The Mixed State of a $\pi$-Striped Superconductor
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.