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

Abstract

Experimentally, the phase of the amplitude for electron transmission through a quantum dot (transmission phase) shows the same pattern between consecutive resonances. Such universal behavior, found for long sequences of resonances, is caused by correlations of the signs of the partial-width amplitudes of the resonances. We investigate the stability of these correlations in terms of a statistical model. For a classically chaotic dot, the resonance eigenfunctions are assumed to be Gaussian distributed. Under this hypothesis, statistical fluctuations are found to reduce the tendency towards universal phase evolution. Long sequences of resonances with universal behavior only persist in the semiclassical limit of very large electron numbers in the dot and for specific energy intervals. Numerical calculations qualitatively agree with the statistical model but quantitatively are closer to universality.

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

“…While the early experiments [23,24] showed sequences of perfectly universal phase evolution with phase-lapses in every conductance valley (except for extremely low electron fillings in the dot [25]), recent measurements using a new way to reliably extract the transmission phase from the conductance of an Aharonov-Bohm interferometer [29] detected several conductance minima without phase-lapses [30,31]. Though it has not been possible to achieve a complete statistics in these last experiments, the findings are consistent with the predicted departure from the universal behavior of a perfect phase-locking of conductance peaks [26,28].…”

“…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 model system and the numerical calculations follow those of Ref. [28] for spinless non-interacting electrons.…”

“…The parameters σ 2 n and ρ n are specified by the two-point correlation function C(r, r ; E n ). The form (14) readily allows to calculate the probability of having the two PWAs of the n th resonance with the same sign [28], i.e., P(γ l n γ r n > 0) =…”

“…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.…”