Mean-field phase diagram of negative-U Hofstadter-Hubbard model

It has been predicted that topological superconductivity supporting Majorana quasiparticles can

be produced by proximity coupling the Dirac metal at the surface of a topological insulator to an

ordinary superconductor, effectively giving rise to p-wave superconductivity. We investigate here

the phase diagram of a p-wave superconductor in two dimensions, modeled as a system of spinless

electrons on a lattice with nearest neighbor attractive interaction, exposed to a magnetic field. We

solve the mean-field Bogoliubov-de Gennes equations, in both the pairing and density channels, in

a self-consistent, gauge-invariant fashion. We find that as the interaction strength is increased, the

system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully

gapped in the bulk but has topological chiral edge current, followed by a vortex phase in which

either the vortices form a lattice with one vortex per unit cell, and the fermionic spectrum contains

a low-energy Majorana band, or the vortices form dimers with two vortices per unit cell, and the

low-energy band is gapped. The observable consequences of skyrmions as well as Majorana fermions

are indicated.