Majorana-Hubbard Model on the Triangular Lattice

Of late, there has been a growing body of experimental work that brings us closer to an undoubted realization of Majorana fermions in condensed matter systems. In two-dimensions these quasiparticles arise as zero energy vortex bound states on the surface of a topological superconductor. And in the presence of a lattice of these vortices, interactions between these Majorana zero modes (MZMs) fall off exponentially with the superconducting coherence length. This motivates the construction of a tight-binding model to describe the low energy physics. Given that the vortex lattice usually has a triangular geometry, we study the role of interactions in this setup using a combination of mean field theory and numerical simulation of ladder variants of the model using the density-matrix renormalization-group technique. Our analysis indicates an interaction driven phase transition into a critical phase.