Realization of intrinsically broken Dirac cones in graphene via the momentum-resolved electronic band structure

A way to represent the band structure that distinguishes between energy-momentum and energy-crystal momentum relationships is proposed upon the band-unfolding concept. This momentum-resolved band structure offers better understanding of the physical processes requiring the information of wave functions in momentum space and provides a direct connection to angle-resolved photoelectron spectroscopy (ARPES) spectra. Following this approach, we demonstrate that Dirac cones in graphene are intrinsically broken in momentum space and can be described by a conceptual unit cell smaller than the primitive unit cell. This hidden degree of freedom can be measured by ARPES experiments as missing weight that is retrievable by investigating the effect of different polarized light. Having the energy-momentum relationship, we provide alternative understanding of the retrieved momentum intensity beyond the periodic-zone scheme, that is, the retrieved momentum intensity is assisted with the properties of final states, not from the Dirac cones directly. The revealed broken Dirac cones and momenta supplied by the lattice give interesting ingredients for designing advanced nanodevices.