-source voltage $V$. The dc contribution of the backscattered current oscillates as a function of impurity frequency with the period depending on the Luttinger interaction strength. Furthermore, the oscillation of the dc contribution of the backscattered current is not a finite-length effect, which is different from that in the case of system with a static point impurity, and the oscillation characteristic is also connected with $V$. However, the final current-noise relation is similar to that in the case of a static point impurity.

Physical Review B•Mar 24, 2006•17 citations

Transport properties of single-channel quantum wires with an impurity: Influence of finite length and temperature on average current and noise

Fabrizio Dolcini, Björn Trauzettel, Inès Safi A +1 more

The inhomogeneous Tomonaga-Luttinger liquid model describing an interacting quantum wire adiabatically coupled to noninteracting leads is analyzed in the presence of a weak impurity within the wire. Due to strong electronic correlations in the wire, the effects of impurity backscattering, finite bias, finite temperature, and finite length lead to characteristic nonmonotonic parameter dependencies of the average current. We discuss oscillations of the nonlinear current voltage characteristics that arise due to reflections of plasmon modes at the impurity and quasi-Andreev reflections at the contacts, and show how these oscillations are washed out by decoherence at finite temperature. Furthermore, the finite-frequency current noise is investigated in detail. We find that the effective charge extracted in the shot noise regime in the weak backscattering limit decisively depends on the noise frequency $\ensuremath{\omega}$ relative to ${v}_{F}∕gL$, where ${v}_{F}$ is the Fermi velocity, $g$ the Tomonaga-Luttinger interaction parameter, and $L$ the length of the wire. The interplay of finite bias, finite temperature, and finite length yields rich structure in the noise spectrum which crucially depends on the electron-electron interaction. In particular, the excess noise, defined as the change of the noise due to the applied voltage, can become negative and is nonvanishing even for noise frequencies larger than the applied voltage, which are signatures of correlation effects.

arXiv:cond-mat/0409320•Physical Review B•Apr 13, 2005•86 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

Initial Correlation Effects in Time-Dependent Transport with One-Dimensional Interacting Leads

Enrico Perfetto, Gianluca Stefanucci, Michele Cini

We study theoretically the memory effects due to different kinds of initial conditions in the transport properties of one-dimensional systems described by the Tomonaga-Luttinger model. We show that in presence of electron–electron interactions the sudden switching of a weak link between two initially uncontacted reservoirs induces a qualitative change in the transient current with respect to the contacted case. In particular the different switching process produces a change in the power-law temporal relaxation of the current towards the steady-state as well as a significant suppression of the transient oscillations. Even more dramatic is the response to a sudden interaction quench, which remarkably leads to a current–voltage characteristic differing from the one displayed if the system was initially interacting.

Nanoscience and Nanotechnology Letters•Nov 1, 2011•2 citations

Kadanoff-Baym approach to quantum transport through interacting nanoscale systems: From the transient to the steady-state regime

Petri Myöhänen, Adrian Stan, Gianluca Stefanucci +1 more

We propose a time-dependent many-body approach to study the short-time dynamics of correlated electrons in quantum transport through nanoscale systems contacted to metallic leads. This approach is based on the time propagation of the Kadanoff-Baym equations for the nonequilibrium many-body Green's function of open and interacting systems out of equilibrium. An important feature of the method is that it takes full account of electronic correlations and embedding effects in the presence of time-dependent external fields, while at the same time satisfying the charge conservation law. The method further extends the Meir-Wingreen formula to the time domain for initially correlated states. We study the electron dynamics of a correlated quantum wire attached to two-dimensional leads exposed to a sudden switch on of a bias voltage using conserving many-body approximations at Hartree-Fock, second Born and GW level. We obtain detailed results for the transient currents, dipole moments, spectral functions, charging times, and the many-body screening of the quantum wire as well as for the time-dependent density pattern in the leads, and we show how the time dependence of these observables provides a wealth of information on the energy level structure of the quantum wire out of equilibrium. For moderate interaction strengths the second Born and GW results are in excellent agreement at all times. We find that many-body effects beyond the Hartree-Fock approximation have a large effect on the qualitative behavior of the system and lead to a bias-dependent gap closing and quasiparticle broadening, shortening of the transient times and washing out of the step features in the current-voltage curves.

