  We study the scattering phase shift of Dirac fermions at graphene edge. We
find that when a plane wave of a Dirac fermion is reflected at an edge of
graphene, its reflection phase is shifted by the geometric phase resulting from
the change of the pseudospin of the Dirac fermion in the reflection. The
geometric phase is the Pancharatnam-Berry phase that equals the half of the
solid angle on Bloch sphere determined by the propagation direction of the
incident wave and also by the orientation angle of the graphene edge. The
geometric phase is finite at zigzag edge in general, while it always vanishes
at armchair edge because of intervalley mixing. To demonstrate its physical
effects, we first connect the geometric phase with the energy band structure of
graphene nanoribbon with zigzag edge. The magnitude of the band gap of the
nanoribbon, that opens in the presence of the staggered sublattice potential
induced by edge magnetization, is related to the geometric phase. Second, we
numerically study the effect of the geometric phase on the Veselago lens formed
in a graphene nanoribbon. The interference pattern of the lens is distinguished
between armchair and zigzag nanoribbons, which is useful for detecting the
geometric phase.
