Topologically Protected States in One-Dimensional Systems (Memoirs of the American Mathematical Society; Volume 247, Number 1173) by C. L. Fefferman, J. P. Lee-Thorp, and M. I. Weinstein - 2017

American Mathematical Society, 2017. Paperback. New Book. Paperback. Feffermam, Lee-Thorp, and Weinstein study a class of periodic Schrödinger operators that, in distinguished cases, can be proved to have linear band-crossings or Dirac points. Then they show that adding an edge--through the adiabatic modulation of these periodic potentials by a domain wall--results in the bifurcation of spatially localized edge states. These bounded states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator, they say, and their model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. (2017 Ringgold, Inc., Portland, OR)