Circuit theory of crossed Andreev reflection

Abstract

We consider transport in a three-terminal device attached to one superconducting and two normal-metal terminals, using the circuit theory of mesoscopic superconductivity. We compute the nonlocal conductance of the current out of the first normal-metal terminal in response to a bias voltage between the second normal-metal terminal and the superconducting terminal. The nonlocal conductance is given by competing contributions from crossed Andreev reflection and electron cotunneling, and we determine the contribution from each process. The nonlocal conductance vanishes when there is no resistance between the superconducting terminal and the device, in agreement with previous theoretical work. Electron cotunneling dominates when there is a finite resistance between the device and the superconducting reservoir. Dephasing is taken into account, and the characteristic time scale is the particle dwell time. This gives rise to an effective Thouless energy. Both the conductance due to crossed Andreev reflection and electron cotunneling depend strongly on the Thouless energy. We suggest experimental determination of the conductance due to crossed Andreev reflection and electron cotunneling in measurement of both energy and charge flow into one normal-metal terminal in response to a bias voltage between the other normal-metal terminal and the superconductor.

Microscopic theory of Cooper pair beam splitters based on carbon nanotubes

“…2 In this case a key issue which was extensively addressed theoretically is the competition between CAR processes and direct tunneling of electrons between the normal leads. The cancellation between the two contributions to the nonlocal conductance for thick tunnel barriers was shown to be removed by introducing ferromagnetic leads, 6 increasing the barrier transparency, 7 or taking into account Coulomb interactions. 8 The importance of nonequilibrium effects at large bias voltages has been also analyzed.…”

Andreev Reflection and Creation of Spin-Entangled Charge Carriers in Double Barrier Junctions

“…In particular, we have concentrated on the role of the local (LAR) and nonlocal (crossed Andreev reflection -CAR) Andreev reflections [1][2][3][4][5][6][7][8] both in the single-particle transport as well as the pairwise spin entangled transport. The charge transport can be decomposed into two components, local if the entangled quasiparticles enter the same lead and nonlocal if they enter different leads.…”

Spin Dependent Electron Tunneling in a Ferromagnet Superconductor Ferromagnet Junction

“…The second one, nonlocal processes, occurs in a region where there is no drive current. It is characteristic of multi-terminal junctions [1] and consists of the crossed Andreev (CAR) reflection and elastic co-tunneling (EC) [2][3][4][5][6][7][8]. It has been shown [1,8] that when the distance l between the ferromagnetic electrode metals is smaller than or comparable to the superconducting coherence length ξ, an injection of an electron (or hole) with a subgap energy leads to the additional nonlocal transport processes named the CAR and EC [2].…”