Quantum Oscillations in the mixed state of d-wave superconductor

We show that the low-energy density of quasiparticle states in the mixed state of ultra-clean d-wave superconductors is characterized by pronounced quantum oscillations in the regime where the cyclotron frequency $\hbar\omega_c \ll \Delta_0$, the d-wave pairing gap. Such oscillations as a function of magnetic field B are argued to be due to the internodal scattering of the d-wave quasiparticles near wavevectors $(\pm k_D,\pm k_D)$ by the vortex lattice as well as their Zeeman coupling. The periodicity of the oscillations is set by the condition $k_D \sqrt{hc/(eB)} \equiv k_D' \sqrt{hc/(eB')}\pmod {2\pi}$. We find that there is additional structure within each period which grows in complexity as the Dirac node anisotropy increases.