Higher-Order Topological Insulators with Fractional Charges Modulated by Lorentz Transformation

Topological insulators represent a new phase of matter, characterized by conductive surfaces, while their bulk remains insulating. When the dimension of the system exceeds that of the topological state by at least two, the insulators are classified as higher-order topological insulators (HOTI). The appearance of higher-order topological states, such as corner states, can be explained by the filling anomaly, which leads to the fractional spectral charges in the unit cell. Previously reported fractional charges have been quite limited in number and size. In this work, based on the two-dimensional (2D) Su-Schrieffer-Heeger model lattice, we demonstrated a new class of HOTIs with adjustable fractional charges that can take any value ranging from 0 to 1, achieved by utilizing the Lorentz transformation. Furthermore, this transformation generates novel bound-state-in-continuum-like corner states, even when the lattice is in a topological trivial phase, offering a new approach to light beam localization. This work paves the way for fabricating HOTIs with diverse corner states that offer promising applicative potential.