Vortex Configurations and Bound States of Dirac Fermions

We investigate bound states of Dirac fermions in vortex configurations of a complex scalar field, which describe the low-energy effective theory of various topological phases and Lorentz-violating semimetals. We introduce a corresponding tight-binding model on the square lattice that admits vortex textures in its hopping amplitudes. We study the spectral properties of the electronic states systematically, including the dependence of energy eigenvalues and the inverse-participation ratios of eigenstates on the system size. We demonstrate that vortex configurations harbor robust zero-energy bound states with unusual dimensionality.