Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2008-11-17
Phys. Rev. B 79, 045429 (2009)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
9 pages, 6 figures, to be published in Phys. Rev. B
Scientific paper
10.1103/PhysRevB.79.045429
The paper addresses boundary electronic properties of graphene with a complex edge structure of the armchair/zigzag/armchair type. It is shown that the finite zigzag region supports edge bound states with discrete equidistant spectrum obtained from the Green's function of the continuum Dirac equation. The energy levels exhibit the coupling between the valley degree of freedom and the orbital quantum number, analogous to a spin-orbit interaction. The characteristic feature of the spectrum is the presence of a zero mode, the bound state of vanishing energy. It resides only in one of the graphene valleys, breaking spontaneously Kramers' symmetry of the edge states. This implies the spontaneous valley polarization characterized by the valley isospin $\pm 1/2$. The polarization is manifested by a zero-magnetic field anomaly in the local tunneling density of states, and is directly related to the local electric Hall conductivity.
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