Conformal Vortex Crystals

Abstract

We investigate theoretically globally nonuniform configurations of quantized-flux vortices in clean superconductors trapped by an external force field that induces a nonuniform vortex density profile. Using an extensive series of numerical simulations, we demonstrate that, for suitable choices of the force field, and bellow a certain transition temperature, the vortex system self-organizes into highly inhomogeneous conformal crystals in a way as to minimize the total energy. These nonuniform structures are topologically ordered and can be mathematically mapped into a triangular Abrikosov lattice via a conformal transformation. Above the crystallization temperature, the conformal vortex crystal becomes unstable and gives place to a nonuniform polycrystalline structure. We propose a simple method to engineer the potential energy profile necessary for the observation of conformal crystals of vortices, which can also be applied to other 2D particle systems, and suggest possible experiments in which conformal or quasi-conformal vortex crystals could be observed in bulk superconductors and in thin films.

9 pages, 4 figures

References in corpus (10)

• Vortex Imaging in the pi-Band of Magnesium Diboride
• Dipole-induced vortex ratchets in superconducting films with arrays of micromagnets
• Magnetic flux pinning in superconductors with hyperbolic-tesselation arrays of pinning sites
• Topological defects in the crystalline state of one-component plasmas of non-uniform density
• Emergent structure of multi-dislocation ground states in curved crystals
• Neutral versus charged defect patterns in curved crystals
• Pinning, Ordering, and Dynamics of Vortices in Conformal Crystal and Gradient Pinning Arrays
• Quantitative Chemistry and the Discrete Geometry of Conformal Atom-Thin Crystals
• Enhancing superconducting critical current by randomness
• Thomson rings in a disk

Cited by in corpus (11)

• Observation of a gel of quantum vortices in a superconductor at very low magnetic fields
• Spontaneous Skyrmion Conformal Lattice and Transverse Motion During dc and ac Compression
• Structural Transitions in Vortex Systems with Anisotropic Interactions
• Superfluids, vortices and spinning charged operators in 4d CFT
• Disordering, Clustering, and Laning Transitions in Particle Systems with Dispersion in the Magnus Term
• Harnessing the superconducting diode effect through inhomogeneous magnetic fields
• Defects in Conformal Crystals: Discrete vs. Continuous Disclination Models
• Enhancing the effective critical current density in a Nb superconducting thin film by cooling in an inhomogeneous magnetic field
• Skyrmion Lattice Manipulation with Electric Currents and Thermal Gradients in MnSi
• Vortex Guidance and Transport in Channeled Pinning Arrays
• Anti-Holomorphic Modes in Vortex Lattices