# Enhancement of crossed Andreev reflection in normal-superconductor-normal junction of thin topological insulator

## TL;DR

This paper theoretically studies how hybridization in thin topological insulator NSN junctions enhances crossed Andreev reflection, revealing high CAR probabilities and complex shot noise behaviors influenced by various parameters.

## Contribution

It introduces the role of surface state coupling in thin TIs on subgap transport, especially CAR, and demonstrates how to optimize CAR probability and analyze shot noise characteristics.

## Key findings

- CAR probability can exceed 97% with proper coupling and gating.
- Hybridization induces oscillations in conductance as a function of superconductor length.
- Shot noise cross correlation can switch sign depending on doping and transport channels.

## Abstract

We theoretically investigate the subgapped transport phenomena through a normal-superconductor-normal (NSN) junction made up of ultra thin topological insulator with proximity induced superconductivity. The dimensional crossover from three dimensional ($3$D) topological insulator (TI) to thin two-dimensional ($2$D) TI introduces a new degree of freedom, the so-called hybridization or coupling between the two surface states. We explore the role of hybridization in transport properties of the NSN junction, especially how it affects the crossed Andreev reflection (CAR). We observe that a rib-like pattern appears in CAR probability profile while examined as a function of angle of incidence and length of the superconductor. Depending on the incoming and reflection or transmission channel, CAR probability can be maneuvered to be higher than $97\%$ under suitable coupling between the two TI surface states along with appropriate gate voltage and doping concentration in the normal region. Coupling between the two surfaces also induces an additional oscillation envelope in the behavior of the angle averaged conductance, with the variation of the length of the superconductor. The behavior of co-tunneling (CT) probability is also very sensitive to the coupling and other parameters. Finally, we also explore the shot noise cross correlation and show that the behavior of the same can be monotonic or non-monotonic depending on the doping concentration in the normal region. Under suitable circumstances, shot noise cross correlation can change sign from positive to negative or vice versa depending on the relative strength of CT and CAR.