arXiv:cond-mat/9708179 · Physical review. B, Condensed matter

Resonance in a Tomonaga-Luttinger liquid

Inès Safi A

Published Nov 15, 1997• 9 citations

Abstract

We study a homogeneous Tomonaga-Luttinger liquid with backscattering potential. A perturbative computation of the conductance at and near resonance is given. We find that the backscattering of one electron dominates that of two electrons for an interaction parameter $K$\ensuremath{\geqslant}$\frac{1}{3}$ and that the resonance point depends on temperature. Our results may be relevant for recent experiments on shot noise in the fractional quantum Hall effect, where the charge $\frac{1}{3}$ and not $\frac{2}{3}$ is measured on resonance.

DOI: 10.1103/physrevb.56.r12691

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arXiv:cond-mat/9708179 · Physical review. B, Condensed matter

Resonance in a Tomonaga-Luttinger liquid

Inès Safi A

Published Nov 15, 1997• 9 citations

arXiv HTML PDF

Abstract

K

\ensuremath{\geqslant}

\frac{1}{3}

and that the resonance point depends on temperature. Our results may be relevant for recent experiments on shot noise in the fractional quantum Hall effect, where the charge

\frac{1}{3}

and not

\frac{2}{3}

is measured on resonance.

DOI: 10.1103/physrevb.56.r12691

Related papers

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.

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K

\ensuremath{\geqslant}

\frac{1}{3}

and that the resonance point depends on temperature. Our results may be relevant for recent experiments on shot noise in the fractional quantum Hall effect, where the charge

\frac{1}{3}

and not

\frac{2}{3}

is measured on resonance.

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.

1/T

-type low-temperature behavior.