2021/08/27 by James Bartlett, James H. Bartlett, Haiping Hu +1
Mathematics · Physics and Astronomy · #Brillouin zone #Fermion #Hermitian matrix #Lattice (music) #MAJORANA #Mathematical analysis #Mathematics #Photorefractive and Nonlinear Optics #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Topological Materials and Phenomena #Topological insulator #Topology (electrical circuits) #Winding number #cond-mat.mes-hall #quant-ph
paper · pdf · doi:10.1103/physrevb.104.195131
published as Phys. Rev. B 104, 195131 (2021) · 10 pages, 9 Figures
openalex publication_date 2021/08/27 · arxiv created 2021/11/15 · arxiv updated 2021/11/18 · openalex created_date 2021/11/22 · openalex updated_date 2026/08/06
Topological characterization of non-Hermitian band structures demands more than a straightforward generalization of the Hermitian cases. Even for one-dimensional tight-binding models with nonreciprocal hopping, the appearance of point gaps and the skin effect leads to the breakdown of the usual bulk-boundary correspondence. Luckily, the correspondence can be resurrected by introducing a winding number for the generalized Brillouin zone for systems with even number of bands and chiral symmetry. Here, we analyze the topological phases of a nonreciprocal hopping model on the stub lattice, where one of the three bands remains flat. Due to the lack of chiral symmetry, the biorthogonal Zak phase is no longer quantized, invalidating the winding number as a topological index. Instead, we show that a Z2 invariant can be defined from Majorana's stellar representation of the eigenstates on the Bloch sphere. The parity of the total azimuthal winding of the entire Majorana constellation correctly predicts the appearance of edge states between the bulk gaps. We further show that the system is not a square-root topological insulator, despite the fact that its parent Hamiltonian can be block diagonalized and related to a sawtooth lattice model. The analysis presented here may be generalized to understand other non-Hermitian systems with multiple bands.