Nanocomposites and nanomaterials

Scattering matrix approach to nonlinear proximity effects in hybrid normal metal-superconductor structures
E.E. Zubov1,2
1 Department of Superconducting Electronics, G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine. Academician Vernadsky Blvd., 36, Kyiv-03142, Ukraine
2 Faculty of Physics and Technology, Donetsk National University, 600-richchia Str., 21, Vinnytsia-21021, Ukraine. E-mail: eezubov@ukr.net

Conventional theories of the proximity effect [1] are based on decoupling two-particle correlators using collective variables for a mean field Hamiltonian and are linear on the tunneling matrix element squared and gap function. This work starts from the site tunneling Hamiltonian, the unitary symmetry of which has been broken by entering quasi-averages in the form of abnormal single-particle correlators. To construct a time dependent perturbation theory, the averaging is performed over the unperturbed Hamiltonian, which corresponds to the energy of the chemical potential. In the case of a homogeneous superconductor, an infinite series of loopless diagrams gives the well-known BCS gap equation. It is shown that at a critical value of the barrier transparency, the gap disappears abruptly. In Fig. 1 frequency dependence of the homogeneous electron spectral density of a superconductor is shown for sufficiently large barrier transparency values N at temperature T = 0 K. Good qualitative agreement with the known experimental data on the differential conductivity of the copper-aluminum tunnel junctions was obtained [2].
The study was partly carried out within the Fundamental Research Programme funded by the Ministry of Education and Science of Ukraine (Project No. 0120U102059).

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