Related papers: Bosonic Andreev bound state
We discuss the topology of Bogoliubov excitation bands from a Bose-Einstein condensate in an optical lattice. Since the Bogoliubov equation for a bosonic system is non-Hermitian, complex eigenvalues often appear and induce dynamical…
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…
There have been several criteria for the existence of topological edge states in 1D non-Hermitian two-band sublattice-symmetric tight-binding Hamiltonians. The generalized Brillouin zone (GBZ) approach uses the integration of the Berry…
We consider a Bogolibov-de Geenes (BdG) Hamiltonian, which is a non-Hermitian Hamiltonian with pseudo-Hermiticity, for a system of (pseudo) spin-$1/2$ bosons in a honeycomb lattice under the condition that the population difference between…
Since the theoretical prediction and experimental observation of the thermal Hall effect of magnons, a variety of novel phenomena that may occur in magnonic systems have been proposed. In this paper, we review the recent advances in the…
We investigate the bulk-boundary correspondence for massless Dirac fermion in $\alpha$-${T}_3$ lattice where the Berry phase can be continuously tuned from $\pi $ (graphene) to $0$ ($T_3$ or dice lattice) without modifying the energy…
Andreev bound states (ABSs) in hybrid semiconductor-superconductor nanowires can have near-zero energy in parameter regions where band topology predicts trivial phases. This surprising fact has been used to challenge the interpretation of a…
The energy spectrum of bosonic excitations from a condensate is given by the spectrum of a non-Hermitian Hamiltonian constructed from a bosonic Bogoliubov-de Gennes (BdG) Hamiltonian in general even though the system is essentially…
Unlike their fermionic counterparts, the dynamics of Hermitian quadratic bosonic Hamiltonians are governed by a generally non-Hermitian Bogoliubov-de Gennes effective Hamiltonian. This underlying non-Hermiticity gives rise to a dynamically…
Despite the extensive studies of topological states, their characterization in strongly nonlinear classical systems has been lacking. In this work, we identify the proper definition of Berry phase for nonlinear bulk modes and characterize…
In recent research, it has been shown that non-Hermitian systems exhibit sensitivity to boundaries, and it is caused by the non-Hermitian skin effect. In this work, we construct the non-Bloch band theory in bosonic Bogoliubov--de Gennes…
The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked `non-Hermitian skin effect' necessitates redefinition of topological invariants in a generalized…
We consider chiral, generally nonlinear density waves in one dimension, modelling the bosonized edge modes of a two-dimensional fermionic topological insulator. Using the coincidence between bosonization and Lie-Poisson dynamics on an…
The Bernard-LeClair (BL) symmetry classes generalize the ten-fold way classes in the absence of Hermiticity. Within the BL scheme, time-reversal and particle-hole come in two flavors, and "pseudo-Hermiticity" generalizes Hermiticity. We…
We study the charge character of the Andreev bound states (ABSs) in one-dimensional topological superconductors with spatial inversion symmetry (SIS) breaking. Despite the absence of the SIS, we show a hidden symmetry for the Bogoliubov de…
Among non-Hermitian systems, pseudo-Hermitian phases represent a special class of physical models characterized by real energy spectra and by the absence of non-Hermitian skin effects. Here, we show that several pseudo-Hermitian phases in…
In this work we consider general fermion systems in two spatial dimensions, both with and without charge conservation symmetry, which realize a nontrivial fermionic topological order with only Abelian anyons. We address the question of…
We examine different topological phases in three-dimensional non-centrosymmetric superconductors with time-reversal symmetry by using three different types of topological invariants. Due to the bulk boundary correspondence, a non-zero value…
Non-Hermitian systems exhibit striking exceptions from the paradigmatic bulk-boundary correspondence, including the failure of bulk Bloch band invariants in predicting boundary states and the (dis)appearance of boundary states at parameter…
We demonstrate the existence of topologically nontrivial phase in a one-dimensional fermionic lattice system subjected to synthetic gauge fields, which is beyond the standard Altland-Zirnbauer classification of topological insulators. The…