Phase lapses in scattering through multi-electron quantum dots: Mean-field and few-particle regimes

TL;DR

This paper investigates the evolution of transmission phase in multi-electron quantum dots, showing that mean-field electrostatic models explain universal behavior for large N, while correlations affect small N regimes.

Contribution

It demonstrates that mean-field models account for universal phase behavior in large quantum dots, and exact few-particle calculations reveal correlation effects in small systems.

Findings

Universal phase behavior for N > 10 explained by mean-field models.

Correlation effects cause non-universal phase behavior for N < 10.

Transmission occurs through a single level in the universal regime.

Abstract

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., N-dependent) behavior of the transmission phase, ensuing from Fano resonances, which is consistent with experiments with a few (N < 10) carriers. Our results suggest that in the universal regime the coherent transmission takes place through a single level while in the few-particle regime the correlated scattering state is determined by the number of bound particles.