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Register a new userBoundary effects in two-band superconductors
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We present a microscopic study of the behavior of the order parameters near boundaries of a two-band superconducting material, described by the standard tight-binding Bardeen-Cooper-Schrieffer model. We find superconducting surface states. The relative difference between bulk and surface critical temperatures is a nontrivial function of the interband coupling strength. For superconductors with weak interband coupling, boundaries induce variations of the gaps with the presence of multiple length scales, despite non-zero interband Josephson coupling.
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We present a systematic study of the response properties of two-band (multi-gap) superconductors with spin-singlet (s-wave) pairing correlations, which are assumed to be caused by both intraband (lambda_{ii}, i=1,2) and interband (lambda_{12}) pairing interactions. In this first of three planned publications we concentrate on the properties of such superconducting systems in global and local thermodynamic equilibrium, the latter including weak perturbations in the stationary long-wavelength limit. The discussion of global thermodynamic equilibrium must include the solution (analytical in the Ginzburg-Landau and the low temperature limit) of the coupled self-consistency equations for the two energy gaps Delta_i(T), i=1,2. These solutions allow to study non-universal behavior of the two relevant BCS-Muhlschlegel parameters, namely the specific heat discontinuity Delta C/C_N and the zero temperature gaps Delta_i(0)/pi k_B T_c, i=1,2. The discussion of a local equilibrium situation includes the calculation of the supercurrent density as a property of the condensate, and the calculation of both the specific heat capacity and the spin susceptibility as properties of the gas of thermal excitations in the spirit of a microscopic two-fluid description. Non-monotonic behavior in the temperature dependences of the gaps and all these local response functions is predicted to occur particularly for very small values of the interband pair-coupling constant lambda_{12}.
A model of a clean two-band s-wave superconductor with cylindrical Fermi surfaces, different Fermi velocities v_{1,2}, and a general 2x2 coupling matrix V_{alpha beta} is used to study the order parameter distribution in vortex lattices. The Eilenberger weak coupling formalism is used to calculate numerically the spatial distributions of the pairing amplitudes Delta_1_ and Delta_2_ of the two bands for vortices parallel to the Fermi cylinders. For generic values of the interband coupling V_{12}, it is shown that, independently of the couplings V_{alpha beta}, of the ratio v_1 /v_2, of the temperature, and the applied field, the length scales of spatial variation of Delta_1 and of Delta_2 are the same within the accuracy of our calculations. The only exception from this single length-scale behavior is found for V_{12} --> 0, i.e., for nearly decoupled bands.
The effects of spin independent hybridization potential and spin orbit coupling on two band superconductor with equal time s-wave inter band pairing order parameter is investigated theoretically. To study symmetry classes in two band superconductors the Gorkov equations are solved analytically. By defining spin singlet and spin triplet s wave order parameter due to two band degree of freedom the symmetry classes of Cooper pair are studied. For spin singlet case it is shown that spin independent hybridization generates Cooper pair belongs to even frequency spin singlet even momentum even band parity (ESEE) symmetry class for both intraband and interband pairing correlations. For spin triplet order parameter, intraband pairing correlation generates odd frequency spin triplet even momentum even band parity (OTEE) symmetry class whereas, interband pairing correlation generates even frequency spin triplet even momentum odd band parity ETEO) class. For the spin singlet, spin orbit coupling generates pairing correlation that belongs to odd frequency spin singlet odd momentum even band parity (OSOE) symmetry class and even frequency spin singlet even momentum even band parity (ESEE) for intraband and interband pairing correlation respectively. In the spin triplet case for itraband and interband correlation, spin orbit coupling generates even-frequency spin triplet odd momentum even band parity (ETOE) and even frequency spin triplet even momentum odd band parity (ETEO) respectively.
The microscopic theory of Josephson effect in point contacts between two-band superconductors is developed. The general expression for the Josephson current, which is valid for arbitrary temperatures, is obtained. We considered the dirty superconductors with interband scattering, which produces the coupling of the Josephson currents between different bands. The influence of phase shifts and interband scattering rates in the banks is analyzed near critical temperature Tc. It is shown that for some values of parameters the critical current can be negative, which means the pi-junction behavior.
We consider the behaviour of the fluctuating specific heat and conductivity in the vicinity of the upper critical field line for a two-band superconductor. Multiple-band effects are pronounced when the bands have very different coherence lengths. The transition to superconductive state is mainly determined by the properties of the rigid condensate of the strong band, while the weak band with a large coherence length of the Cooper pairs causes the nonlocality in fluctuation behaviour and break down of the simple Ginzburg-Landau picture. As expected, the multiple-band electronic structure does not change the functional forms of dominating divergencies of the fluctuating corrections when the magnetic field approaches the upper critical field. The temperature dependence of the coefficients, however, is modified. The large in-plane coherence length sets the field scale at which the upper critical field has upward curvature. The amplitude of fluctuations and fluctuation width enhances at this field scale due to reduction of the effective z-axis coherence length. We also observe that the apparent transport transition displaces to lower temperatures with respect to the thermodynamic transition. Even though this effect exists already in a single-band case at sufficiently high fields, it may be strongly enhanced in multiband materials.
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