Ground State Vortex Lattice Structures in d-wave Superconductors

TL;DR

This paper predicts field-induced structural transitions in the vortex lattice of d-wave superconductors, driven by anisotropic susceptibility effects, with potential experimental observability at specific magnetic field strengths.

Contribution

It introduces a realistic model showing discontinuous vortex lattice transitions in d-wave superconductors due to nonlocal susceptibility effects, including a novel ground state orientation change.

Findings

Ground state transition from one vortex lattice orientation to another at ~5 Tesla.

Discontinuous transition to a centered square vortex lattice at ~28 Tesla.

Susceptibility effects caused by Dirac quasiparticle-hole excitations drive the transitions.

Abstract

We show in a realistic $d_{x^{2}-y^{2}}$ symmetry gap model for a cuprate superconductor that the clean vortex lattice has discontinuous structural transitions (at and near T=0), as a function of the magnetic field $B$ along the c-axis. The transitions arise from the singular nonlocal and anisotropic susceptibility of the $d_{x^{2}-y^{2}}$ superconductor to the perturbation caused by supercurrents associated with vortices. The susceptibility, due to virtual Dirac quasiparticle-hole excitation, is calculated carefully, and leads to a ground state transition for the triangular lattice from an orientation along one of the crystal axis to one at 45$^o$ to them, i.e, along the gap zero direction. The field scale is seen to be 5 Tesla $ \sim (\Delta_{0}/ta)^{2}\Phi_{0}$, where $\Delta_{0}$ is the gap maximum, $t$ is the nearest neighbour hopping, $a$ is the lattice constant, and $\Phi_{0}$ is the flux quantum. At much higher fields ($\sim 28T$) there is a discontinuous transition to a centred square structure. The source of the differences from existing calculations, and experimental observability are discussed, the latter especially in view of the very small (a few degrees $K$ per vortex) differences in the ground state energy.