Topological edge states for disordered bosonic systems

29 Aug 2017  ·  Peano Vittorio, Schulz-Baldes Hermann ·

Quadratic bosonic Hamiltonians over a one-particle Hilbert space can be described by a Bogoliubov-de Gennes (BdG) Hamiltonian on a particle-hole Hilbert space. In general, the BdG Hamiltonian is not selfadjoint, but only $J$-selfadjoint on the particle-hole space viewed as a Krein space... Nevertheless, its energy bands can have non-trivial topological invariants like Chern numbers or winding numbers. By a thorough analysis for tight-binding models, it is proved that these invariants lead to bosonic edge modes which are robust to a large class of possibly disordered perturbations. Furthermore, general scenarios are presented for these edge states to be dynamically unstable, even though the bulk modes are stable. read more

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Mathematical Physics Mathematical Physics