Tunnelling of charge in a Luttinger liquid: Conduction and noise

We have calculated the two-probe Landauer conductance of a one-channel quantum wire containing a Luttinger liquid and connected to two noninteracting leads through tunnel barriers. The tunneling conductance shows broad resonances as a function of the bias voltage, this being a manifestation of the spin-charge separation. In the limit of zero bias and zero barrier, the tunneling conductance reduces to the ballistic contact value $\frac{{e}^{2}}{h}$ per channel.We have calculated the two-probe Landauer conductance of a one-channel quantum wire containing a Luttinger liquid and connected to two noninteracting leads through tunnel barriers. The tunneling conductance shows broad resonances as a function of the bias voltage, this being a manifestation of the spin-charge separation. In the limit of zero bias and zero barrier, the tunneling conductance reduces to the ballistic contact value $\frac{{e}^{2}}{h}$ per channel.

Physical review. B, Condensed matterMay 15, 19961 citation

Electron Conduction in a Luttinger Liquid with Asymmetric Barrier Potentials under a Weak Magnetic Field

Shogo Kawaguchi

In this paper, we study the effect of a weak magnetic field and the charging energy on electron conduction in a Luttinger liquid with two impurities. We consider the situation in which the two potential barriers are different in the symmetric tunneling and asymmetric tunneling limits. We focus on the dependence of the charge conductance on the temperature, the charging energy and the magnetic field. It is shown that the asymmetry of the potential barrier obstructs the resonant conduction in the symmetric tunneling limit. On the other hand, in the asymmetric tunneling limit, we treat the cases of excitation both with and without a gap. For excitation without a gap, the charging energy changes the exponent of the temperature dependence of the conductance, and there appears resonant conduction under zero magnetic field. Contrastingly, for excitation with a gap, the charging energy does not change the exponent of the conductance, and there appears resonant conduction unrelated to the magnetic field. Our results suggest that there is no spin-filter phase in the asymmetric tunneling limit.In this paper, we study the effect of a weak magnetic field and the charging energy on electron conduction in a Luttinger liquid with two impurities. We consider the situation in which the two potential barriers are different in the symmetric tunneling and asymmetric tunneling limits. We focus on the dependence of the charge conductance on the temperature, the charging energy and the magnetic field. It is shown that the asymmetry of the potential barrier obstructs the resonant conduction in the symmetric tunneling limit. On the other hand, in the asymmetric tunneling limit, we treat the cases of excitation both with and without a gap. For excitation without a gap, the charging energy changes the exponent of the temperature dependence of the conductance, and there appears resonant conduction under zero magnetic field. Contrastingly, for excitation with a gap, the charging energy does not change the exponent of the conductance, and there appears resonant conduction unrelated to the magnetic field. Our results suggest that there is no spin-filter phase in the asymmetric tunneling limit.

Progress of Theoretical PhysicsApr 1, 20060 citations

Photo-induced tunneling of a Luttinger liquid

Maura Sassetti, Ulrich Weiß, Bernhard Krämer

Solid State CommunicationsFeb 1, 199614 citations

Non-equilibrium quantum noise in chiral Luttinger liquids

Claudio Chamon, Denise E. Freed, Xiao-Gang Wen

We study non-equilibrium noise in Chiral Luttinger Liquids using the Landauer-Buttiker Scattering approach, obtaining the current/voltage noise spectrum for a four-terminal measurement scheme. Experimental consequences of the tunneling of charges are present in the four-terminal measurement of both the low-frequency shot noise ( $ω$ near 0), and the high-frequency Josephson noise ( $ω$ near $ω_J=e^*V/\hbar$ ). Within perturbation theory, an algebraic singularity is present (to all orders) at the Josephson frequency $ω_J=e^*V/\hbar$ , whose position depends on the charge $e^*$ of the tunneling particles, either electrons or fractionally charged quasiparticles. We show in a non-perturbative calculation for an exactly solvable point that the singularity at the quasiparticle frequency exists only in the limit of vanishing coupling, whereas the singularity at the electron frequency is present for all coupling strengths. The vanishing coupling limit corresponds to perfectly quantized Hall conductance in the case of quasiparticle tunneling between edge states in the fractional quantum Hall regime, and thus tunneling destroys the singularity at the quasiparticle frequency concomitantly with the quantized current.We study non-equilibrium noise in Chiral Luttinger Liquids using the Landauer-Buttiker Scattering approach, obtaining the current/voltage noise spectrum for a four-terminal measurement scheme. Experimental consequences of the tunneling of charges are present in the four-terminal measurement of both the low-frequency shot noise ($ω$ near 0), and the high-frequency Josephson noise ($ω$ near $ω_J=e^*V/\hbar$). Within perturbation theory, an algebraic singularity is present (to all orders) at the Josephson frequency $ω_J=e^*V/\hbar$, whose position depends on the charge $e^*$ of the tunneling particles, either electrons or fractionally charged quasiparticles. We show in a non-perturbative calculation for an exactly solvable point that the singularity at the quasiparticle frequency exists only in the limit of vanishing coupling, whereas the singularity at the electron frequency is present for all coupling strengths. The vanishing coupling limit corresponds to perfectly quantized Hall conductance in the case of quasiparticle tunneling between edge states in the fractional quantum Hall regime, and thus tunneling destroys the singularity at the quasiparticle frequency concomitantly with the quantized current.

arXiv:cond-mat/9507064Jul 18, 19950 citations

Transmissions Through Barriers and Resonant Tunneling in a Luttinger Liquid

C. L. Kane

Springer eBooksJan 1, 19931 citation

\frac{{e}^{2}}{h}

per channel.

ω

near 0), and the high-frequency Josephson noise (

ω

near

ω_J=e^*V/\hbar

). Within perturbation theory, an algebraic singularity is present (to all orders) at the Josephson frequency

ω_J=e^*V/\hbar

, whose position depends on the charge

e^*

of the tunneling particles, either electrons or fractionally charged quasiparticles. We show in a non-perturbative calculation for an exactly solvable point that the singularity at the quasiparticle frequency exists only in the limit of vanishing coupling, whereas the singularity at the electron frequency is present for all coupling strengths. The vanishing coupling limit corresponds to perfectly quantized Hall conductance in the case of quasiparticle tunneling between edge states in the fractional quantum Hall regime, and thus tunneling destroys the singularity at the quasiparticle frequency concomitantly with the quantized current.