  At low temperatures the interactions between like-oriented steps on a surface
are believed to be dominated by elastic repulsions. This belief is based on the
results of the classical continuum field theories of elasticity. Electrostatic
interactions are also believed to have a role but no theory has yet been
developed for their description. In our paper we critically revisit the
assumptions of these theories, and found that the ab initio approaches, based
on the Born-Oppenheimer distinction between the valence electrons and the ions
degrees of freedom, allow to identify distinctly both elastic and electrostatic
contributions to the step energy and the step interaction energy. By using
ab-initio calculations and specifying to the case of the technologically
important (001)surface of GaAs, we show that the elastic interactions are not
always repulsive and attractive step interactions between like-oriented steps
are also possible. Furthermore, the repulsiveness and attractiveness of the
step interactions depend on the step atomic structure.
