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Long Range Coulomb Interaction and the Majorana Fermions

We have investigated the effects of long-range Coulomb interaction on the topological superconducting phase in a quasi-one dimensional semiconductor wire, proximity coupled to a s-wave using the exact diagonalization approach. We find that in accordance with previous studies the addition of Coulomb interaction results in an enlargement of the region of parameter values where topological superconductivity can be observed. However, we also find that although the interaction decreases the bulk gap for values of the magnetic field close to the phase transition point, for moderate magnetic fields away from the transition point, the interaction actually enhances the bulk gap which can be important for observation of topological superconductivity in this system.