Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars

Topological characterization of non-Hermitian band structures demands more than a straightforward generalization the Hermitian cases. Even for one-dimensional tight-binding models with nonreciprocal hopping, appearance point gaps and skin effect leads to breakdown usual bulk-boundary correspondence. Luckily, correspondence can be resurrected by introducing winding number generalized Brillouin zone systems even bands chiral symmetry. Here, we analyze topological phases hopping model on stub lattice, where one three remains flat. Due lack symmetry, biorthogonal Zak phase is no longer quantized, invalidating as index. Instead, show that $Z_2$ invariant defined from Majorana's stellar representation eigenstates Bloch sphere. The parity total azimuthal entire Majorana constellation correctly predicts edge states between bulk gaps. We further system not square-root insulator, despite fact its parent Hamiltonian block diagonalized related sawtooth lattice model. analysis presented here may understand other multiple bands.