Stable Flat Bands, Topology, and Superconductivity of Magic Honeycomb Network

We uncover a rich phenomenology of the self-organized honeycomb network superstructure of one-dimensional metals in a nearly-commensurate charge-density wave 1T-TaS${}_2$, which may play a significant role in understanding global topology of phase diagrams and superconductivity. The key observation is that the emergent honeycomb network magically supports a cascade of flat bands, whose unusual stability we thoroughly investigate. Furthermore, by combining the weak-coupling mean-field and strong-coupling approaches, we argue that the superconductivity will be strongly enhanced in the network. This provides a natural cooperative mechanism of the charge order and superconductivity, which coexist side-by-side in the 1T-TaS${}_2$. Not only explaining the superconductivity, we show that abundant topological band structures including several symmetry-protected band crossings and corner states, which are closely related to that of the higher-order topology, appear. The results reported here can be generically applicable to various other systems with similar network superstructures.