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:0905.3842 · Physical Review B

Screening of a Luttinger liquid wire by a scanning tunneling microscope tip. II. Transport properties

M. Guigou, Thierry Martin, Adeline Crépieux C

Published Jul 22, 2009• 8 citations
arXivHTMLPDF

Abstract

We study the effect of an electrostatic coupling between a scanning tunneling microscope tip and a Luttinger liquid wire on the tunneling current and noise between the two. Solving the Dyson equations nonperturbatively for a local interaction potential, we derive the Green's functions associated to the wire and to the tip. Interestingly, the electrostatic coupling leads to the existence of new correlators, which we call mixed Green's functions, which are correlators between the bosonic fields of the wire and the tip. Next, we calculate the transport properties up to second order with the amplitude of the tunnel transfer; the profile of the tunneling current is strongly modified by the presence of screening. The zero-frequency noise is modified in a similar way but the Fano factor remains unchanged. We also consider the effect of the screening on the asymmetry of the finite-frequency nonsymmetrized noise and on the conductance.

DOI
10.1103/physrevb.80.045421

Related papers

Screening of a Luttinger liquid wire by a scanning tunneling microscope tip. I. Spectral properties

M. Guigou, Thierry Martin, Adeline Crépieux C

The screening effect due to a scanning tunneling microscope tip which is placed in the vicinity of an interacting quantum wire is considered. With the help of a bosonization procedure, we are able to determine nonperturbatively the Green's functions of the quantum wire in the presence of both electrostatic screening by the tip and Coulomb interactions in the wire. In our approach we justify that the working Hamiltonian of the whole system is quadratic when ${K}_{c}>1/2$ and can be solved by integration over the degrees of freedom of the tip. Once the Green's functions are known, we calculate the spectral properties. We show that the spectral function, as well as the tunneling density of states, is affected by the screening and that the local density of states strongly deviates from its unscreened value when the tip gets close to the wire. Moreover, we observe that the spatial extension of the deviation of the local density of states is related to both the Coulomb interactions parameter and the screening strength.

arXiv:0904.4019•Physical Review B•Jul 22, 2009•12 citations

Conductance of Tomonaga-Luttinger liquid wires and junctions with resistances

Abhiram Soori, Diptiman Sen

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

•Mar 1, 2011•7 citations

Time-resolved transport properties of a Y junction of Tomonaga-Luttinger liquid wires

Amit Agarwal

We study time-resolved transport properties of a Y junction composed of interacting one-dimensional quantum wires using a bosonization approach. In particular, we investigate the ac conductivity of the Y junction formed from finite-length Tomonaga-Luttinger liquid wires based on a plasmon scattering approach for injected charge pulses of arbitrary shapes. In addition, we calculate the tunneling current and quantum noise of the Y junction arising from pointlike tunneling impurities at the junction, including finite-temperature effects. Our results will be useful for designing nanoelectronic quantum circuits and for interpreting time-resolved experiments [Kamata et al., Nat. Nanotechnol. 9, 177 (2014)] in interacting wires and their junctions.

arXiv:1406.7726•Physical Review B•Nov 4, 2014•4 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 of one dimensional correlated electrons

Maura Sassetti, Gianaurelio Cuniberti, Bernhard Krämer

Several recent results concerning frequency dependent and nonlinear transport of one-dimensional correlated electrons are reviewed. The frequency dependent conductance of a Luttinger liquid is discussed. For zero-range interaction the conductance is similar to that of a non-interacting ideal quantum wire, with a renormalized zero-frequency limit. For a screened Coulomb potential, the conductance as a function of the frequency shows features of the elementary excitations. They can be simulated in terms of a capacitance, an inductance and a resistance. The non-linear DC-conductance of the Luttinger liquid in presence of a tunnel barrier shows Coulomb blockade if the interaction is of finite range. The capacitance scales in the same way as for the system without the tunnel barrier. The linear DC-response of a tunnel barrier as a function of the frequency and the voltage of a monochromatic driving field shows oscillations which can be interpreted as signature of a frequency-induced depinning of a charge density wave.

Editions Frontières eBooks•Jun 29, 2006•0 citations

Conductance of Tomonaga-Luttinger liquid wires and junctions with resistances

Abhiram Soori, Diptiman Sen

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.

arXiv:1011.5058•Europhysics Letters (EPL)•Mar 1, 2011•13 citations
We study the effect of an electrostatic coupling between a scanning tunneling microscope tip and a Luttinger liquid wire on the tunneling current and noise between the two. Solving the Dyson equations nonperturbatively for a local interaction potential, we derive the Green's functions associated to the wire and to the tip. Interestingly, the electrostatic coupling leads to the existence of new correlators, which we call mixed Green's functions, which are correlators between the bosonic fields of the wire and the tip. Next, we calculate the transport properties up to second order with the amplitude of the tunnel transfer; the profile of the tunneling current is strongly modified by the presence of screening. The zero-frequency noise is modified in a similar way but the Fano factor remains unchanged. We also consider the effect of the screening on the asymmetry of the finite-frequency nonsymmetrized noise and on the conductance.
The screening effect due to a scanning tunneling microscope tip which is placed in the vicinity of an interacting quantum wire is considered. With the help of a bosonization procedure, we are able to determine nonperturbatively the Green's functions of the quantum wire in the presence of both electrostatic screening by the tip and Coulomb interactions in the wire. In our approach we justify that the working Hamiltonian of the whole system is quadratic when Kc>1/2{K}_{c}>1/2Kc​>1/2 and can be solved by integration over the degrees of freedom of the tip. Once the Green's functions are known, we calculate the spectral properties. We show that the spectral function, as well as the tunneling density of states, is affected by the screening and that the local density of states strongly deviates from its unscreened value when the tip gets close to the wire. Moreover, we observe that the spatial extension of the deviation of the local density of states is related to both the Coulomb interactions parameter and the screening strength.
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 study time-resolved transport properties of a Y junction composed of interacting one-dimensional quantum wires using a bosonization approach. In particular, we investigate the ac conductivity of the Y junction formed from finite-length Tomonaga-Luttinger liquid wires based on a plasmon scattering approach for injected charge pulses of arbitrary shapes. In addition, we calculate the tunneling current and quantum noise of the Y junction arising from pointlike tunneling impurities at the junction, including finite-temperature effects. Our results will be useful for designing nanoelectronic quantum circuits and for interpreting time-resolved experiments [Kamata et al., Nat. Nanotechnol. 9, 177 (2014)] in interacting wires and their junctions.
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.
Several recent results concerning frequency dependent and nonlinear transport of one-dimensional correlated electrons are reviewed. The frequency dependent conductance of a Luttinger liquid is discussed. For zero-range interaction the conductance is similar to that of a non-interacting ideal quantum wire, with a renormalized zero-frequency limit. For a screened Coulomb potential, the conductance as a function of the frequency shows features of the elementary excitations. They can be simulated in terms of a capacitance, an inductance and a resistance. The non-linear DC-conductance of the Luttinger liquid in presence of a tunnel barrier shows Coulomb blockade if the interaction is of finite range. The capacitance scales in the same way as for the system without the tunnel barrier. The linear DC-response of a tunnel barrier as a function of the frequency and the voltage of a monochromatic driving field shows oscillations which can be interpreted as signature of a frequency-induced depinning of a charge density wave.
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.