Multiple Majorana edge modes in magnetic topological insulator–superconductor heterostructures

We numerically investigate the electronic transport properties (i.e., electron tunneling and Andreev reflection) of a topological superconductor composed of a magnetic topological insulator and superconductors. A phase diagram is provided to distinguish various topological phases and their corresponding distinct Majorana edge modes. When superconductors are proximity coupled with the top and bottom surfaces of a magnetic topological insulator thin film, a quantum phase transition from topological insulator to quantum anomalous Hall effect passes through the regime possessing both chiral and helical edge modes. The hallmark feature is that the coefficient of electron tunneling is quantized to be $5/4$ and the remaining scattering processes exhibit an identical probability with a magnitude of $1/4$ in the coexisting states with a Chern number of $\mathcal{N}=\ifmmode\pm\else\textpm\fi{}1$. When the superconductors are proximity coupled with a nonmagnetic topological insulator thin film, we find that the perfectly quantized electron tunneling or crossed Andreev reflection can alternately appear via tuning the chemical potential.