  Large Chern number phases in a Haldane model become possible if there is a
multiplication of Dirac points in the underlying graphene model. This is
realized by considering long-distance hopping integrals. Through variation of
these integrals, it is possible to arrive at supermerging band touchings, which
up to N7 graphene are unique in parameter space. They result from the
synchronized motion of all supplementary Dirac points into the regular +/-K
points of graphene. The energy dispersion power law is usually larger than the
topological charge associated with them. Moreover, adding distant-neighbor
hoppings in the Haldane mass allows one to sweep large Chern number phases in
the topological insulator.
