The Majorana-Hubbard Model

When a vortex lattice forms in a superconducting layer on a topological insulator a Majorana fermion is predicted to appear in each vortex core. Hopping and interaction terms between the Majorana fermions lead to a novel generalization of the Hubbard model. Furthermore, the hopping amplitude is predicted to vanish at a special value of the chemical potential in the topological insulator, allowing the phase diagram to be studied as a function of the ratio of interaction strength to hopping amplitude. I will present results on the interesting phase diagrams, which includes supersymmetric critical points, in both one and two dimensions.