Majorana Edge States in Interacting One-Dimensional Systems

Majorana fermions are exotic particles that are their own
anti-particles. Originally discussed in the context of high-energy
physics, these particles remain elusive and have not yet been
detected. Recently, a number of proposals have been made for a solid-
state realization of Majorana fermions. It turns out that in these
setups they are expected to be spatially localized and amenable to
detection. One of these proposals involves a quantum wire in the
presence of spin-orbit interaction, magnetic field and
proximity-induced superconductivity, where for appropriate parameter
strength Majorana states appear at the two ends of the quantum
wire. While the analysis was originally performed in a non-interacting
picture, we show that for weak interactions the Majorana edge states
persist. On the other hand, strong interactions generically destroy
the induced superconducting gap that stabilizes the Majorana edge
states.