Induced Triplet Pairing in clean s-wave Superconductor/Ferromagnet layered structures

摘要

We study induced triplet pairing correlations in cleanferromagnet/superconductor/ferromagnet heterostructures. The pairing state inthe superconductor is the conventional singlet s-wave, and the angle $\alpha$between the magnetizations of the two ferromagnetic layers is arbitrary. We usea numerical fully self-consistent solution of the microscopic equations andobtain the time-dependent triplet correlations via the Heisenberg equations ofmotion. We find that in addition to the usual singlet correlations, tripletcorrelations, odd in time as required by the Pauli principle, are induced inboth the ferromagnets and the superconductor. These time-dependent correlationsare largest at times of order of the inverse of the Debye cutoff frequency,$\omega_D$, and we find that within that time scale they are often spatiallyvery long ranged. We discuss the behavior of the characteristic penetrationlengths that describe these triplet correlations. We also find that theferromagnets can locally magnetize the superconductor near the interface, andthat the local magnetization then undergoes strongly damped oscillations. Thelocal density of states exhibits a variety of energy signatures, which wediscuss, as a function of ferromagnetic strength and $\alpha$.