Phase lapses in transmission through interacting two-level quantum dots
We investigate the appearance of π lapses in the transmission phase θ 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, modelled by spinless or spinful electrons, respectively. We investigate the effect of finite temperatures T. For small T and sufficiently small single-particle spacings δ of the dot levels we find π phase lapses between two transmission peaks in an overwhelming part of the parameter space of the level-lead couplings. For large δ 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 δ and generic dot-lead couplings (that is up to cases with special symmetry) the 'universal' phase lapse behaviour 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 δ correlations are found to strongly alter the mean-field picture.