Quantum Oscillations in a $\pi$-Striped Superconductor

Within Bogoliubov-de Gennes theory, a semiclassical approximation is used to calculate the Fermi surface area associated with quantum oscillations in a model of a $\pi$-striped superconductor, where the d-wave superconducting order parameter oscillates spatially with zero average value. This system has a non-zero density of particle-hole states at the Fermi energy, which form Landau-like levels in the presence of a magnetic field. The oscillation frequency found for large pairing interaction, for $\pi$-stripes with period 8, is close to that reported for experimental measurements in the cuprates. A comparison is made of this theory to data for quantum oscillations in the specific heat measured by Riggs et al.