Axial magnetic catalysis in hyperbolic Dirac materials

Lattice sites patterned on a surface with constant negative curvature comprise a class of 2D materials, named hyperbolic lattices. It has been demonstrated that certain hyperbolic lattices host massless Dirac fermions living on a negatively curved space. Here we present a method for introducing a time-reversal symmetry preserving axial magnetic field onto hyperbolic Dirac systems, through a modified nearest-neighbor hopping scheme. The axial magnetic field is shown to promote a flat band in these systems at zero energy. On such flat bands electron-electron interactions prevail, catalyzing the formation of various density-wave and topological phases at weak coupling.