Crossed Andreev reflection in altermagnets

Crossed Andreev reflection (CAR) is a scattering phenomenon occurring in a superconductor (SC) connected to two metallic leads, where an incident electron on one side of the SC emerges on the opposite side as a hole. Despite its significance, CAR detection is often impeded by the prevalent electron tunneling (ET), wherein the incident electron exits on the opposing side as an electron. One approach to augment CAR over ET involves employing two antiparallel ferromagnets across the SC. However, this method is constrained by the low polarization in ferromagnets and necessitates the application of a magnetic field. Altermagnets (AMs) present a promising avenue for detecting and enhancing CAR due to their distinct Fermi surfaces for the two spins. Here, we propose a configuration utilizing two AMs rotated by $90^{\circ}$ with respect to each other on either side of an SC to enhance CAR. We calculate local and nonlocal conductivities across the AM-SC-AM junction using the Landauer-B\"uttiker scattering approach. Our findings reveal that in the strong phase of AMs, CAR overwhelmingly dominates nonlocal transport. In the weak phase, CAR can exhibit significant enhancement for larger values of the altermagnetic parameter compared to the scenario where AMs are in the normal metallic phase. As a function of the length of the SC, the conductivities exhibit oscillations reminiscent of Fabry-P\'erot interference.