Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov√Bohm to the Little√Parks regime - Gvozdikov, V. M. (ФІЗИКА НИЗЬКИХ ТЕМПЕРАТУР, 2000)
The Aharonov√Bohm (AB) oscillations of the free energy, critical temperature Tc, magnetization M, and magnetic susceptibility c as functions of the magnetic flux Ф through the hollow in a stack of mesoscopic superconducting cylinders are studied both analytically and numerically. The shape of theseoscillations at low temperature T and small level broadening n is generally nonsinusoidal and hassingularities that depend on the superconducting order parameter D and stacking sequence. The periodof the oscillations is equal to the normal flux quantum Ф0. The harmonic amplitudes of the ABoscillations decrease exponentially if the diameter 2R of the cylinders becomes greater than thecoherence length. Further increase of R results in a complete depression of the AB oscillations and the development of the parabolic Little√Parks (LP) oscillations of Tc(Ф), with half the period, Фs=Ф0/2. Therefore a crossover from the AB to LP oscillations takes place as the diameter 2R is increased. It isshown that the temperature behavior of the magnetic susceptibility below the superconducting transitionis cµexp(-T/T*), where T*=·-v0/2p2R. Such dependence of c(T) has been observed recently in Ag wires coated with thin Nb layers in a weak external field [19] (v0 is the Fermi velocity, and ·-is Planck▓s constant).