Crossed Andreev reflection at spin-active interfaces

Abstract

With the aid of the quasiclassical Eilenberger formalism we develop a theory of non-local electron transport across three-terminal ballistic normal-superconducting-normal (NSN) devices with spin-active NS interfaces. The phenomenon of crossed Andreev reflection (CAR) is known to play the key role in such transport. We demonstrate that CAR is highly sensitive to electron spins and yields a rich variety of properties of non-local conductance which we describe non-perturbatively at arbitrary voltages, temperature, spin-dependent interface transmissions and their polarizations. Our results can be applied to multi-terminal hybrid structures with normal, ferromagnetic and half-metallic electrodes and can be directly tested in future experiments.Comment: 11 pages, 7 figures; figures 6 and 7 are corrected; version published in Phys. Rev.

General framework for transport in spin-orbit-coupled superconducting heterostructures: Nonuniform spin-orbit coupling and spin-orbit-active interfaces

“…We start by analyzing the appropriate Bogoliubovde Gennes (BdG) Hamiltonian and develop a generalized Blonder-Tinkham-Klapwijk (BTK) [58] formalism to calculate the current-voltage characteristics for our general setup. We phenomenologically model what we call the spin-orbit-active interface as a generalization of a spin-active interface [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74], which itself is a generalization of a single Z parameter used in the original BTK approach. We find that the rich physics emanating from non-uniform SOC and/or spin-orbit-active interface is not only of fundamental interest but also highly relevent for interpreting the results of experiments.…”

10.1007/s11448-008-3005-1

“…Nonlocal effects in the coherent electron transport across hybrid structures composed of a superconductor (S) attached to two normal (N) terminals have recently become the subject of intensive experimental [1][2][3] and theoretical [4][5][6][7][8][9][10][11][12] investigations. Provided the distance L between two N terminals (see Fig.…”

“…Turning now to the nonlocal resistance (12) we substitute expressions (10) and (9) into Eq. (12) and, neglecting the small cross-conductance term G 12 G 21 in the denominator, we obtain (13) where = /( ) is the cross resistance in the normal state.…”

Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires

“…The physical separation between the junctions of the twowires with the superconductor is of the order of the size of the Cooper-pair. This leads to the realization of a normal-superconductor-normal (NSN) junction which allows for direct tunneling of electrons from one wire to the other and also allows a finite amplitude for the crossed Andreev reflection (CAR) process 25,26,27,28,29,30,31,32,33,34,35 in addition to the normal reflection and Andreev reflection (AR) processes.In an earlier study of the NSN junction 23 , we showed that the NSN junction has more than two fixed points unlike the normal two-wire junction (as mentioned above) or the junction of LL with a bulk superconductor (NS junction) which has only two fixed points -(i) the Andreev fixed point where the amplitude for Andreev reflection (AR), r A = 1 and normal reflection amplitude, r = 0 and which is unstable and (ii) the disconnected fixed point where r A = 0 and r = 1, and which is stable 12,13 . We showed that there exists a fixed point with intermediate values of transmission and reflection.…”

“…The physical separation between the junctions of the twowires with the superconductor is of the order of the size of the Cooper-pair. This leads to the realization of a normal-superconductor-normal (NSN) junction which allows for direct tunneling of electrons from one wire to the other and also allows a finite amplitude for the crossed Andreev reflection (CAR) process 25,26,27,28,29,30,31,32,33,34,35 in addition to the normal reflection and Andreev reflection (AR) processes.…”