Crossed Andreev reflection in quantum wires with strong spin-orbit interaction

We theoretically study tunneling of Cooper pairs from an $s$-wave superconductor into two semiconductor quantum wires with strong spin-orbit interaction under magnetic field, which approximate helical Luttinger liquids. The entanglement of electrons within a Cooper pair can be detected at low temperatures by the electric current cross correlations in the wires. By controlling the relative orientation of the wires, either lithographically or mechanically, on the substrate, these current correlations can be tuned, as dictated by the initial spin entanglement. This proposal of a spin-to-charge readout of quantum correlations is alternative to a recently proposed utilization of the quantum spin Hall insulator.

Figure 1

Single-particle electron dispersion with Rashba and Dresselhaus SOI. Zeeman splitting $2\xi$ is induced at $k=0$ by a magnetic field in the $z$ direction, and the chemical potential is set in this gap. One-dimensional effective theory is then linearized near $\pm k_F$, which define respectively the right- and left-moving electron branches.

Figure 2

$S$-wave superconductor bridging two identical wires. The lower wire is rotated by angle $\theta$ with respect the upper wire. The superconductor is biased by $V$ with respect to the wires.