Stable Flatbands, Topology, and Superconductivity of Magic Honeycomb Networks

Abstract

We uncover a rich phenomenology of conducting honeycomb network superstructure, which plays a significant role in understanding the phase diagram topology and superconductivity of chargedensity wave materials such as 1T-TaS2. One of the most important theoretical questions about these materials is to understand the emerging superconductivity inside the nearly-commensurate charge-density wave state. Our key observation is that the conducting domain walls inside the charge-ordered state form a honeycomb network and the network magically supports a cascade of flat bands, whose unusual stability we thoroughly investigate. Furthermore, by combining the weak-coupling and strong-coupling approaches, we show that the superconductivity will be strongly enhanced in the network. This provides a natural mechanism for emerging superconductivity, and so explains the phase diagram topology of these charge density wave materials. Not only explaining emerging superconductivity, we show that abundant topological states including the corner states, which are closely related to that of the higher-order topology, appear.

Topological Materials Discovery from Crystal Symmetry

“…As discussed in Sec. VII, AXIs have recently been recognized to be HO-TIs; additionally, recent theoretical investigations [397] of the CDW phase in 1T-TaS 2 [ICSD 52115, SG 164 (P 3m1)] [398] have demonstrated the presence of higherorder-topological corner states. T -symmetric TSM-CDWs are therefore likely to provide a promising venue for elucidating and exploring novel response effects in helical TCIs and HOTIs -phases of matter that owe their existence to the interplay of symmetry and topology in solid-state materials.…”

Line-graph-lattice crystal structures of stoichiometric materials

“…Immediate extensions include the development of related algorithms to search for other lattices and families of lattices known to host flat bands. This includes Tasaki's lattices [58], lattices that are constructed entirely from cliques but are not line graphs [59], and decorated or superlattices built from 1D chains [60,61]. Our search can also be run on a database of monolayer materials.…”

Singular flat bands

“…In this case, the gap opening at the band-crossing point is almost negligible while the flat band obtains a small dispersion due to the finite value of t 2 =t 1 . Second, the nearly commensurate-charge density wave (NC-CDW) phase of 1 T-TaS 2 corresponds to the regime t 2 =t 1 � 0 because the second nearest-neighbor hopping processes as well as the longer range hopping parameters are exponentially suppressed due to the large insulating domains [159]. Third, in the trans-Au-THTAP, both t 2 =t 1 and λ are non-negligible although they are small enough to have a nearly flat band [160].…”