Phase lapses in transmission through interacting two-level quantum dots

TL;DR

This study explores the conditions under which pi phase lapses occur in the transmission phase of a two-level quantum dot with Coulomb interaction, revealing the influence of level spacing, temperature, and dot-lead coupling symmetry.

Contribution

It provides a comprehensive analysis of phase lapses in two-level quantum dots using renormalization group methods, highlighting the effects of Coulomb interaction and level spacing on phase behavior.

Findings

Pi phase lapses occur between transmission peaks for small temperature and level spacing.

Large level spacing makes phase lapses depend on the sign of level-lead couplings.

Coulomb interaction increases the separation of transmission resonances.

Abstract

We investigate the appearance of pi lapses in the transmission phase theta of a two-level quantum dot with Coulomb interaction U. Using the numerical and functional renormalization group methods we study the entire parameter space for spin-polarized as well as spin-degenerate dots, modeled by spinless or spinful electrons, respectively. We investigate the effect of finite temperatures T. For small T and sufficiently small single-particle spacings delta of the dot levels we find pi phase lapses between two transmission peaks in an overwhelming part of the parameter space of the level-lead couplings. For large delta the appearance or not of a phase lapse between resonances depends on the relative sign of the level-lead couplings in analogy to the U=0 case. We show that this generic scenario is the same for spin-polarized and spin-degenerate dots. We emphasize that in contrast to dots with more levels, for a two-level dot with small delta and generic dot-lead couplings (that is up to cases with special symmetry) the "universal" phase lapse behavior is already established at U=0. The most important effect of the Coulomb interaction is to increase the separation of the transmission resonances. The relation of the appearance of phase lapses to the inversion of the population of the dot levels is discussed. For the spin-polarized case and low temperatures we compare our results to recent mean-field studies. For small delta correlations are found to strongly alter the mean-field picture.