Long-range Coulomb interaction and Majorana fermions

We report on our exact diagonalization studies of the effects of screened and unscreened long-range Coulomb interaction on the topological superconductivity (TS) phase in a quasi-one-dimensional semiconductor wire, proximity-coupled to an s-wave superconductor. We found that inclusion of the Coulomb interaction results in an enlargement of the region of parameter values where TS can be observed. This enlargement is proportional to the screening length of the Coulomb interaction. We also found that the interaction decreases the superconducting bulk gap. Some screening of the Coulomb interaction was found to be essential for observing TS in a quasi-one-dimensional semiconductor wire proximity-coupled to an s-wave superconductor. The theoretical framework employed here is quite general and can be used to address the issue of orbital effects and multichannel two-dimensional quantum wire for observation of TS in the presence of the Coulomb interaction between electrons.