Non-Bloch band theory in bosonic Bogoliubov–de Gennes systems

Diagonalization of a bosonic Bogoliubov--de Gennes system is intrinsically a non-Hermitian problem, although its Hamiltonian is Hermitian. Here, the authors study the non-Hermitian nature of bosonic Bogoliubov--de Gennes systems by constructing a non-Bloch band theory. Such systems have a unique non-Hermitian Brillouin zone, where Hermitian and non-Hermitian regions coexist. Accordingly, its non-Hermitian skin effect shows instability against infinitesimal instability and reentrant behavior.