Quantum Oscillations in the mixed state of d-wave superconductor

TL;DR

This paper demonstrates that ultra-clean d-wave superconductors exhibit quantum oscillations in quasiparticle states within the mixed state, driven by vortex lattice scattering and Zeeman effects, with complexity increasing with anisotropy.

Contribution

It reveals the presence of quantum oscillations in the low-energy quasiparticle density of states of d-wave superconductors due to vortex scattering and Zeeman coupling, highlighting their dependence on anisotropy.

Findings

Quantum oscillations occur in the mixed state of d-wave superconductors.

Oscillation periodicity is determined by the nodal wavevector and magnetic field.

Complex internal structure of oscillations increases with Dirac node anisotropy.

Abstract

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.