Transport theory of multiterminal hybrid structures
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We derive a microscopic transport theory of multiterminal hybrid structures in which a superconductor is connected to several spin-polarized electrodes. We discuss the non-perturbative physics of extended contacts, and show that such contacts can be well represented by averaging out the phase of the electronic wave function. The intercontact Andreev reflection and elastic cotunneling conductances are identical if the phase can be averaged out, namely in the presence of at least one extended contact. The maximal conductance of a two-channel contact is proportional to (e2/h)(a0/D)2exp[-D/ξ(ω*)], where D is the distance between the contacts, a0 the lattice spacing, ξ(ω) is the superconducting coherence length, and ω* is the cross-over frequency between a perturbative regime ( ω < ω*) and a non perturbative regime ( ω* < ω < Δ).
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