Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator

We study the proximity effect between an $s$-wave superconductor and the surface states of a strong topological insulator. The resulting two-dimensional state resembles a spinless $p_x+i{p}_y$ superconductor, but does not break time reversal symmetry. This state supports Majorana bound states at vortices. We show that linear junctions between superconductors mediated by the topological insulator form a nonchiral one-dimensional wire for Majorana fermions, and that circuits formed from these junctions provide a method for creating, manipulating, and fusing Majorana bound states.