Topologically protected states in a spider web lattice

Abstract

Topological phases and edge-state topological protection are explicitly related by the bulk-edge correspondence which assumes the existence a real space boundary in one-dimensional (1D), 2D, or 3D systems. Extensions of this picture to systems where the boundary is present in the domain of generalized coordinates may generate unusual topological behavior in real space. In this paper, we discuss topological radial states in molecules with rotational symmetry and staggered hopping amplitudes in the radial direction. In the absence of the central site, the model is characterized as a weak topological insulator supporting radial edge states in the topological phase. When the central site is considered, we show that it behaves as an effective perturbation coupled in different ways to the radial inner edge, depending on the type of orbital considered at this central site. Tuning the parameters of the central orbital allows for a precise control over the radial inner edge physics of the model. We further break rotational symmetry by studying sliced molecules, which creates open boundaries in the azimuthal direction also, and show that higher-order boundary (corner) modes are present and how they can be driven into an energy gap through coupling with the central orbital. The results are corroborated by numerical conductance studies.