Transport through two interacting resonant levels connected by a Fermi sea

TL;DR

This paper investigates finite-bias transport through two interacting resonant levels connected via a Fermi sea, revealing oscillatory behaviors influenced by impurity distance, Fermi momentum, and interactions, using time-dependent density matrix renormalization group.

Contribution

It introduces a detailed analysis of non-linear transport through coupled resonant levels, including methodological insights and the impact of interactions on oscillatory phenomena.

Findings

Oscillations in current and occupations depend on bias, impurity distance, and Fermi momentum.

Relative phase of dot occupations is influenced by RKKY interactions.

Bias affects current behavior similarly to the one-impurity case.

Abstract

We study transport at finite bias, i.e. beyond the linear regime, through two interacting resonant levels connected by a Fermi sea, by means of time-dependent density matrix renormalization group. We first consider methodological issues, like the protocol that leads to a current-currying state and the characterization of the steady state. At finite sizes both the current and the occupations of the interacting levels oscillate as a function of time. We determine the amplitude and period of such oscillations as a function of bias. We find that the occupations on the two dots oscillate with a relative phase which depends on the distance between the impurities and on the Fermi momentum of the Fermi sea, as expected for RKKY interactions. Also the approximant to the steady-state current displays oscillations as a function of the distance between the impurities. Such a behavior can be explained by resonances in the free case. We then discuss the incidence of interaction on such a behavior. We conclude by showing the effect of the bias on the current, making connection with the one-impurity case.