A resolvent expansion for a 3D Hamiltonian yields approximate quasiperiodic 2D edge states for incommensurate line defects in honeycomb Schrödinger operators, with energies dense in the bulk spectral gap.
An operator generalization of the logarithmic residue theorem and the theorem of Rouché
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Continuum honeycomb Schr\"odinger operators with incommensurate line defects
A resolvent expansion for a 3D Hamiltonian yields approximate quasiperiodic 2D edge states for incommensurate line defects in honeycomb Schrödinger operators, with energies dense in the bulk spectral gap.