arXiv:0711.3638 · Physical Review B

Voltage profile and four-terminal resistance of an interacting quantum wire

Liliana Arrachea, Carlos Naón, Mariano J. Salvay

Published Jun 24, 2008• 13 citations

Abstract

We investigate the behavior of the four-terminal resistance ${R}_{4\text{pt}}$ in a quantum wire described by a Luttinger liquid in two relevant situations: (i) in the presence of a single impurity within the wire and (ii) under the effect of asymmetries introduced by disordered voltage probes. In the first case, interactions leave a signature in a power-law behavior of ${R}_{4\text{pt}}$ as a function of the voltage $V$ and the temperature $T$. In the second case interactions tend to mask the effect of the asymmetries. In both scenarios the occurrence of negative values of ${R}_{4\text{pt}}$ is explained in simple terms.

DOI: 10.1103/physrevb.77.233105

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arXiv:0711.3638 · Physical Review B

Voltage profile and four-terminal resistance of an interacting quantum wire

Liliana Arrachea, Carlos Naón, Mariano J. Salvay

Published Jun 24, 2008• 13 citations

arXiv HTML PDF

Abstract

We investigate the behavior of the four-terminal resistance

{R}_{4\text{pt}}

in a quantum wire described by a Luttinger liquid in two relevant situations: (i) in the presence of a single impurity within the wire and (ii) under the effect of asymmetries introduced by disordered voltage probes. In the first case, interactions leave a signature in a power-law behavior of

{R}_{4\text{pt}}

as a function of the voltage

V

and the temperature

T

. In the second case interactions tend to mask the effect of the asymmetries. In both scenarios the occurrence of negative values of

{R}_{4\text{pt}}

is explained in simple terms.

DOI: 10.1103/physrevb.77.233105

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We analyze the behavior of the four-terminal resistance, relative to the two-terminal resistance of an interacting quantum wire with an impurity, taking into account the invasiveness of the voltage probes. We consider a one-dimensional Luttinger model of spinless fermions for the wire. We treat the coupling to the voltage probes perturbatively, within the framework of non-equilibrium Green function techniques. Our investigation unveils the combined effect of impurities, electron-electron interactions and invasiveness of the probes on the possible occurrence of negative resistance.We analyze the behavior of the four-terminal resistance, relative to the two-terminal resistance of an interacting quantum wire with an impurity, taking into account the invasiveness of the voltage probes. We consider a one-dimensional Luttinger model of spinless fermions for the wire. We treat the coupling to the voltage probes perturbatively, within the framework of non-equilibrium Green function techniques. Our investigation unveils the combined effect of impurities, electron-electron interactions and invasiveness of the probes on the possible occurrence of negative resistance.

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Luttinger-liquid behavior of one-dimensional correlated electron systems is characterized by power-law scaling of a variety of physical observables with exponents determined by a single interaction dependent parameter $K$ . We suggest a setup to study Luttinger-liquid behavior in quantum wires which allows us to determine $K$ from two independent measurements: transport through a quantum dot embedded in the wire and the charge on the dot. Consistency of the two $K$ 's for a single probe would provide strong experimental evidence for the Luttinger-liquid paradigm.Luttinger-liquid behavior of one-dimensional correlated electron systems is characterized by power-law scaling of a variety of physical observables with exponents determined by a single interaction dependent parameter $K$. We suggest a setup to study Luttinger-liquid behavior in quantum wires which allows us to determine $K$ from two independent measurements: transport through a quantum dot embedded in the wire and the charge on the dot. Consistency of the two $K$'s for a single probe would provide strong experimental evidence for the Luttinger-liquid paradigm.

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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.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/0409320Physical Review BApr 13, 200586 citations

We investigate the behavior of the four-terminal resistance

{R}_{4\text{pt}}

{R}_{4\text{pt}}

as a function of the voltage

V

and the temperature

T

. In the second case interactions tend to mask the effect of the asymmetries. In both scenarios the occurrence of negative values of

{R}_{4\text{pt}}

is explained in simple terms.

We investigate how the conductance

G

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

G

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

G

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.

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.

K

. We suggest a setup to study Luttinger-liquid behavior in quantum wires which allows us to determine

K

from two independent measurements: transport through a quantum dot embedded in the wire and the charge on the dot. Consistency of the two

K

's for a single probe would provide strong experimental evidence for the Luttinger-liquid paradigm.

{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.