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تسجيل مستخدم جديدMeasurement of the full distribution of the persistent current in normal-metal rings
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We have measured the persistent current in individual normal metal rings over a wide range of magnetic fields. From this data, we extract the first six cumulants of the single-ring persistent current distribution. Our results are consistent with the theoretical prediction that this distribution should be nearly Gaussian (i.e., that these cumulants should be nearly zero) for diffusive metallic rings. This measurement highlights the particular sensitivity of persistent current to the mesoscopic fluctuations within a single coherent volume.
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Quantum mechanics predicts that the equilibrium state of a resistive electrical circuit contains a dissipationless current. This persistent current has been the focus of considerable theoretical and experimental work, but its basic properties remain
a topic of controversy. The main experimental challenges in studying persistent currents have been the small signals they produce and their exceptional sensitivity to their environment. To address these issues we have developed a new technique for detecting persistent currents which offers greatly improved sensitivity and reduced measurement back action. This allows us to measure the persistent current in metal rings over a wider range of temperature, ring size, and magnetic field than has been possible previously. We find that measurements of both a single ring and arrays of rings agree well with calculations based on a model of non-interacting electrons.
We develop a method for calculation of charge transfer statistics of persistent current in nanostructures in terms of the cumulant generating function (CGF) of transferred charge. We consider a simply connected one-dimensional system (a wire) and dev
elop a procedure for the calculation of the CGF of persistent currents when the wire is closed into a ring via a weak link. For the non-interacting system we derive a general formula in terms of the two-particle Greens functions. We show that, contrary to the conventional tunneling contacts, the resulting cumulant generating function has a doubled periodicity as a function of the counting field. We apply our general formula to short tight-binding chains and show that the resulting CGF perfectly reproduces the known evidence for the persistent current. Its second cumulant turns out to be maximal at the switching points and vanishes identically at zero temperature. Furthermore, we apply our formalism for a computation of the charge transfer statistics of genuinely interacting systems. First we consider a ring with an embedded Anderson impurity and employing a self-energy approximation find an overall suppression of persistent current as well as of its noise. Finally, we compute the charge transfer statistics of a double quantum dot system in the deep Kondo limit using an exact analytical solution of the model at the Toulouse point. We analyze the behaviour of the resulting cumulants and compare them with those of a noninteracting double quantum dot system and find several pronounced differences, which can be traced back to interaction effects.
We introduce a variant of the replica trick within the nonlinear sigma model that allows calculating the distribution function of the persistent current. In the diffusive regime, a Gaussian distribution is derived. This result holds in the presence o
f local interactions as well. Breakdown of the Gaussian statistics is predicted for the tails of the distribution function at large deviations.
The fractional Aharonov-Bohm oscillation (FABO) of narrow quantum rings with two electrons has been studied and has been explained in an analytical way, the evolution of the period and amplitudes against the magnetic field can be exactly described. F
urthermore, the dipole transition of the ground state was found to have essentially two frequencies, their difference appears as an oscillation matching the oscillation of the persistent current exactly. A number of equalities relating the observables and dynamical parameters have been found.
A general scheme is developed to deal with 1D lattice systems that could be topologically complicated. It is aimed to give a complete study of two coupled normal metal rings. Our method starts with an investigation of the local expressions of the eig
enfunctions. By connecting different parts of the system, all the eigenvalues and eigenfunctions can be obtained. It is found that there is a possibility for the existence of localized states, which is beyond previous expectations.
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