The Bulk-Edge Correspondence for Disordered Chiral Chains

Monday, 29 January, 2018

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We study one-dimensional insulators obeying a chiral symmetry in the single-particle picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given Hamiltonian with nearest neighbor hopping the two indices are equal. We also give a new formulation of the index in terms of the Lyapunov exponents of the zero energy Schr\"odinger equation, which illustrates the conditions for a topological phase transition occurring in the mobility gap regime.


Gian Michele Graf
Jacob Shapiro