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arXiv:1406.2297

One-dimensional strongly interacting electrons with single impurity: conductance reemergence

V. V. Afonin, Victor Yu. Petrov

Published Jun 9, 2014• 0 citations
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Abstract

We show that conductance of 1D channel with one point-like impurity critically depends on asymptotic behavior of e-e interaction at small momenta k (about inverse length of a channel). Conductance reemerges (contrary to the case of point-like repulsive potential) if potential V(k=0)= 0. For example, this happens if the bare e-e interaction is screened by the charges in the bulk. The relation of this phenomena to the long-range order present in the Luttinger model is discussed.

DOI
10.48550/arxiv.1406.2297

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We show that conductance of 1D channel with one point-like impurity critically depends on asymptotic behavior of e-e interaction at small momenta k (about inverse length of a channel). Conductance reemerges (contrary to the case of point-like repulsive potential) if potential V(k=0)= 0. For example, this happens if the bare e-e interaction is screened by the charges in the bulk. The relation of this phenomena to the long-range order present in the Luttinger model is discussed.
We show that the conductance of a 1D channel with one point-like impurity critically depends on the asymptotic behavior of the e - e interaction at low momenta k (about the inverse length of the channel). The conductance reemerges (contrary to the case of a point-like repulsive potential) if the potential satisfies the condition V ( k = 0) = 0. For example, this happens if the bare e - e interaction is screened by the charges in the bulk. The relation of this phenomenon to the long-range order present in the Luttinger model is discussed. We consider spinless electrons but generalization is straightforward.
It is well known that while forward scattering has no effect on the conductance of one-dimensional systems, backscattering off a static impurity suppresses the current. We study the effect of a time-dependent point impurity on the conductance of a one-channel quantum wire. At strong repulsive interaction (Luttinger liquid parameter g<1/2), backscattering renders the conductance greater than its value e^2/h in the absence of the impurity. A possible experimental realization of our model is a constricted Hall bar at fractional filling factors ν=1/(2n+1) with a time-dependent voltage at the constriction.
We study the effect of screening of an impurity charge by conduction electrons on resonant tunneling at arbitrary energy of the impurity level. We examine the exactly solvable model of the resonant level. We find the ground-state solutions of the model at all possible Coulomb interactions. The principle of equivalence between its universal behavior and the Kondo model is proved. However, the dependence of its scale invariant variable on the bare variables has different forms in two different regions of the parameter variations. This means that besides the well-known Kondo-like fixed point of the renormalization at weak Coulomb interaction a new stable point exists. The latter determines a singular low-energy behavior of the impurity. Based on the solution, the tunneling amplitude is calculated. It is shown that for a narrow gap or quasi-one-dimensional junction a severe renormalization of the one-electron half-width ${\mathrm{\ensuremath{\Gamma}}}_{0}$ occurs ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{R}}$\ensuremath{\propto}${\mathrm{\ensuremath{\Gamma}}}_{0}$(${\mathrm{\ensuremath{\Gamma}}}_{0}$/D${)}^{\mathrm{\ensuremath{\alpha}}/(1\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}})}$. The comparison with perturbation results is discussed. Finally the conductance of the junction with randomly located impurities is calculated to clarify the crucial role of the non-Fermi-liquid behavior on the resonant tunneling under certain conditions.
The persistent current and charge stiffness of a one-dimensional Luttinger liquid on a ring threaded by a magnetic flux are calculated by Monte Carlo simulation. By changing the random impurity potential strength and the electron-electron interaction, we see a crossover behavior between weak- and strong-impurity limits. For weak-impurity potentials, interactions enhance impurity effects, that is, interactions decrease the current and the stiffness. On the other hand, interactions tend to screen impurities when the impurity potential is strong. Temperature dependence of the persistent current and the charge stiffness shows a peak at a characteristic temperature, consistent with a recent single-impurity study.