Topologically protected states in one-dimensional continuous systems and Dirac points

Charles L. Fefferman, James P. Lee-Thorp, Michael I. Weinstein

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


We study a class of periodic Schrödinger operators on R that have Dirac points. The introduction of an "edge" via adiabatic modulation of a periodic potential by a domain wall results in the bifurcation of spatially localized "edge states," associated with the topologically protected zero-energymode of an asymptotic one-dimensionalDirac operator. The bound states we construct can be realized as highly robust transverse-magnetic electromagnetic modes for a class of photonic waveguideswith a phase defect. Ourmodel captures many aspects of the phenomenon of topologically protected edge states for 2D bulk structures such as the honeycomb structure of graphene.

Original languageEnglish (US)
Pages (from-to)8759-8763
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number24
StatePublished - 2014

All Science Journal Classification (ASJC) codes

  • General


  • Floquet-Bloch theory
  • Hill's equation
  • Multiple scale analysis
  • Surface states
  • Wave-packets


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