Bound states at disclinations: an additive rule of real and reciprocal space topology - He, Qinghua; Sun, Jinhua; Deng, Hai-Yao; Wakabayashi, Katsunori; Liu, Feng (Frontiers in Physics, 2023)
We propose an additive rule between the real-space topological invariant $s$ of disclinations (related to the Burgers vector $B$) and the reciprocal-space topological invariant $p$ of bulk wave functions (the vectored Zak phase). The disclination-induced bound states appear only if $(s+p/2π)$ is nonzero modulo lattice constant. These disclination-bound states are robust against perturbations respecting $C_4$ point group symmetry and other perturbations within an amplitude determined by $p$. Besides the bound states, the proposed additive rule also suggests that a half-bound state extends over only half of a sample and a hybrid-bound state, which always have a nonvanishing component of $s+p/2π$.