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Extended defects in graphene, such as linear edges, break the translationalinvariance and can also have an impact on the symmetries specific to masslessDirac-like quasiparticles in this material. The paper examines the consequencesof a broken Dirac fermion parity in the framework of the effective boundaryconditions varying from the Berry-Mondragon mass confinement to a zigzag edge.The parity breaking reflects the structural sublattice asymmetry of zigzag-typeedges and is closely related to the previously predicted time-reversalsymmetric edge states. We calculate the local and global densities of the edgestates and show that they carry a specific polarization, resembling, to someextent, that of spin-polarized materials. The lack of the parity leads to anonanalytical particle-hole asymmetry in the edge-state properties. We use ourfindings to interpret recently observed tunneling spectra in zigzag-terminatedgraphene. We also propose a graphene-based tunneling device where theparticle-hole asymmetric edge states result in a strongly nonlinearconductance-voltage characteristics, which could be used to manipulate thetunneling transport.

Boundary-induced violation of the Dirac fermion parity and its signatures in local and global tunneling spectra of graphene