  We revisit the spectral problem for Bloch electrons in a two-dimensional
bipartite honeycomb lattice under a uniform magnetic field. It is well-known
that such a honeycomb structure is realized in graphene. We present a
systematic framework to compute the perturbative magnetic flux expansions near
two distinct band edges. We then analyze the nonperturbative bandwidth of the
spectrum. It turns out that there is a novel similarity between the spectrum
near the Dirac point in the honeycomb lattice and the spectrum in the
supersymmetric sine-Gordon quantum mechanics. We finally confirm a nontrivial
vacuum-instanton-bion threesome relationship. Our analysis heavily relies on
numerical experiments.
