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• W3204182388 abstract "We consider a Bogoliubov--de Gennes (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 the two spin components, i.e., magnetization, is a constant. Such a system is capable of acting as a topological amplifier, under time-reversal symmetry, with stable bulk bands but unstable edge modes which can be populated at an exponentially fast rate. We quantitatively study the topological properties of this model within the framework of the 38-fold way for non-Hermitian systems. We find, through the symmetry analysis of the Bloch Hamiltonian, that this model is classified either as two copies of symmetry class $text{AIII}+{ensuremath{eta}}_{ensuremath{-}}$ or two copies of symmetry class $text{A}+ensuremath{eta}$ depending on whether the (total) system is time-reversal symmetric, where $ensuremath{eta}$ is the matrix representing pseudo-Hermiticity and ${ensuremath{eta}}_{ensuremath{-}}$ indicates that pseudo-Hermiticity and chiral symmetry operators anticommute. We prove, within the context of non-Hermitian physics where eigenstates obey the bi-orthonormality relation, that a stable bulk is characterized by a single topological invariant, the Chern number for the Haldane model, independent of pairing interactions. We construct a convenient analytical description for the edge modes of the Haldane model in semi-infinite planes, which is expected to be useful for models built upon copies of the Haldane model across a broad array of disciplines. We adapt the theorem in our recent work [Ling and Kain, Phys. Rev. A 104, 013305 (2021)] to pseudo-Hermitian Hamiltonians that are less restrictive than BdG Hamiltonians and apply it to highlight that the vanishing of an unconventional commutator between number-conserving and number-nonconserving parts of the Hamiltonian indicates whether a system can be made to act as a topological amplifier." @default.
• W3204182388 created "2021-10-11" @default.
• W3204182388 creator A5027187224 @default.
• W3204182388 creator A5063076286 @default.
• W3204182388 date "2022-02-22" @default.
• W3204182388 modified "2023-09-27" @default.
• W3204182388 title "Topological study of a Bogoliubov–de Gennes system of pseudo-spin- <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> bosons with conserved magnetization in a honeycomb lattice" @default.
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