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

We theoretically investigate the subgapped transport phenomena through a normal-superconductor-normal (NSN) junction made up of ultrathin topological insulator with proximity-induced superconductivity. The dimensional crossover from three-dimensional topological insulator (TI) to thin two-dimensional 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 riblike 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 cotunneling (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 nonmonotonic 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.