Varying topological properties of two-dimensional honeycomb lattices composed of endohedral fullerenes

Abstract

Honeycomb lattices (HLs) have been widely explored for realization of massless Dirac quasiparticles and intriguing topological properties in both the quantum and classical regimes, with elemental and artificial atoms as the corresponding building blocks. Here we provide a demonstration showing that when the fullerene molecules of ${\mathrm{C}}_{28}$ are used as prototypical building blocks, stable two-dimensional (2D) HLs can also be achieved, with the structural, electronic, and topological properties tuned via proper atom encapsulation. Specifically, whereas a closely packed structure is preferred for the ${\mathrm{C}}_{28}$ lattice, honeycomb structures with different spacial symmetries are energetically favored for both the Bi@${\mathrm{C}}_{28}$ and In@${\mathrm{C}}_{28}$ endohedral fullerenes. In particular, Bi@${\mathrm{C}}_{28}$-HL is revealed to be a quantum spin Hall insulator because of strong spin-orbit coupling effects in the $f$ molecular orbitals, while In@${\mathrm{C}}_{28}$-HL is a quantum valley Hall insulator resulting from mirror symmetry breaking. The present study offers superatom-based platforms for realizing quantum spin Hall and quantum valley Hall effects in 2D systems, with distinctly enhanced tunability and robustness against atomic-scale imperfections.