  A model of an anti-phase modulated d-wave superconductor has been proposed to
describe the decoupling between Cu-O planes in 1/8 doped
La$_{2-x}$Ba$_{x}$CuO$_{4}$. Unlike a uniform d-wave superconductor, this model
exhibits an extended Fermi surface. Within Bogoliubov-de Gennes theory, we
study the mixed state of this model and compare it to the case of a uniform
d-wave superconductor. We find a periodic structure of the low-energy density
of states, with a period that is proportional to $B$, corresponding to Landau
levels that are a coherent mixture of particles and holes. These results are
also discussed in the context of experiments which observe quantum oscillations
in the cuprates, and are compared to those for models in which the Fermi
surface is reconstructed due to translational symmetry breaking in the
non-superconducting state and to a model of a Fermi-arc metal.
