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Phase lapses in scattering through multi-electron quantum dots Mean-field and few-particle.pdf

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

a r X i v : 0 7 0 6 .2 0 8 4 v 1 [ c o n d - m a t .m e s - h a l l ] 1 4 J u n 2 0 0 7 Phase lapses in scattering through multi-electron quantum dots: Mean-field and few-particle regimes Andrea Bertoni? CNR-INFM National Research Center on nanoStructures and bioSystems at Surfaces (S3), Via Campi 213/A, 41100 Modena, Italy Guido Goldoni CNR-INFM National Research Center on nanoStructures and bioSystems at Surfaces (S3), Via Campi 213/A, 41100 Modena, Italy and Dipartimento di Fisica, Universita? di Modena e Reggio Emilia, 41100 Modena, Italy Abstract We show that the observed evolution of the transmission phase through multi-electron quantum dots with more than ～ 10 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. PACS numbers: 73.63.Kv, 03.65.Nk, 72.10.-d 73.23.Hk 1 I. INTRODUCTION Among the experiments that exploit the coherent dynamics of carriers, the one performed in 1997 by Schuster et al.1, in which the transmission phase of an electron scattered through a quantum dot (QD) was measured, constitute an ideal test on the validity of different theoretical models for the inclusion of electron-electron interaction. In fact, the ability to model coherent carrier transport experiments in low-dimensional semiconductor systems is essential for designing possible future devices for coherent electronics o