Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov√Bohm to the Little√Parks regime

Анотація

The Aharonov√Bohm (AB) oscillations of the free energy, critical temperature T_c, 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 these oscillations at low temperature T and small level broadening n is generally nonsinusoidal and has singularities that depend on the superconducting order parameter D and stacking sequence. The period of the oscillations is equal to the normal flux quantum Ф₀. The harmonic amplitudes of the AB oscillations decrease exponentially if the diameter 2R of the cylinders becomes greater than the coherence 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 T_c(Ф), with half the period, Ф_s=Ф₀/2. Therefore a crossover from the AB to LP oscillations takes place as the diameter 2R is increased. It is shown that the temperature behavior of the magnetic susceptibility below the superconducting transition is 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).