Dephasing due to electron-electron interaction in a diffusive ring

We study the effect of the electron-electron interaction on the weak localization correction of a ring pierced by a magnetic flux. We compute exactly the path integral giving the magnetoconductivity for an isolated ring. The results are interpreted in a time representation. This allows to characterize the nature of the phase coherence relaxation in the ring. The nature of the relaxation depends on the time regime (diffusive or ergodic) but also on the harmonics $n$ of the magnetoconductivity. Whereas phase coherence relaxation is non exponential for the harmonic $n=0$, it is always exponential for harmonics $n\neq0$. Then we consider the case of a ring connected to reservoirs and discuss the effect of connecting wires. We recover the behaviour of the harmonics predicted recently by Ludwig & Mirlin for a large perimeter (compared to the Nyquist length). We also predict a new behaviour when the Nyquist length exceeds the perimeter.Comment: 21 pages, RevTeX4, 8 eps figures; version of 10/2006 : eqs.(100-102) of section V.C correcte

Aharonov-Casher oscillations of spin current through a multichannel mesoscopic ring

The Aharonov-Casher (AC) oscillations of spin current through a 2D ballistic ring in the presence of Rashba spin-orbit interaction and external magnetic field has been calculated using the semiclassical path integral method. For classically chaotic trajectories the Fokker-Planck equation determining dynamics of the particle spin polarization has been derived. On the basis of this equation an analytic expression for the spin conductance has been obtained taking into account a finite width of the ring arms carrying large number of conducting channels. It was shown that the finite width results in a broadening and damping of spin current AC oscillations. We found that an external magnetic field leads to appearance of new nondiagonal components of the spin conductance, allowing thus by applying a rather weak magnetic field to change a direction of the transmitted spin current polarization.Comment: 16 pages, 6 figure

Weak localization effects in granular metals

The weak localization correction to the conductivity of a granular metal is calculated using the diagrammatic technique in the reciprocal grain lattice representation. The properties of this correction are very similar to that one in disordered metal, with the replacement of the electron mean free path $\ell$ by the grain diameter $d$ and the dimensionless conductance $g$ by the tunnelling dimensionless conductance $g_{T}$. In particular, we demonstrate that at zero temperature no conducting phase can exist for dimensions $D\leq 2$. We also analyze the WL correction to magnetoconductivity in the weak field limit.Comment: 4 pages, 3 figures; minor corrections adde

Diagrammatic method of integration over the unitary group, with applications to quantum transport in mesoscopic systems

A diagrammatic method is presented for averaging over the circular ensemble of random-matrix theory. The method is applied to phase-coherent conduction through a chaotic cavity (a ``quantum dot'') and through the interface between a normal metal and a superconductor.Comment: 37 pages RevTeX, 21 postscript figures include

Spin-Orbit Coupling, Antilocalization, and Parallel Magnetic Fields in Quantum Dots

We investigate antilocalization due to spin-orbit coupling in ballistic GaAs quantum dots. Antilocalization that is prominent in large dots is suppressed in small dots, as anticipated theoretically. Parallel magnetic fields suppress both antilocalization and also, at larger fields, weak localization, consistent with random matrix theory results once orbital coupling of the parallel field is included. In situ control of spin-orbit coupling in dots is demonstrated as a gate-controlled crossover from weak localization to antilocalization.Comment: related papers at http://marcuslab.harvard.ed

On the Phase Boundaries of the Integer Quantum Hall Effect. II

It is shown that the statements about the observation of the transitions between the insulating phase and the integer quantum Hall effect phases with the quantized Hall conductivity $\sigma_{xy}^{q}$ $\geq 3e^{2}/h$ made in a number of works are unjustified. In these works, the crossing points of the magnetic field dependences of the diagonal resistivity at different temperatures at $\omega_{c}\tau \approx 1$ have been misidentified as the critical points of the phase transitions. In fact, these crossing points are due to the sign change of the derivative $d\rho_{xx}/dT$ owing to the quantum corrections to the conductivity.Comment: 3 pages, 2 figure

Non-equilibrium electronic transport and interaction in short metallic nanobridges

We have observed interaction effects in the differential conductance $G$ of short, disordered metal bridges in a well-controlled non-equilibrium situation, where the distribution function has a double Fermi step. A logarithmic scaling law is found both for the temperature and for the voltage dependence of $G$ in all samples. The absence of magnetic field dependence and the low dimensionality of our samples allow us to distinguish between several possible interaction effects, proposed recently in nanoscopic samples. The universal scaling curve is explained quantitatively by the theory of electron-electron interaction in diffusive metals, adapted to the present case, where the sample size is smaller than the thermal diffusion length.Comment: Published version, 6 Pages, 6 postscript figures, 1 tabl

Symmetry of two terminal, non-linear electric conduction

The well-established symmetry relations for linear transport phenomena can not, in general, be applied in the non-linear regime. Here we propose a set of symmetry relations with respect to bias voltage and magnetic field for the non-linear conductance of two-terminal electric conductors. We experimentally confirm these relations using phase-coherent, semiconductor quantum dots.Comment: 4 pages, 4 figure

Anomalous Aharonov--Bohm gap oscillations in carbon nanotubes

The gap oscillations caused by a magnetic flux penetrating a carbon nanotube represent one of the most spectacular observation of the Aharonov-Bohm effect at the nano--scale. Our understanding of this effect is, however, based on the assumption that the electrons are strictly confined on the tube surface, on trajectories that are not modified by curvature effects. Using an ab-initio approach based on Density Functional Theory we show that this assumption fails at the nano-scale inducing important corrections to the physics of the Aharonov-Bohm effect. Curvature effects and electronic density spilled out of the nanotube surface are shown to break the periodicity of the gap oscillations. We predict the key phenomenological features of this anomalous Aharonov-Bohm effect in semi-conductive and metallic tubes and the existence of a large metallic phase in the low flux regime of Multi-walled nanotubes, also suggesting possible experiments to validate our results.Comment: 7 figure

Aharonov-Bohm signature for neutral excitons in type-II quantum dot ensembles

It is commonly believed that the Aharonov-Bohm (AB) effect is a typical feature of the motion of a charged particle interacting with the electromagnetic vector potential. Here we present a magnetophotoluminescence study of type-II InP/GaAs self-assembled quantum dots, unambiguously revealing the Aharonov-Bohm-type oscillations for neutral excitons when the hole ground state changes its angular momentum from lh = 0 to lh = 1, 2, and 3. The hole ring parameters derived from a simple model are in excellent agreement with the structural parameters for this system.Comment: Revised version, 10 pages, 3 figure