Effective spin-orbit gaps in the s and p orbital bands of an artificial honeycomb lattice

Abstract

Muffin-tin methods have been instrumental in the design of honeycomb lattices that show, in contrast to graphene, separated s and in-plane p bands, a p orbital Dirac cone, and a p orbital flat band. Recently, such lattices have been experimentally realized using the two-dimensional electron gas on Cu(111). A possible next avenue is the introduction of spin-orbit coupling to these systems. Intrinsic spin-orbit coupling is believed to open topological gaps and create a topological flat band. Although Rashba coupling is straightforwardly incorporated in the muffin-tin approximation, intrinsic spin-orbit coupling has only been included either for a very specific periodic system, or only close to the Dirac point. Here, we introduce effective intrinsic and Rashba spin-orbit terms in the Hamiltonian for both periodic and finite-size systems. We observe a strong band opening over the entire Brillouin zone between the p orbital flat band and the Dirac cone hosting a pronounced edge state, robust against the effects of Rashba spin-orbit coupling.

Size effects on atomic collapse in the dice lattice

“…The present study is motivated by the experiments with electronic lattices such as Lieb [25] and honeycomb with sp hybridization [26,27], which might serve as potential platform to realize also the dice lattice. The artificial lattices of such kind have approximately ten times larger lattice constant that atomically-thin materials and thus much weaker electronelectron interactions.…”

“…In addition, one should note the typical sample size difference between atomic samples and electronic artificial lattices. The latter have a size of order of 10 sites along each side [25][26][27], making the role of edges significant in any studied effect. To analyze the role of size effects on the possibility of observation of atomic collapse we consider quantum dots of circular shape made of dice lattice.…”