Topologically Protected States in One-Dimensional Systems

Charles Fefferman · James P. Lee-Thorp · M. I. Weinstein

Apr. 2017 · Memoirs of the American Mathematical Society Boek 248 · American Mathematical Soc.

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The authors study a class of periodic Schrodinger operators, which in distinguished cases can be proved to have linear band-crossings or ``Dirac points''. They 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. The authors' 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 the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.

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C. L. Fefferman: Princeton University, New Jersey,
J. P. Lee-Thorp: Columbia University, New York, NY,
M. I. Weinstein: Columbia University, New York, NY