Topologically Protected States in One-dimensional Systems

Released on by Charles Fefferman
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  • Topologically Protected States in One-dimensional Systems Book Detail

  • Author : Charles Fefferman
  • Release Date : 2017
  • Publisher :
  • Genre : Dirac equation
  • Pages : 118
  • ISBN 13 : 9781470437077
  • File Size : 78,78 MB
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Topologically Protected States in One-dimensional Systems by Charles Fefferman PDF Summary

Book Description: We study a class of periodic Schrödinger operators, which in distinguished cases can be proved to have linear band-crossings or "mDirac points". We then show that the introduction of an "edge", via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized "edge states". These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. Our model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states we construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.

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