What happens when fermions hop on a lattice with crystalline defects? The answer depends on topological quantum numbers that specify the action of lattice rotations and translations in the low energy theory. We find that disclinations and dislocations—defects of crystalline symmetries—generally lead to a certain “emanant” quantized magnetic flux in the continuum. To demonstrate these facts, we study in detail tight-binding models whose low-energy descriptions are (2+1)D Dirac cones. Our map from lattice to continuum defects explains the crystalline topological response to disclinations and dislocations, and motivates the fermion crystalline equivalence principle used in the classification of crystalline topological phases.

Pizza and drinks will be served after the seminar in ATL 2117.