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Spectral properties of periodic systems cut at an angle

Mathematical Physics 2021-10-28 v2 Materials Science math.MP Spectral Theory

Abstract

We consider a semi-periodic two-dimensional Schr\"odinger operator which is cut at an angle. When the cut is commensurate with the periodic lattice, the spectrum of the operator has the band-gap Bloch structure. We prove that in the incommensurable case, there are no gaps: the gaps of the bulk operator are filled with edge spectrum.

Keywords

Cite

@article{arxiv.2104.00760,
  title  = {Spectral properties of periodic systems cut at an angle},
  author = {David Gontier},
  journal= {arXiv preprint arXiv:2104.00760},
  year   = {2021}
}