Zero Bias Conductance in d‐Wave Superconductor/Ferromagnet/d‐Wave Superconductor Trilayers

Abstract

Zero bias conductance (ZBC) in ballistic voltage-biased d-wave superconductor/ferromagnet/d-wave superconductor (DFD) junctions is studied theoretically, for various orientations of superconducting electrodes. We show that ZBC increases with exchange field h in the F barrier, up to some maximum value of h which is of the order of the pair potential in the superconducting electrodes. We find that for a given exchange field, ZBC monotonically decreases with temperature. When the exchange field h is smaller or of the order of the superconducting gap Δ, ZBC has a distinct kink at some characteristic temperature T Ã . It appears that for this temperature Δ(T Ã ) ¼ h.Thus, observing T Ã where the kink in the ZBC temperature dependence occurs provides a reliable measurement method to determine exchange fields of the order of the superconducting gap.

Amplitudes of minima in dynamic conductance spectra of the SNS Andreev contact

“…The KGN theory frameworks were extended by us earlier to introduce the anisotropy of the superconducting gap, as well as some effect of ferromagnet barrier on Andreev transport. [10][11][12][13] We approximate the spatial variation of the pair potential by step function ∆(θ)Θ(|z| − d/2), where ∆(θ) = ∆ max (1+0.5A(cos(4πθ)−1)) reflects anisotropy of the order parameter ∆ in the k xy momentum space (corresponds to the ab-plane of the real space), such that tan(θ) = k y /k x . 9 The coefficient A reflects the gap anisotropy in percentages, while ∆ max is the maximum amplitude.…”

“…Note that, the solution of time dependent BdGEs in the limit of vanishing voltage must turn into the stationary quasiparticle wave function of an superconductor/normal metal junction. In the theory used here 5,[10][11][12][13] voltage dependent solutions evolve from the bound states (while in Ref. 6 the solutions evolving from the scattering states play the dominant role) and quasiparticle start their motion in the electric field from energy |E| < ∆ after each Andreev reflection.…”

“…The theoretical model for calculation current voltage characteristic and dynamic conductance, used here is based on formalism previously developed by Kümmel, Gunsenheimer, and Nicolsky 5 and further adopted by Popović et al [10][11][12][13] Details of calculation can be found in these references and we therefore will give a very brief insight into the formalism used.…”

“…The other numerical way to overcome the minima divergences is to extend the KGN model and involve some superconducting gap anisotropy in the k-space. [10][11][12][13] We used 2% anisotropy and standard four-fold superconducting s-wave order parameter distribution.…”