Vortex lattices and critical fields in anisotropic superconductors

TY - JOUR

T1 - Vortex lattices and critical fields in anisotropic superconductors

AU - Speight, Martin

AU - Winyard, Thomas

N1 - Publisher Copyright: © 2025 The Author(s). Published by IOP Publishing Ltd.

PY - 2025/3/5

Y1 - 2025/3/5

N2 - A method is developed to compute minimal energy vortex lattices in a general Ginzburg-Landau model of a superconductor subjected to an applied magnetic field. The model may have any number of components and may be spatially anisotropic. The novelty of this method is that it makes no assumptions about the orientation of the vortex lines or the period vectors of the lattice’s unit cell: these are all determined dynamically. Methods to compute the first and second critical magnetic fields, H c 1 and H c 2 , in this class of models are also developed. These methods are applied to a simple anisotropic single-component model, and to an anisotropic two-component model of strong current theoretical interest (a so-called s + id model). It is found, in both cases, that at low applied field the vortex lines can tilt very significantly away from the direction of the applied field (by as much as 40∘ for the single-component and 30∘ for the s + id model). The optimal lattice in the s + id model is qualitatively very different from the conventional triangular Abrikosov lattice, exhibiting a phase transition from a system of Skyrmion chains when the external field is orthogonal to the basal plane to a deformed Abrikosov lattice when applied in the basal plane.

AB - A method is developed to compute minimal energy vortex lattices in a general Ginzburg-Landau model of a superconductor subjected to an applied magnetic field. The model may have any number of components and may be spatially anisotropic. The novelty of this method is that it makes no assumptions about the orientation of the vortex lines or the period vectors of the lattice’s unit cell: these are all determined dynamically. Methods to compute the first and second critical magnetic fields, H c 1 and H c 2 , in this class of models are also developed. These methods are applied to a simple anisotropic single-component model, and to an anisotropic two-component model of strong current theoretical interest (a so-called s + id model). It is found, in both cases, that at low applied field the vortex lines can tilt very significantly away from the direction of the applied field (by as much as 40∘ for the single-component and 30∘ for the s + id model). The optimal lattice in the s + id model is qualitatively very different from the conventional triangular Abrikosov lattice, exhibiting a phase transition from a system of Skyrmion chains when the external field is orthogonal to the basal plane to a deformed Abrikosov lattice when applied in the basal plane.

KW - anisotropic

KW - Ginzburg-Landau

KW - lattices

KW - solitons

KW - superconductors

KW - vortex

UR - https://www.scopus.com/pages/publications/86000284622

U2 - 10.1088/1751-8121/adb7a7

DO - 10.1088/1751-8121/adb7a7

M3 - Article

AN - SCOPUS:86000284622

SN - 1751-8113

VL - 58

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 9

M1 - 095203

ER -