A four-band hexapole model of a honeycomb plasmonic crystal exhibits symmetry-enforced nodal loops around K and K' that survive weak symmetry breaking and can be gapped by a Kekulé distortion.
Valley-momentum locking in a graphene superlattice with Y-shaped Kekul\'e bond texture
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abstract
Recent experiments by Guti\'errez $\textit{et al.}$ [Nature Phys. $\textbf{12}$, 950 (2016)] on a graphene-copper superlattice have revealed an unusual Kekul\'e bond texture in the honeycomb lattice --- a Y-shaped modulation of weak and strong bonds with a wave vector connecting two Dirac points. We show that this so-called "Kek-Y" texture produces two species of massless Dirac fermions, with valley isospin locked parallel or antiparallel to the direction of motion. In a magnetic field $B$ the valley degeneracy of the $B$-dependent Landau levels is removed by the valley-momentum locking --- but a $B$-independent and valley-degenerate zero-mode remains.
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Nodal lines in a honeycomb plasmonic crystal with synthetic spin
A four-band hexapole model of a honeycomb plasmonic crystal exhibits symmetry-enforced nodal loops around K and K' that survive weak symmetry breaking and can be gapped by a Kekulé distortion.