  We identify qualitative trends in the stacking sequence dependence of
carrier-carrier interaction phenomena in multilayer graphene. Our theory is
based on a new approach which explicitly exhibits the important role in
interaction phenomena of the momentum-direction dependent intersite phases
determined by the stacking sequence. Using this method, we calculate and
compare the self-energies, density--density response functions, collective
modes, and ground-state energies of several different few layer graphene
systems. The influence of electron--electron interactions on important
electronic properties can be understood in terms of competition between
intraband exchange, interband exchange and correlation contributions that vary
systematically with stacking arrangement.
