Anomalous crossed Andreev reflection in a mesoscopic superconducting ring hosting Majorana fermions

We investigate the Majorana physics and its effect on the electron transport in the nontopological superconductor (NS)-topological superconductor (TS) double junctions of a loop geometry. We find that, depending on the ratio between the lengths of two topologically different regions and the localization lengths of the Majorana fermions formed between them, two completely different transport mechanisms are working: perfect crossed Andreev reflection (CAR) for the short NS segment and perfect normal Andreev reflection for the short TS segment. The difference is explained in terms of the topologically distinct properties of subgap states in two regions, which have not been revealed so far. The exotic dependence of the CAR process on the magnetic flux threading the loop is uncovered and can be used to detect the Majorana fermions.