# Perfect crossed Andreev reflection in Dirac hybrid junctions in the quantum Hall regime

## TL;DR

This paper proposes a method to achieve perfect crossed Andreev reflection in Dirac semimetal junctions under quantum Hall conditions, enabling high-efficiency Cooper pair splitting and spin injection, with controllable parameters and measurable conductance signatures.

## Contribution

It introduces two setups for quantum Hall-superconductor-quantum Hall junctions in Dirac materials that realize unity CAR probability without bias, advancing quantum transport control.

## Key findings

- CAR probability can reach unity in proposed setups
- CAR is controllable by magnetic field, geometry, and doping
- Quantized spin injection per CAR event identified

## Abstract

Perfect crossed Andreev reflection (CAR) is striking for high-efficiency Cooper pair splitting which bears promising applications in quantum communication. Recent experimental advances have disclosed the way to explore CAR in Dirac fermion systems under ultra-strong magnetic fields. We develop a scattering approach to study quantum Hall-superconductor-quantum Hall (QH-S-QH) junctions formed by a two-dimensional (2D) time-reversal symmetric Dirac semimetal. We propose two different setups of the hybrid junction in the quantum limit where only zeroth Landau levels are involved in transport to exploit perfect CAR. In both setups, the CAR probability can reach unity without applying bias voltage and is controllable by the magnetic field strength, junction width, length and doping of the superconductor. CAR dominates the nonlocal transport and is directly measurable by the differential conductances. We also identify a quantized spin injection per CAR event in one of the two setups. Our proposal is experimentally feasible and will be helpful for exploring high-efficiency Cooper pair splitting and spin injection in Dirac materials.