  We show that for a system of localized electrons in an impurity band, which
form an Anderson insulating state at zero temperature, there can appear quantum
oscillations of the magnetization, i.e. the Anderson insulator can exhibit the
de Haas-van Alphen effect. This is possible when the electronic band from which
the localized states are formed has an extremum that traces out a nonzero area
in reciprocal space. Our work extends existing theories for clean band
insulators of this form to the situation where they host an impurity band. We
show that the energies of these impurity levels oscillate with magnetic field,
and compute the conditions under which these oscillations can dominate the de
Haas-van Alphen effect. We discuss our results in connection with experimental
measurements of quantum oscillations in Kondo insulators, and propose other
experimental systems where the impurity band contribution can be dominant.
