Quantum oscillations in the mixed state of d-wave superconductors

We show that the low-energy density of quasiparticle states in the mixed state of ultraclean d_x²−y²-wave superconductors exhibits quantum oscillations even in the regime where the cyclotron frequency ℏω_c⪡Δ₀, 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 nodal quasiparticles near wave vectors (±k_D,±k_D) by the vortex lattice as well as their Zeeman coupling. While the nominal periodicity of the oscillations is set by the condition k_D[hc∕(eB)]^1∕2≡k_D^′[hc∕(eB^′)]^1∕2(mod 2π), we find that there is additional structure within each period that grows in complexity as the Dirac node anisotropy increases.