Strain-induced intervortex interaction and vortex lattices in tetragonal superconductors

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 magnetic field approaches the upper critical field 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 CeCoIn 5 .

Observation of a gel of quantum vortices in a superconductor at very low magnetic fields

“…Stress builds up close to defects and modifies the superconducting length scales (and the Ginzburg-Landau parameter), producing an effective interaction between the crystal lattice and the vortex lattice 36,37 . Recently, it has been shown that stress induced intervortex interaction can lead to square vortex lattice in tetragonal superconductors 38 . Such a coupling between crystalline elasticity and superconductivity can be treated using the dependence of T c with pressure, dT c /dP 36,[39][40][41] .…”

Anisotropic magnetocrystalline coupling of the skyrmion lattice in MnSi

“…Summarizing, crucial aspects of our work are: (i) We establish RUS as a tool to not only give information about elasticity but also about dissipation mechanisms of the atomic lattice with high precision, sensitive to detect changes in the magneto-crystalline coupling that determines the orientation of the SKX (Note [29]). (ii) In analogy to superconducting vortices [30,31], the magnetocrystalline coupling in the SKX phase enables one to manipulate the skyrmions by external stress. (iii) Our work also reveals how the stability of the SKX phase changes as a function of its orientation with respect to the crystalline lattice.…”

Rotational transition, domain formation, dislocations and defects in vortex systems with combined six- and 12-fold anisotropic interactions

“…Theoretical approaches used to study structural transitions of the VL include modifications to the London model [17][18][19] , the addition of four-fold symmetric terms to the Ginzburg-Landau free energy 20 , Eilenberger theory 21 , modified Ginzburg-Landau approaches 22 , and modifications to the vortex interactions produced by strain fields 23 . Vortex lattice ordering can also be studied using molecular dynamics (MD) methods, which treat the vortices as point particles with bulk Bessel function interactions or thin film Pearl interactions.…”