Mesoscopic behavior of the transmission phase through confined correlated electronic systems

Abstract

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 singlechannel leads. We focus on transmission zeros and the associated π-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 levels. We identify different regimes of parameters where the presence of electronic correlations is responsible for the increase or the decrease of the number of transmission zeros vs. electrochemical potential on the dot. We show that within the two models considered, interaction effects do not reproduce the universal behavior of alternating resonances and phase lapses, experimentally observed in manyelectron Coulomb blockaded dots.

Transmission phase of a quantum dot and statistical fluctuations of partial-width amplitudes

“…The observed phase locking has posed a theoretical puzzle since it appears to contradict the expectation that eigenstates of different resonances are uncorrelated. Numerous theoretical papers have addressed the emergence of universal behavior in large QDs [1][2][3][7][8][9][10][11][12][13][14][15][16][17]. Some works have pointed to the importance of electronic correlations in establishing universal behavior [15], while detailed many-body numerical calculations recently disputed such a view [17].…”

Correlation between peak-height modulation and phase lapses in transport through quantum dots

“…Switching to the problem of the phase evolution between the n th and (n + 1) st CB peaks, we distinguish the case where the transmission amplitude at intermediate energies is dominated by the contributions arising from these two resonances, from that with large fluctuations of the level width among different levels, where far-away resonances might characterize the intermediate behavior. The first scenario supposes the absence of strong fluctuations of the level-widths, and has been termed [27] restricted off-resonance (ROR) behavior. The second scenario of large PWA fluctuations, termed unrestricted off-resonance (UOR) behavior, is expected (and numerically verified [27,28]) to be rare.…”

“…The first scenario supposes the absence of strong fluctuations of the level-widths, and has been termed [27] restricted off-resonance (ROR) behavior. The second scenario of large PWA fluctuations, termed unrestricted off-resonance (UOR) behavior, is expected (and numerically verified [27,28]) to be rare.…”

“…The statistical properties of the wave-function distribution have been shown to result in a phase-locking of the conductance that is not perfect, but more and more likely to be observed as the semiclassical limit of large kL is attained [26][27][28]. Here, k is the electron wave-vector in the QD and L is the distance between its entry and exit (see Fig.…”

Embedding method for the scattering phase in strongly correlated quantum dots

“…Recent progress in that direction was obtained studying the statistical properties of the parity correlations between succesive wave functions in ballistic chaotic quantum dots [13]. Another interesting path followed for the analysis of the experimental results is a many-body extension of the constant-interaction model (CIM) for the description of resonances in quantum dots [14,15,16]. In the regime where the distance between resonances is much smaller than the width of the resonant levels Karrasch et al found that the number of phase lapses could be increased by moderate interactions.…”