Strain-induced inter-vortex interaction and vortex lattices in tetragonal superconductors

TL;DR

This paper investigates how strain-induced inter-vortex interactions influence vortex lattice structures in tetragonal superconductors, revealing a field-dependent transition from square to triangular lattices and back, with implications for understanding vortex behavior in materials like CeCoIn5.

Contribution

It introduces the role of strain fields in inter-vortex interactions and explains the evolution of vortex lattice structures under varying magnetic fields in tetragonal superconductors.

Findings

Square vortex lattice favored at low fields due to strain interactions.

Triangular lattice stabilized at intermediate fields.

Vortex lattice reverts to triangular near upper critical field Hc2.

Abstract

In superconductors with strong coupling between superconductivity and elasticity manifested in a strong dependence of transition temperature on pressure, there is an additional contribution to inter-vortex interactions due to the strain field generated by vortices. When vortex lines are along the $c$ axis of a tetragonal crystal, a square vortex lattice (VL) is favored at low vortex densities, because the vortex-induced strains contribution to the inter-vortex interactions is long range. At intermediate magnetic fields, the triangular lattice is stabilized. The triangular lattice evolves to the square lattice upon increasing magnetic field, and eventually the system locks to the square structure. We argue, however, that as $B$ approaches $H_{c2}$ the elastic inter-vortex interactions disappear faster than the standard London interactions, so that VL should return to the triangular structure. Our results are compared to VLs observed in the heavy fermion superconductor $\mathrm{CeCoIn_5}$.