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

We show that two intriguing features of mesoscopic transport, namely, the modulation of Coulomb blockade peak heights and the transmission phase lapses occurring between subsequent peaks, are closely related. Our analytic arguments are corroborated by numerical simulations for chaotic ballistic quantum dots. The correlations between the two properties are experimentally testable. The statistical distribution of the partial-width amplitude, at the heart of the previous relationship, is determined, and its characteristic parameters are estimated from simple models.

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

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.

Scattering phase of quantum dots: emergence of universal behavior.

We investigate scattering through chaotic ballistic quantum dots in the Coulomb-blockade regime. Focusing on the scattering phase, we show that large universal sequences emerge in the short wavelength limit, where phase lapses of π systematically occur between two consecutive resonances. Our results are corroborated by numerics and are in qualitative agreement with existing experiments.

Spin relaxation near the metal-insulator transition: dominance of the Dresselhaus spin-orbit coupling.

We identify the Dresselhaus spin-orbit coupling as the source of the dominant spin-relaxation mechanism in the impurity band of a wide class of n-doped zinc blende semiconductors. The Dresselhaus hopping terms are derived and incorporated into a tight-binding model of impurity sites, and they are shown to unexpectedly dominate the spin relaxation, leading to spin-relaxation times in good agreement with experimental values. This conclusion is drawn from two complementary approaches: an analytical diffusive-evolution calculation and a numerical finite-size scaling study of the spin-relaxation time.

What is measured in the scanning gate microscopy of a quantum point contact?

The conductance change due to a local perturbation in a phase-coherent nanostructure is calculated. The general expressions to first and second order in the perturbation are applied to the scanning gate microscopy of a two-dimensional electron gas containing a quantum point contact. The first-order correction depends on two scattering states with electrons incoming from opposite leads and is suppressed on a conductance plateau; it is significant in the step regions. On the plateaus, the dominant second-order term likewise depends on scattering states incoming from both sides. It is always negative, exhibits fringes, and has a spatial decay consistent with experiments.

Persistent currents in one dimension: the counterpart of Leggett's theorem.

We discuss the sign of the persistent current of N electrons in one dimensional rings. Using a topology argument, we establish lower bounds for the free energy in the presence of arbitrary electron-electron interactions and external potentials. Those bounds are the counterparts of upper bounds derived by Leggett. Rings with odd (even) numbers of polarized electrons are always diamagnetic (paramagnetic). We show that unpolarized electrons with N being a multiple of four exhibit either paramagnetic behavior or a superconductorlike current-phase relation.