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.