Electronic transport in hybrid mesoscopic structures: A nonequilibrium Green function approach

We present a unified transport theory of hybrid structures, in which a confined normal state (N) sample is sandwiched between two leads each of which can be either a ferromagnet (F) or a superconductor (S) via tunnel barriers. By introducing a four-dimensional Nambu-spinor space, a general current formula is derived within the Keldysh nonequilibrium Green function formalism, which can be applied to various kinds of hybrid mesoscopic systems with strong correlations even in the nonequilibrium situation. Such a formula is gauge invariant. We also demonstrate analytically for some quantities, such as the difference between chemical potentials, superconductor order parameter phases, and ferromagnetic magnetization orientations, that only their relative value appears explicitly in the current expression. When applied to specific structures, the formula becomes of the Meir-Wingreen-type favoring strong correlation effects, and reduces to the Landauer-Buttiker-type in noninteracting systems such as the double-barrier resonant structures, which we study in detail beyond the wide-band approximation. We find that the spin-dependent density of states of the ferromagnetic lead(s) is reflected in the resonant peak and resonant shoulder structure of the I-V characteristics of F/I/N/I/F structures with large level spacing. The tunnel magnetoresistance that exhibits complex behaviors as a function of the bias voltage, can be either positive or negative, suppressed or enhanced within the resonant peak region(s), depending on the couplings to the leads. The Andreev current spectrum of F/I/N/I/S structures consists of a series of resonant peaks as a function of the gate voltage, of which the number and amplitude are strongly dependent on the bias voltage, degree of spin polarization of the ferromagnetic lead, energy gap of the superconducting lead, and the level configuration of the central region. In S/I/N/I/S resonant structures with asymmetric superconducting energy gaps, the Josephson current through a single resonant level is slightly enhanced in contrast to the significant enhancement of the Josephson current in S/N/S junctions. The current-phase relation is relevant to the level position and the couplings to the superconducting leads.