Topological Phase Transition Induced by Partial Ordering of Heavy Alkali Adatoms in Graphene Monolayer

Topological insulators host robust, spin-polarized edge states, hence they are
promising candidates in the building of quantum computers and in spintronics.
Graphene is a quasi two dimensional, perfect semiconductor, with a very weak spin-orbit coupling.
Stable topological phases, respecting time reversal symmetry can occur if the spin-orbit coupling (SOC) is non-negligible, and thus several approaches emerged to enlarge graphene's SOC.
One of them is to dope it with heavy atoms.
In this presentation I will talk about the topological phases of alkali adatom doped graphene.
These adatoms induce SOC and can partially self-organise themselves into a mosaic Kekulé pattern through the RKKY interaction in a sufficiently low temperature.
While at higher temperature the adatom's distribution becomes random.
I will discuss the topological flavour of the induced gap,
and show the counterintuitive result, that the system can undergo a phase transition, where the lower temperature phase is trivial and the higher temperature
phase is topological.