  Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host
two pairs of massless two-dimensional Dirac fermions in the absence of or with
negligible spin-orbit coupling. It is known that the existence of non-zero
electric polarization in reduced momentum space which is associated with a
hidden chiral symmetry will lead to the zero-energy flat band of zigzag
nanoribbon. The Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral
charges at different valleys can be realized in a confined ribbon of finite
width. In the laterally diffusive regime, the finite-size correction to
conductivity is always positive and goes inversely with the square of the
lateral dimension W, which is different from the finite-size correction
inversely with W from boundary modes. This anomalous finite-size conductivity
reveals the signature of the chiral anomaly in graphene, and is measurable
experimentally.
