Klein bound states in single-layer graphene

The Klein paradox, introduced in the study of chiral tunneling in single-layer graphene, is shown to also manifest in graphene bound states with a 1D square-well potential. Such bound states occur both below and above the potential well. We derive bound-state wave functions, in the absence and in the presence of an external transverse magnetic field, and calculate the corresponding electronic currents and dipole transition rates, which can be experimentally probed. The role of parity and time-reversal symmetries is discussed. Our results are also relevant for the physics of bound states of light in periodic optical waveguide structures.