Electromigration forces on atoms on graphene nanoribbons: The role of adsorbate-surface bonding

Atom diffusion on surfaces induced by a bias voltage or external electric fields has received increasing attention in both experimental and theoretical studies. In this work, we study such electromigration phenomena by placing different atom types on two-dimensional armchair graphene nanoribbons in an electric field along the ribbon and examining the electromigration force with ab- initio simulation techniques. Our findings show that the forces are related to the induced charges in the adsorbate-surface bonds rather than to the induced atomic charges, and the left/right effective bond order can be used to predict the force direction. Focusing in particular on 3d orbital transition metal atoms, we show how a simple model of a metal atom on benzene can explain the forces in an inorganic chemistry picture. This study demonstrates how the underlying bonding and molecular orbital structure becomes relevant for the definition of electromigration forces on the nanoscale. Accordingly extended models including the ligand field of the atoms might provide a better understanding of adsorbate diffusion on surfaces under non-equilibrium conditions.