Y. Levinson

Dephasing in a quantum dot due to coupling with a quantum point contact

We consider the dephasing of an one-electron state in a quantum dot due to charge fluctuations in a biased quantum point contact coupled to the dot capacitively. The contribution to the dephasing rate due to the bias depends on temperature and bias in the same way as shot-noise in the point contact at zero frequency, but do not follow the |t|2(1 − |t|2) suppression.

Adiabatic transport in nanostructures

A confined system of noninteracting electrons, subject to the combined effect of a time-dependent potential and different external chemical potentials, is considered. The current flowing through such a system is obtained by using the adiabatic approximation in an iterative manner. A formula is derived for the charge pumped through an unbiased system (all external chemical potentials are kept at the same value); it reproduces the Brouwer formula for a two-terminal nanostructure. The formalism presented yields the effect of the chemical-potential bias on the pumped charge on one hand, and the modification of the Landauer formula (which gives the current in response to a constant chemical-potential difference) brought about by the modulating potential on the other. Corrections to the adiabatic approximation are derived and discussed.

Thermodynamic properties of a small superconducting grain

The reduced BCS Hamiltonian for a metallic grain with a finite number of electrons is considered. The crossover between the ultrasmall regime, in which the level spacing d is larger than the bulk superconducting gap D and the small regime, where D*d, is investigated analytically and numerically. The condensation energy, spin magnetization, and tunneling peak spectrum are calculated analytically in the ultrasmall regime, using an approximation controlled by 1/ln N as a small parameter, where N is the number of interacting electron pairs. The condensation energy in this regime is perturbative in the coupling constant l and is proportional to dNl 2 5l 2 v D . We find that also in a large regime withD.d, in which pairing correlations are already rather well developed, the perturbative part of the condensation energy is larger than the singular, BCS part. The condition for the condensation energy to be well approximated by the BCS result is found to be roughly D.Adv D. We show how the condensation energy can, in principle, be extracted from a measurement of the spin magnetization curve and find a reentrant susceptibility at zero temperature as a function of magnetic field, which can serve as a sensitive probe for the existence of superconducting correlations in ultrasmall grains. Numerical results are presented, which suggest that in the large N limit the 1/N correction to the BCS result for the condensation energy is larger than D.

Pumping at resonant transmission and transferred charge quantization

We consider pumping through a small quantum dot separated from the leads by two point contacts, whose conductances, G1 and G2, serve as pumping parameters. When the dot is pinched, i.e., G1,G2⪡e2/h, we find that there is a “resonance line” in the parameter plane {G1,G2} along which the Fermi energy in the leads aligns with the energy of the quasi-bound state in the quantum dot. When G1 and G2 are modulated periodically and adiabatically such that the pumping contour defined by G1=G1(t) and G2=G2(t) encircles the resonance line, the current is quantized: the charge pumped through the dot during each period of the modulation is close to a single electronic charge.

Broken unitarity and phase measurements in Aharonov-Bohm interferometers.

Aharonov-Bohm mesoscopic solid-state interferometers yield a conductance which contains a term cos(phi+beta), where phi relates to the magnetic flux. Experiments with a quantum dot on one of the interfering paths aim to relate beta to the dots intrinsic Friedel transmission phase alpha(1). For closed systems, which conserve the electron current (unitarity), the Onsager relation requires that beta = 0 or pi. For open systems, we show that in general beta depends on the details of the broken unitarity. Although it gives information on the resonances of the dot, beta is generally not equal to alpha(1). A direct relation between beta and alpha(1) requires specific ways of opening the system, which are discussed.

The Fano Effect in Aharonov-Bohm interferometers

After briefly reviewing the Fano effect, we explain why it may be relevant to various types of Aharonov–Bohm interferometers. We discuss both closed (electron conserving) and open interferometers, in which one path contains either a simple quantum dot or a decorated quantum dot (with more than one internal state or a parallel path. The possible relevance to some hitherto unexplained experimental features is also discussed.

CURRENT NOISE IN AN IRRADIATED POINT CONTACT

We propose a new approach to calculate current and current correlations in a ballistic quantum point contact interacting with a classical field. The approach is based on the concept of scattering states for a time dependent Hamiltonian neglecting electron-electron interaction. Using this approach we calculated the spectra of the current noise in a biased point contact irradiated by a weak random field. For typical radiation frequencies \nu less than the temperature T and the bias voltage V we find a narrow peak of width \nu on top of a broad background of width \max (T,eV).

Surface acoustic-wave attenuation by a two-dimensional electron gas in a strong magnetic field.

The propagation of a surface acoustic wave (SAW) on GaAs/

Acoustoelectric effect in a finite-length ballistic quantum channel

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