Scattering phases in quantum dots: an analysis based on lattice models

The transmission phase through a quantum dot with few electrons shows a complex, non-universal behavior. Here we combine configuration-interaction calculations ---treating rigorously Coulomb interaction--- and the Friedel sum rule to provide a rationale for the experimental findings. The phase evolution for more than two electrons is found to strongly depend on dot's shape and electron density, whereas from one to two the phase never lapses. In the Coulomb (Kondo) regime the ...

n this article we study the Friedel phase of the electron transport in two different systems of quantum dots which exhibit bound states in the continuum (BIC). The Friedel phase jumps abruptly in the energies of the BICs, which is associated to the vanishing width of these states, as shown by Friedrich and Wintgen in Phys. Rev. A \textbf{31}, 3964 (1985). This odd behavior of the Friedel phase has consequences in the charge through the Friedel sum rule. Namely, if the energy ...

The scattering phase shift of an electron transferred through a quantum dot is studied within a model Hamiltonian, accounting for both the electron--electron interaction in the dot and a finite temperature. It is shown that, unlike in an independent electron picture, this phase may exhibit a phase lapse of $ \pi $ {\em between } consecutive resonances under generic circumstances.

We show that the observed evolution of the transmission phase through multi-electron quantum dots with more than approximately ten electrons, which shows a universal (i.e., independent of N) as yet unexplained behavior, is consistent with an electrostatic model, where electron-electron interaction is described by a mean-field approach. Moreover, we perform exact calculations for an open 1D quantum dot and show that carrier correlations may give rise to a non-universal (i.e., ...

Measurements of the transmission phase in transport through a quantum dot embedded in an Aharonov-Bohm interferometer show systematic sequences of phase lapses separated by Coulomb peaks. Using a two-level quantum dot as an example we show that this phenomenon can be accounted for by the combined effect of asymmetric dot-lead coupling and interaction-induced "population switching" of the levels, rendering this behavior generic. In addition, we use the notion of spectral shift...

We study the effects of Kondo correlations on the transmission phase shift of a quantum dot coupled to two leads in comparison with the experimental determinations made by Aharonov-Bohm (AB) quantum interferometry. We propose here a theoretical interpretation of these results based on scattering theory combined with Bethe ansatz calculations. We show that there is a factor of 2 difference between the phase of the S-matrix responsible for the shift in the AB oscillations, and ...

We illustrate the relation between the scattering phase appearing in the Friedel sum rule and the phase of the transmission amplitude for quantum scatterers connected to two one-dimensional leads. Transmission zero points cause abrupt phase changes $\pm\pi$ of the phase of the transmission amplitude. In contrast the Friedel phase is a continuous function of energy. We investigate these scattering phases for simple scattering problems and illustrate the behavior of these model...

We investigate scattering through chaotic ballistic quantum dots in the Coulomb blockade regime. Focusing on the scattering phase, we show that large universal sequences emerge in the short wavelength limit, where phase lapses of $\pi$ systematically occur between two consecutive resonances. Our results are corroborated by numerics and are in qualitative agreement with existing experiments.

We study correlated two-level quantum dots, coupled in effective 1-channel fashion to metallic leads; with electron interactions including on-level and inter-level Coulomb repulsions, as well as the inter-orbital Hund's rule exchange favoring the spin-1 state in the relevant sector of the free dot. For arbitrary dot occupancy, the underlying phases, quantum phase transitions (QPTs), thermodynamics, single-particle dynamics and electronic transport properties are considered; a...

We investigate the effect of electronic correlations on the transmission phase of quantum coherent scatterers, considering quantum dots in the Coulomb blockade regime connected to two single-channel leads. We focus on transmission zeros and the associated \pi-phase lapses that have been observed in interferometric experiments. We numerically explore two types of models for quantum dots: (i) lattice models with up to eight sites, and (ii) resonant level models with up to six l...