AUTHOR=He Qinghua , Sun Jinhua , Deng Hai-Yao , Wakabayashi Katsunori , Liu Feng 

TITLE=Bound states at disclinations: an additive rule of real and reciprocal space topology

JOURNAL=Frontiers in Physics

VOLUME=Volume 11 - 2023

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1213158

DOI=10.3389/fphy.2023.1213158

ISSN=2296-424X

ABSTRACT=We propose an additive rule between the real-space topological invariant $\mathbf{s}$ of disclinations (related to the Burgers vector $\mathbf{B}$) and the reciprocal-space topological invariant $\mathbf{p}$ of bulk wave functions (the vectored Zak phase). The disclination-induced bound states appear only if $(\mathbf{s}+\mathbf{p}/2\pi)$ 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 $\mathbf{p}$. 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 $\mathbf{s}+\mathbf{p}/2\pi$.