Isothermal reentrant effect in a mesoscopic cylindrical structure of a superconductor coated with a normal metal layer G. A. Gogadze ∗ and S. N. Dolya B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47, Lenin Ave., Kharkov 61103, Ukraine. (Dated: November 10, 2018) The coherent phenomena in mesoscopic cylindrical normal metal (N) - superconductor (S) struc- tures have been investigated theoretically. The magnetic moment (persistent current) of such a structure has been calculated numerically and (approximately) analytically. It is shown that the current in the N-layer corresponding to the free energy minimum is always diamagnetic. As the field increases, the magnetic moment (current) exhibits jumps at certain values of the trapped magnetic flux and the NS structure changes to a state with smaller absolute value of the diamagnetic moment. This occurs when the persistent current is unable to screen the external field. The magnetic moment increase stepwise and the system changes into a new stable state. The magnetic field penetrates into a larger volume of the N-layer. The new state has smaller absolute value of the diamagnetic moment. Experimentally, this is interpreted as the presence of a paramagnetic addition in the sys- tem (paramagnetic reentrant effect). The results obtained are in qualitative agreement with the experiments conducted by P. Visani, A. C.Mota, and A. Pollini, Phys. Rev. Lett. 65 , 1514 (1990). PACS numbers: 74.45.+C, 74.50.+r There have been numerous attempts to explain the paramagnetic reentrant effect theoretically [5–7]. How- ever, the predicted amplitudes of the effect were too small ( except for [6] ) to account for the experimental facts. Fauchere, Belzig and Blatter [6] explain the large param- agnetic effect assuming strong repulsive electron-electron interaction in noble metals. The proximity effect in the N metal induces an order parameter will be shifted by π from the order parameter Δ of the bulk superconduc- tor. This generates the paramagnetic instability of the Andreev states, and the density of states of the NS struc- ture exhibits a single peak near zero energy. The theory developed in Ref. [6] essentially relies on the assumption of the repulsive electron interaction in the normal region. The Meissner effect in a mesoscopic cylindrical struc- ture consisting of a superconductor coated with a pure normal-metal layer has interesting features due to the coherent quantum effects in the normal metal. They are observable when there is a good contact between S and N constituents. This problem within the quasiclassical Eilenberger formalism was first investigated theoretically by Zaikin [1]. Maki and Haas [7] made the assumption that in no- ble metals (Ag, Au) p-wave superconductors may occur with a transition temperature of order 10 mK. Below T$_{c}$ p -wave triplet superconductivity emerges around the pe- riphery of the cylinder. The diamagnetic current flowing in the periphery is compensated by a quantized param- agnetic current in the opposite direction thus providing a simple explanation for the reentrant effect. As in [5], the authors of [7] also allow for paramagnetic current in the system, which flows in the opposite direction to the dia- magnetic current. Its amplitude is sufficient to explain the reentrant effect, but this theory says nothing about the temperature and field dependences of magnetic sus- ceptibility at ultra-low temperatures and in low magnetic fields. Recent advanced technologies of preparation of pure samples have enabled to investigate the coherence prop- erties of mesoscopic samples taking a proper account of the proximity effect [2]. The samples were superconduct- ing Nb wires with a radius R of tens of microns coated with a thin layer d of high-purity Cu, Ag or Au. Mota and co-workers [3] detected surprising behavior of the magnetic susceptibility χ of a cylindrical NS structure (N and S are for the normal metal and the superconduc- tor, respectively) at very low temperatures ( T < 100 mK ) in an external magnetic field parallel to the NS boundary. Most intriguingly, a decrease in the sample temperature below a certain point T$_{r}$ (at a fixed field) produced a paramagnetic reentrant effect: the decrease of magnetic susceptibility of the structure is changed to an unexpected grow. A similar behavior was observed in the isothermal reentrant effect in a field decreasing to a certain value H$_{r}$ below which the susceptibility started to grow sharply. It is emphasized in Ref. [4] that the de- tected magnetic response of the NS structure is similar to the properties of the persistent currents in mesoscopic normal rings. A theoretical basis for understanding the paramagnetic reentrant effect has been proposed in [8–10]. The theory is essentially based on the properties of the quantized levels of the NS structure. The Meissner effect is rather special in a superconducting cylinder coated with a pure normal-metal layer. The applied magnetic field gener- ates superconducting current in the surface layer whose ∗ Electronic address: gogadze@ilt.kharkov.ua arXiv:1001.0090v1 [cond-mat.supr-con] 31 Dec 2009 I. INTRODUCTION