Quantum Oscillations for a Pair Density Wave State

Pair density waves lead to a reconstruction of the Fermi surface because of the non-zero momentum of the pairs. But it has been controversial whether such a reconstruction shows up in quantum oscillation measurements because of particle-hole mixing. In this work, we study this problem by solving the Bogoliubov-deGennes equation for a vortex lattice pair density wave state using a Landau level basis and calculating how the density of states varies as a function of magnetic field. We then use this to address the relation of the quantum oscillation period to the reconstructed and unreconstructed Fermi surfaces.