From quantized local Andreev reflection to perfect crossed Andreev reflection in topological insulator–superconductor hybrid systems

We systemically investigate the quantized local Andreev reflection (LAR) and crossed Andreev reflection (CAR) in four-terminal topological insulator--superconductor hybrid systems based on the Kane-Mele model and Haldane model corresponding to the quantum spin Hall (QSH) and quantum anomalous Hall (QAH) systems. We find that although both are driven by edge states, the LAR and CAR behave in different ways. The essential difference between the LAR and CAR is the coherent phases of incoming electrons and outgoing holes in the transport processes. For the LAR, the total phase remains zero, and quantum interference is always constructive. However, for the CAR, the coherent phase varies with system parameters. Fortunately, we find a weak magnetic field can smoothly modify the edge states and then the interference phase; finally, a perfect quantized CAR is realized in the QAH-superconductor hybrid systems. In addition, the quantized LAR is more robust against random disorder because the coherent phases carried by electrons are completely canceled out by holes.