Scattering Phase of Quantum Dots: Emergence of Universal Behavior
Rodolfo Jalabert, Institut de Physique et Chimie des Materiaux de Strasbourg
In a coherent conductor like a quantum dot, the transmission phase is of key importance in determining the transport properties. Unlike the conductance, the transmission phase is not directly measurable. Nevertheless, phase-sensitive experiments have been performed by embedding a quantum dot in one of the arms of an Aharonov-Bohm interferometer. These experiments, observing in-phase behavior between consecutive Coulomb-blockade resonances, have remained unexplained for more than a decade. We provide a solution of this puzzle by showing that wave-function correlations existing in chaotic ballistic quantum dots are responsible for the emergence of large universal sequences of in-phase resonances in the short wavelength limit . In quantum dots with at least one hundred electrons the description of Coulomb blockade physics within a constant charging energy model allows for an effective one-particle description. Smaller dots require going beyond mean-field approaches by including the effect of electronic correlations. We develop a numerical method, using the Density Matrix Renormalization Group algorithm, in order to obtain the transmission phase of a strongly interacting system. We demonstrate that electronic correlations do not generically lead to the in-phase behavior and that small dots are always in the mesoscopic regime of random relative transmission phases .
 R.A. Molina, R.A. Jalabert, D. Weinmann, and Ph. Jacquod; Phys. Rev. Lett. 108, 076803 (2012).
 R.A. Molina, P. Schmitteckert, D. Weinmann, R.A. Jalabert, and Ph. Jacquod; arXiv:1212.2114 (2012).