The gallery of topological and polarized phases in rhombohedral structures beyond graphene

The recent discovery of exotic states in rhombohedral stacked graphene — such as superconductivity, fractional Chern insulators, quarter and half metals and more — is directly tied to the unique properties of the rhombohedral atomic arrangement of layers ofhoneycomb lattices.

In this work, using first-principle calculations and effective modelling we explore the phase diagram of multilayer rhombohedral-stacked Xenes (X=Si,Ge,Sn) as analogues of graphene but with increasing intrinsic spin-orbit coupling strength. We find a diverse landscape of topological spin Hall insulators, valley polarized states, narrow bands and strongly non-trivial Fermiology, tunable with the number of layers in the stack, carrier concentration and displacement field.

Our results strongly suggest the next tunable platform for rich topological, valley-tronic and spin-tronic physics to be multilayer rhombohedral Xenes.