  We present an analytic prescription for computing the edge dispersion E(k) of
a tight-binding Dirac Hamiltonian terminated at an abrupt crystalline edge.
Specifically, we consider translationally invariant Dirac Hamiltonians with
nearest-layer interaction. We present and prove a geometric formula that
relates the existence of surface states as well as their energy dispersion to
properties of the bulk Hamiltonian. We further prove the bulk-boundary
correspondence between the Chern number and the chiral edge modes for quantum
Hall systems within the class of Hamiltonians studied in the paper. Our results
can be extended to the case of continuum theories which are quadratic in the
momentum, as well as other symmetry classes.
