Bosonic Andreev bound state
- URL: http://arxiv.org/abs/2310.09197v1
- Date: Fri, 13 Oct 2023 15:44:01 GMT
- Title: Bosonic Andreev bound state
- Authors: Nobuyuki Okuma
- Abstract summary: A general free bosonic system with a pairing term is described by a bosonic Bogoliubov-de Gennes (BdG) Hamiltonian.
In fermionic BdG systems, a topological invariant of the whole particle (hole) bands can be nontrivial.
In bosonic cases, the corresponding topological invariant is thought to be trivial owing to the stability of the bosonic ground state.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: A general free bosonic system with a pairing term is described by a bosonic
Bogoliubov-de Gennes (BdG) Hamiltonian. The representation is given by a
pseudo-Hermitian matrix, which is crucially different from the Hermitian
representation of a fermionic BdG Hamiltonian. In fermionic BdG systems, a
topological invariant of the whole particle (hole) bands can be nontrivial,
which characterizes the Andreev bound states (ABS) including Majorana fermions.
In bosonic cases, on the other hand, the corresponding topological invariant is
thought to be trivial owing to the stability condition of the bosonic ground
state. In this Letter, we consider a two-dimensional model that realizes a
bosonic analogy of the ABS. The boundary states of this model are located
outside the bulk bands and are characterized by a nontrivial Berry phase (or
polarization) of the hole band. Furthermore, we investigate the zero-energy
flat-band limit in which the Bloch Hamiltonian is defective, where the particle
and hole states are identical to each other. In this limit, the Berry phase is
$\mathbb{Z}_2$ quantized thanks to an emergent parity-time symmetry. This is an
example of a topological invariant that uses the defective nature as a
projection structure. Thus, boundary states in our model are essentially
different from Hermitian topological modes and their variants.
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