Corner states of topological fullerenes

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 nontrivial 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 nanosurfaces. 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 quasicontinuum 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 nanosurface. Experimental implications for fullerenes in the large spin-orbit regime are also pointed out.