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arXiv:0908.2253 · Physical Review B

Symmetric and asymmetric charge transport in interacting asymmetric quantum impurities

Dibyendu Roy

Published Feb 25, 2010• 6 citations
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Abstract

We study steady-state charge transfer across an interacting resonance-level model connected asymmetrically to two leads. For a linear energy dispersion relation of the leads, we calculate current-voltage characteristics of the model exactly employing the scattering Bethe ansatz of Mehta-Andrei and find symmetric transport showing the absence of diode effect. Next we study a lattice version of this model with a nonlinear dispersion for the leads using the Lippmann-Schwinger scattering theory. We find that the inclusion of nonlinearity in the leads' dispersion causes rectification for asymmetric junctions but does not rectify for asymmetric interactions and perfect junctions. The model in the latter case can be mapped into a model of a single noninteracting electron in higher dimensions.

DOI
10.1103/physrevb.81.085330

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We study steady-state charge transfer across an interacting resonance-level model connected asymmetrically to two leads. For a linear energy dispersion relation of the leads, we calculate current-voltage characteristics of the model exactly employing the scattering Bethe ansatz of Mehta-Andrei and find symmetric transport showing the absence of diode effect. Next we study a lattice version of this model with a nonlinear dispersion for the leads using the Lippmann-Schwinger scattering theory. We find that the inclusion of nonlinearity in the leads' dispersion causes rectification for asymmetric junctions but does not rectify for asymmetric interactions and perfect junctions. The model in the latter case can be mapped into a model of a single noninteracting electron in higher dimensions.
The theoretical description of strongly correlated quantum systems out of equilibrium presents several challenges and a number of open questions persist. In this paper we focus on nonlinear electronic transport through an interacting quantum dot maintained at finite bias using a concept introduced by Hershfield [Phys. Rev. Lett. 70, 2134 (1993)] whereby one can express such nonequilibrium quantum impurity models in terms of the system's Lippmann-Schwinger operators. These scattering operators allow one to reformulate the nonequilibrium problem as an effective equilibrium problem associated with a modified Hamiltonian. In this paper we provide a pedagogical analysis of the core concepts of the effective equilibrium theory. First, we demonstrate the equivalence between observables computed using the Schwinger-Keldysh framework and the effective equilibrium approach, and relate the Green's functions in the two theoretical frameworks. Second, we expound some applications of this method in the context of interacting quantum impurity models. We introduce a novel framework to treat effects of interactions perturbatively while capturing the entire dependence on the bias voltage. For the sake of concreteness, we employ the Anderson model as a prototype for this scheme. Working at the particle-hole symmetric point, we investigate the fate of the Abrikosov-Suhl resonance as a function of bias voltage and magnetic field.
Asymmetric current-voltage [I(V)][I(V)][I(V)] curves, known as the diode or rectification effect, in one-dimensional electronic conductors can have their origin from scattering off a single asymmetric impurity in the system. We investigate this effect in the framework of the Tomonaga-Luttinger model for electrons with spin. We show that electron interactions strongly enhance the diode effect and lead to a pronounced current rectification even if the impurity potential is weak. For strongly interacting electrons and not too small voltages, the rectification current ${I}_{r}=[I(V)+I(\ensuremath{-}V)]∕2$, measuring the asymmetry in the current-voltage curve, has a power-law dependence on the voltage with a negative exponent, ${I}_{r}\ensuremath{\sim}{V}^{\ensuremath{-}\ensuremath{\mid}z\ensuremath{\mid}}$, leading to a bump in the current-voltage curve.
We develop an exact nonperturbative framework to compute steady-state properties of quantum impurities subject to a finite bias. We show that the steady-state physics of these systems is captured by nonequilibrium scattering eigenstates which satisfy an appropriate Lippman-Schwinger equation. Introducing a generalization of the equilibrium Bethe ansatz--the nonequilibrium Bethe ansatz--we explicitly construct the scattering eigenstates for the interacting resonance level model and derive exact, nonperturbative results for the steady-state properties of the system.
Quantum dot devices may be tuned to Kondo models which have non-interacting limits such as the Toulouse limit. At sufficiently low temperatures the Toulouse limit can be used to make predictions for charge transport in the devices driven away from equilibrium, e.g. with an ac bias. We investigate non-equilibrium transport in a resonant level model with a single lead which may be mapped onto the Toulouse limit of the one-channel Kondo model. The main results are expressions for the charge current that are exact in the tunnelling couplings, while remaining in the linear response regime of the time-dependent voltage bias. We also show how the line of enquiry directly extends to the tunnelling junction studied by A.~Schiller and S.~Hershfield in which a Kondo impurity interacts separately with two leads.
Through an extension of the Landauer formula, we study the electron transport in an open quantum dot system under a finite bias voltage. The system that we study is an interacting resonant-level model equipped with infinite two leads of a linearized dispersion relation. We explicitly construct many-electron scattering eigenstates whose incident states are free-fermionic. A remarkable feature of the scattering state is the appearance of many-body bound states after the scattering. Extending Landauer's idea, we calculate the average electric current flowing through the quantum dot. We use a renormalization-group technique to deal with the divergences that appear in the limit of the large bandwidth of the leads. As a result, the average electric current is brought to a universal form.
We consider the transport properties of multiple-particle quantum states in a class of one-dimensional systems with a single quantum impurity. In these systems, the local interaction at the quantum impurity induces strong and nontrivial correlations between the multiparticles. We outline an exact theoretical approach, based upon real-space equations of motion and the Bethe ansatz, that allows one to construct the full scattering matrix (SSS matrix) for these systems. In particular, we emphasize the need for a completeness check upon the eigenstates of the SSS matrix, when these states obtained from Bethe ansatz are used for describing the scattering properties. As a detailed example of our approach, we solve the transport properties of two photons incident on a single two-level atom, when the photons are restricted to a one-dimensional system such as a photonic crystal waveguide. Our approach predicts a number of nonlinear effects involving only two photons, including background fluorescence, spatial attraction and repulsion between the photons, as well as the emergence of a two-photon bound state.