  We study the effect of impurities in a supersolid phase in comparison to the
behavior in the solid and superfluid phases. A supersolid phase has been
established for interacting hardcore bosons on a triangular lattice which may
be realizable by ultracold atomic gases. Static vacancies are considered in
this model which always lower the magnitude of the order parameter in the solid
or superfluid phases. In the supersolid phase, however, the impurities directly
affect both order parameters simultaneously and thereby reveal an interesting
interplay between them. In particular the solid order may be enhanced at the
cost of a strong reduction of the superfluidity, which shows that the two order
parameters cannot be in a simple superposition. We also observe an unusual
impurity pinning effect in the solid ordered phase, which results in two
distinct states separated by a first-order transition.
