Corner states of topological fullerenes

TL;DR

This paper explores how topologically protected electronic states in 2D quantum spin Hall systems can manifest as corner states in 3D fullerenes, revealing potential for new topological molecular materials.

Contribution

It demonstrates the existence of corner states in topological fullerenes modeled by Haldane's lattice, linking 2D topological effects to 0D molecular structures.

Findings

Corner states appear in large polyhedral nano-surfaces.

Corner states are in-gap modes separated from other electronic states.

Finite size effects and Berry phases influence the degeneracy and magnetic properties.

Abstract

The unusual electronic properties of the quantum spin Hall or Chern insulator become manifest in the form of robust edge states when samples with boundaries are studied. In this work, we ask if and how the topologically non-trivial electronic structure of these two-dimensional systems can be passed on to their zero-dimensional relatives, namely fullerenes or other closed-cage molecules. To address this question, we study Haldane's honeycomb lattice model on polyhedral nano-surfaces. We find that for sufficiently large surfaces characteristic corner states appear for parameters for which the planar model displays a quantized Hall effect. In the electronic structure, these corner states show up as in-gap modes which are well separated from the quasi-continuum of states. We discuss the role of finite size effects and how the coupling between the corner states lifts the degeneracy in a characteristic way determined by the combined Berry phases which leads to an effective magnetic monopole of charge 2 at the center of the nano-surface. Experimental implications for fullerenes in the large spin-orbit regime are also pointed out.