Majorana modes in a topological insulator/s-wave superconductor heterostructure

In a recent experiment, signatures of Majorana fermion (MF) were found in the vortex core threading a heterostructure composed of n layers of topological insulator (TI) deposited on a bulk s-wave superconductor. Here we provide strong theoretical support to the experiment. First, we demonstrate that MF modes appear on both top and bottom layers of TI, and are well separated for n ~ 6. The top MF becomes more extended with increasing n, in agrement with the experiment. Second, we show both analytically and numerically that right at the vortex core the MF mode is always accompanied by another low energy bound state, leading to a zero-bias peak plus a side peak in the local density of states (LDOS) therein. However, a local scalar impurity at the core can wipe out the accompanying side-peak state while leaving the zero-energy MF mode intact. Consequently the LDOS becomes symmetric about the fermi level, and the peak does not branch near the vortex core, in agreement with the experiment. Finally but unfortunately, while the MF is extremely stable against a single local impurity, the stability in terms of the critical impurity strength is reduced drastically for a moderate concentration (e.g., 10%) of impurities.