Spin Orbit Coupling in Graphene Induced by Heavy Adatoms with Electrons in the Outer-Shell $p$ Orbitals

TL;DR

This study investigates how heavy adatoms with p orbitals induce different types of spin orbit coupling in graphene, revealing the dependence on adatom position and concentration, and demonstrating the stability of topological phases.

Contribution

It provides a detailed analysis of SOC induced by heavy p-orbital adatoms in graphene, highlighting the effects of adatom placement and concentration on electronic properties.

Findings

Adatoms in hollow positions induce intrinsic-like SOC.

Random adatom distribution causes Rashba-like SOC.

SOC strength scales linearly with adatom concentration.

Abstract

Many of the exotic properties proposed to occur in graphene rely on the possibility of increasing the spin orbit coupling (SOC). By combining analytical and numerical tight binding calculations, in this work we study the SOC induced by heavy adatoms with active electrons living in $p$ orbitals. Depending on the position of the adatoms on graphene different kinds of SOC appear. Adatoms located in hollow position induce spin conserving intrinsic like SOC whereas a random distribution of adatoms induces a spin flipping Rashba like SOC. The induced SOC is linearly proportional to the adatoms concentration, indicating the inexistent interference effects between different adatoms. By computing the Hall conductivity we have proved the stability of the topological quantum Hall phases created by the adatoms against inhomogeneous spin orbit coupling . For the case of Pb adatoms, we find that a concentration of 0.1 adatom per carbon atom generates SOC's of the order of $\sim$40$meV$.