Topological edge states for disordered bosonic systems

TL;DR

This paper investigates topological edge states in disordered bosonic systems described by non-selfadjoint BdG Hamiltonians, showing their robustness and potential dynamical instability despite bulk stability.

Contribution

It provides a thorough analysis of topological invariants in bosonic BdG Hamiltonians and demonstrates the existence and robustness of edge states in disordered settings.

Findings

Bosonic edge states are robust to a wide class of disordered perturbations.

Topological invariants like Chern and winding numbers can be defined for non-selfadjoint BdG Hamiltonians.

Edge states can be dynamically unstable even when bulk modes are stable.

Abstract

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.