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arXiv:cond-mat/0304329 · Physical review. B, Condensed matter

Shot noise of a quantum dot with non-Fermi-liquid correlations

Alessandro Braggio, Rosario Fazio, Maura Sassetti

Published Jun 27, 2003• 19 citations
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Abstract

The shot noise of a one-dimensional wire interrupted by two barriers shows interesting features related to the interplay between Coulomb blockade effects, Luttinger correlations, and discrete excitations. At small bias the Fano factor reaches the lowest attainable value, $1/2,$ irrespective of the ratio of the two junction resistances. At larger voltages this asymmetry is power-law renormalized by the interaction strength. We discuss how the measurement of current and these features of the noise allow to extract the Luttinger-liquid parameter.

DOI
10.1103/physrevb.67.233308

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The shot noise of a one-dimensional wire interrupted by two barriers shows interesting features related to the interplay between Coulomb blockade effects, Luttinger correlations, and discrete excitations. At small bias the Fano factor reaches the lowest attainable value, 1/2,1/2,1/2, irrespective of the ratio of the two junction resistances. At larger voltages this asymmetry is power-law renormalized by the interaction strength. We discuss how the measurement of current and these features of the noise allow to extract the Luttinger-liquid parameter.
The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between shot noise and backscattering current crucially depends on the noise frequency relative to the ballistic frequency vF/gL, where vF is the Fermi velocity, g the Luttinger liquid interaction parameter, and L the length of the wire. In contrast to chiral Luttinger liquids, the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but also depends on Andreev-type reflections of plasmons at the contacts, so that the frequency dependence of the noise needs to be analyzed to extract the fractional charge of the bulk excitations. We show that the frequencies needed to see interaction effects in the Fano factor are within experimental reach.
The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in the presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between noise and backscattered current crucially depends on the noise frequency omega relative to the ballistic frequency vF/gL, where vF is the Fermi velocity, g is the Luttinger liquid interaction parameter, and L is the length of the wire. In contrast to chiral Luttinger liquids the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but it also depends on Andreev-type reflections at the contacts, so that the frequency dependence of the noise needs to be analyzed to extract the fractional charge e*=eg of the bulk excitations.
The current noise of a voltage‐biased interacting quantum wire connected to leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between noise and backscattered current crucially depends on the noise frequency ω relative to the ballistic frequency vF/gL, where vF is the Fermi velocity, g the electron interaction strength, and L the length of the wire. In contrast to chiral Luttinger liquids, the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but also to Andreev‐type reflections at the contacts. The frequency dependence of the noise needs to be analyzed to extract the fractional charge e* = eg of the bulk excitations.
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.
One-dimensional interacting electrons in a quantum wire connected to reservoirs are studied theoretically. The difference in the Tomonaga-Luttinger interaction constants between the wire (g)(g)(g) and reservoirs ${(g}_{\ensuremath{\infty}})$ produces the cross correlation between the right- and left-going chiral components of the charge-density wave field. The low-energy asymptotics of this field correlator, which is determined by (g)(g)(g) and ${(g}_{\ensuremath{\infty}}),$ specifies renormalization of physical quantities. We have found that charge of the carriers in the shot noise is determined by ${g}_{\ensuremath{\infty}}$ (no renormalization for the Fermi liquid reservoirs) at any energy, meanwhile the factor g renormalizing the charge and spin susceptibilities emerges in the threshold structures at some rational fillings.
One-dimensional interacting electrons in a quantum wire connected to reservoirs are studied theoretically. The difference in the Tomonaga-Luttinger interaction constants between the wire (g) and reservoirs (g∞)(g_{\infty})(g∞​) produces the cross-correlation between the right- and left-going chiral components of the charge density wave field. The low energy asymptotics of this field correlator, which is determined by (g) and (g∞)(g_{\infty})(g∞​), specifies renormalization of physical quantities. We have found that charge of the carriers in the shot noise is determined by g∞g_\inftyg∞​ (no renormalization for the Fermi liquid reservoirs) at any energy, meanwhile the factor g renormalizing the charge and spin susceptibilities emerges in the threshold structures at some rational fillings.