Dirac fermion quantization on graphene edges: Isospin-orbit coupling, zero modes and spontaneous valley polarization

Abstract

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.

9 pages, 6 figures, to be published in Phys. Rev. B

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• Dirac Green's function approach to graphene-superconductor junctions with well defined edges
• Surface States of a System of Dirac Fermions: A Minimal Model
• Transition between ordinary and topological insulator regimes in two-dimensional resonant magnetotransport
• Subgap states in two dimensional spectroscopy of unconventional superconductors using graphene
• Greens function of semi-infinite Weyl semimetals
• Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling: I. Kinetic equation and anomalous Hall and spin-Hall effects
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• Boundary States in Graphene Heterojunctions
• Fermi arcs formation in Weyl semimetals: the key role of intervalley interaction
• Two-dimensional topological insulators in quantizing magnetic fields
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• Spin-orbit coupling, edge states and quantum spin Hall criticality due to Dirac fermion confinement: The case study of graphene
• Boundary-induced violation of the Dirac fermion parity and its signatures in local and global tunneling spectra of graphene
• Diffusion on edges of insulating graphene with intravalley and intervalley scattering
• Exciton swapping in a twisted graphene bilayer as a solid-state realization of a two-brane model
• Resonance Absorption of Terahertz Radiation in Nanoperforated Graphene
• Photoabsorption spectra and the X-ray edge problem in graphene
• Dynamical charge and pseudospin currents in graphene and possible Cooper pair formation
• Microscopic Green's function approach for generalized Dirac Hamiltonians
• Complete Spin and Valley Polarization by Total External Reflection from Potential Barriers in Bilayer Graphene and Monolayer Transition Metal Dichalcogenides