Topologically Protected States in One-Dimensional Systems

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

• Introduction and outlineFloquet-Bloch and Fourier analysisDirac points of 1D periodic structuresDomain wall modulated periodic Hamiltonian and formal derivation of topologically protected bound statesMain Theorem--Bifurcation of topologically protected statesProof of the Main TheoremAppendix A. A variant of Poisson summationAppendix B. 1D Dirac points and Floquet-Bloch eigenfunctionsAppendix C. Dirac points for small amplitude potentialsAppendix D. Genericity of Dirac points - 1D and 2D casesAppendix E. Degeneracy lifting at Quasi-momentum zeroAppendix F. Gap opening due to breaking of inversion symmetryAppendix G. Bounds on leading order terms in multiple scale expansionAppendix H. Derivation of key bounds and limiting relations in the Lyapunov-Schmidt reductionReferences