We have measured the flux dependence of both real and imaginary conductance of GaAs/GaAlAs isolated mesoscopic rings at 310 MHz. The rings are coupled to a highly sensitive electromagnetic superconducting micro-resonator and lead to a perturbation of the resonance frequency and quality factor. This experiment provides a new tool for the investigation of the conductance of mesoscopic systems without any connection to invasive probes. It can be compared with recent theoretical predictions emphasizing the differences between isolated and connected geometries and the relation between ac conductance and persistent currents. We observe Φ0/2 periodic oscillations on both components of the magnetoconductance. The oscillations of the imaginary conductance whose sign corresponds to diamagnetism in zero field, are 3 times larger than the Drude conductance G0. The real part of the periodic magnetoconductance is of the order of 0.2G0 and is apparently negative in low field. It is thus notably different from the weak localisation oscillations observed in connected rings, which are much smaller and opposite in sign.Mesoscopic metallic rings present a spectacular thermodynamic property : they carry a persistent non dissipative current when they are threaded by a magnetic flux [1][2][3]. The existence of such a persistent current is a consequence of the coherence of the electronic wave functions along the ring. However unlike a superconductor, when connected to a voltage source, the same rings present a finite ohmic conductance whose value is close to its classical expectation given by the Drude formula, which depends only on the elastic scattering time (quantum interference effects give rise to contributions which are only a small fraction of this main classical contribution in the metallic diffusive regime). It has already been pointed out a number of times [4], that the existence of a finite ohmic resistance for a phase coherent sample is not paradoxical when one properly takes into account the influence of the measuring leads. These macroscopic wires connected to the sample play indeed the role of incoherent reservoirs of electrons where thermalisation of the electrons and dissipation take place. Such a strong coupling with a reservoir of electrons can be avoided by studying the current response of a mesoscopic ring to a time dependant flux, which induces an electric field along the ring. Since the early work of Büttiker et al. [5][6][7] subsequently generalized by a number of authors [8][9][10][11][12], it has been shown that the conductance measured by this last technique on an isolated ring is indeed fundamentally different from the conductance of the same sample connected to a voltage source. It essentially depends on the inelastic time τ in (which describes the coupling of the electrons to the thermal bath). Furthermore it is strongly related to the presence of persistent currents through the ring.In its ac version the experiment consists in measuring the complex magnetic susceptibility of the rings χ(ω) = χ ′ (ω) + iχ ′...
We have computed persistent currents in a disordered mesoscopic ring in the presence of small electron-electron interactions, treated in first order perturbation theory. We have investigated both a contact (Hubbard) and a nearest neighbour interaction in 1D and 3D. Our results show that a repulsive Hubbard interaction produces a paramagnetic contribution to the average current (whatever the dimension) and increases the value of the typical current. On the other hand, a nearest neighbour repulsive interaction results in a diamagnetic contribution in 1D and paramagnetic one in 3D, and tends to decrease the value of the typical current in any dimension. Our study is based on numerical simulations on the Anderson model and is justified analytically in the presence of very weak disorder. We have also investigated the influence of the amount of disorder and of the statistical (canonical or grand-canonical) ensemble.
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