  In the anomalous quantum Hall effect (QHE), a hallmark of graphene, nature of
the edge states in magnetic fields poses an important question, since the edge
and bulk should be intimately related in QHE. Here we have theoretically
studied the edge states, focusing on the E=0 edge mode, which is unusual in
that the mode is embedded right within the n=0 bulk Landau level, while usual
QHE edge modes reside across adjacent Landau levels. Here we show that the n=0
Landau level, including the edge mode, has a wave function amplitude
accumulated along zigzag edges whose width scales with the magnetic length,
l_B. This contrasts with the usual QHE where the charge is depleted from the
edge. The implications are: (i) The E=0 edge states in strong magnetic fields
have a topological origin in the honeycomb lattice, so that they are outside
the continuum ("massless Dirac") model. (ii) The edge-mode contribution decays
only algebraically into the bulk, but this is "topologically" compensated by
the bulk contribution, resulting in the accumulation over l_B. (iii) The real
space behavior obtained here should be observable in STM experiments.