arXiv:0906.2136•Physical Review B•Sep 8, 2009•222 citations
We study the time-dependent backscattered current produced in a quantum wire when a local barrier is suddenly switched on. Previous investigations are improved by taking into account the finite length of the device. We establish two different regimes in terms of the relationship between the energy scales associated with the voltage and the length of the system. We show how previous results, valid for wires of infinite length, are modified by the finite size of the system. In particular, our study reveals a rich pattern of temporal steps within which the current suffers an initial relaxation followed by temporary revivals. By employing both analytical and numerical methods we describe peculiar features of this structure. From this analysis one concludes that our results render a recently proposed approach to the determination of the Luttinger parameter, KKK, more realistic.
We study the backscattered current in a Luttinger liquid in the presence of a pointlike weak impurity switched on at finite time, taking into account finite-temperature effects. We show how the well-known results for a static impurity are distorted. We derive a dimensionless parameter ${\ensuremath{\tau}}_{R}$ as a function of the electron-electron interaction and the temperature, such that for ${\ensuremath{\tau}}_{R}<1$ (>1)(>1)(>1) the switching process is relevant (irrelevant). Our results suggest the possibility of determining the value of the Luttinger parameter KKK through time measurements in transport experiments at fixed voltage.
We study theoretically the transport properties of an interacting quantum wire in the presence of a time-dependent point impurity. Using the Keldysh formalism within the framework of Luttinger liquid model, we calculate and analyze the dc contribution of the backscattered current and the shot noise of the system with arbitrary Luttinger interaction strength and impurity position. From some numerical examples, we find that the time-dependent point impurity in the wire can enhance the total current in the strongly interaction regime, and the total current enhancement is dependent on both the impurity potential frequency and the equivalent frequency in relation to the drain-source voltage VVV. The dc contribution of the backscattered current oscillates as a function of impurity frequency with the period depending on the Luttinger interaction strength. Furthermore, the oscillation of the dc contribution of the backscattered current is not a finite-length effect, which is different from that in the case of system with a static point impurity, and the oscillation characteristic is also connected with VVV. However, the final current-noise relation is similar to that in the case of a static point impurity.
The inhomogeneous Tomonaga-Luttinger liquid model describing an interacting quantum wire adiabatically coupled to noninteracting leads is analyzed in the presence of a weak impurity within the wire. Due to strong electronic correlations in the wire, the effects of impurity backscattering, finite bias, finite temperature, and finite length lead to characteristic nonmonotonic parameter dependencies of the average current. We discuss oscillations of the nonlinear current voltage characteristics that arise due to reflections of plasmon modes at the impurity and quasi-Andreev reflections at the contacts, and show how these oscillations are washed out by decoherence at finite temperature. Furthermore, the finite-frequency current noise is investigated in detail. We find that the effective charge extracted in the shot noise regime in the weak backscattering limit decisively depends on the noise frequency $\ensuremath{\omega}$ relative to vF∕gL{v}_{F}∕gLvF​∕gL, where vF{v}_{F}vF​ is the Fermi velocity, ggg the Tomonaga-Luttinger interaction parameter, and LLL the length of the wire. The interplay of finite bias, finite temperature, and finite length yields rich structure in the noise spectrum which crucially depends on the electron-electron interaction. In particular, the excess noise, defined as the change of the noise due to the applied voltage, can become negative and is nonvanishing even for noise frequencies larger than the applied voltage, which are signatures of correlation effects.
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 study theoretically the memory effects due to different kinds of initial conditions in the transport properties of one-dimensional systems described by the Tomonaga-Luttinger model. We show that in presence of electron–electron interactions the sudden switching of a weak link between two initially uncontacted reservoirs induces a qualitative change in the transient current with respect to the contacted case. In particular the different switching process produces a change in the power-law temporal relaxation of the current towards the steady-state as well as a significant suppression of the transient oscillations. Even more dramatic is the response to a sudden interaction quench, which remarkably leads to a current–voltage characteristic differing from the one displayed if the system was initially interacting.
We propose a time-dependent many-body approach to study the short-time dynamics of correlated electrons in quantum transport through nanoscale systems contacted to metallic leads. This approach is based on the time propagation of the Kadanoff-Baym equations for the nonequilibrium many-body Green's function of open and interacting systems out of equilibrium. An important feature of the method is that it takes full account of electronic correlations and embedding effects in the presence of time-dependent external fields, while at the same time satisfying the charge conservation law. The method further extends the Meir-Wingreen formula to the time domain for initially correlated states. We study the electron dynamics of a correlated quantum wire attached to two-dimensional leads exposed to a sudden switch on of a bias voltage using conserving many-body approximations at Hartree-Fock, second Born and GW level. We obtain detailed results for the transient currents, dipole moments, spectral functions, charging times, and the many-body screening of the quantum wire as well as for the time-dependent density pattern in the leads, and we show how the time dependence of these observables provides a wealth of information on the energy level structure of the quantum wire out of equilibrium. For moderate interaction strengths the second Born and GW results are in excellent agreement at all times. We find that many-body effects beyond the Hartree-Fock approximation have a large effect on the qualitative behavior of the system and lead to a bias-dependent gap closing and quasiparticle broadening, shortening of the transient times and washing out of the step features in the current-voltage curves.