| Abrikosov vortex | |
|---|---|
| Name | Abrikosov vortex |
| Caption | Schematic of a vortex lattice in a type-II superconductor |
| Discovered | 1957 |
| Discoverer | Alexei Abrikosov |
| Field | Condensed matter physics |
| Related | Type-II superconductor, Ginzburg–Landau theory |
Abrikosov vortex
An Abrikosov vortex is a quantized magnetic flux tube that penetrates a Type-II superconductor in the mixed state, carrying one quantum of magnetic flux and surrounded by circulating supercurrent. It is a fundamental topological excitation in superconductivity whose arrangement and dynamics determine many macroscopic electromagnetic properties of superconducting materials, with direct relevance to applications in electrical engineering and quantum devices.
The concept of the vortex lattice in type-II superconductors was predicted by Alexei Abrikosov in 1957 within the phenomenological Ginzburg–Landau theory and later connected to microscopic theories such as BCS theory. Abrikosov's work explained experimental observations of partial magnetic penetration and nonzero resistance under current flow in alloys and thin films, earning recognition in the context of the development of modern superconductivity theory. Historical experiments by early experimentalists and later neutron diffraction and magnetic imaging confirmed the existence of ordered vortex lattices often called Abrikosov lattices.
In Ginzburg–Landau theory an Abrikosov vortex appears as a solution where the complex order parameter vanishes at a core and phase winds by 2π around it, producing quantized flux Φ0 = h/2e. The dimensionless Ginzburg–Landau parameter κ = λ/ξ (ratio of magnetic penetration depth to coherence length) determines whether a superconductor is type-I or type-II; for κ > 1/√2 the mixed state with vortices is energetically favored. Microscopic derivations from BCS theory and the Gorkov equations reproduce vortex structure and predict localized quasiparticle states in the core, linking to concepts from Bogoliubov quasiparticles and Andreev reflection. Contemporary extensions employ Eilenberger equations, Bogoliubov–de Gennes equations, and numerical density functional theory adaptations for superconductors to resolve vortex core spectra and multiband effects.
Each Abrikosov vortex carries a flux quantum Φ0 = h/2e determined by fundamental constants h and electron charge e; the factor 2 reflects Cooper pairing in BCS theory. The core radius is set by the coherence length ξ where the superconducting gap suppresses to zero; the circulating current decays over the London penetration depth λ. Inside the core discrete Caroli–de Gennes–Matricon bound states appear, observable as subgap peaks in tunnelling spectra measured by STM. In unconventional superconductors (e.g., cuprate superconductors, iron-based superconductors, and Sr2RuO4) vortex cores can host exotic states such as zero-energy modes linked to Majorana fermions or broken symmetries.
Vortex motion under applied current produces voltage via the Josephson relation and leads to dissipation; the Lorentz-like Magnus force and viscous drag determine dynamics described in models like the Bardeen–Stephen flux-flow theory. Real materials contain defects and inhomogeneities that pin vortices, modeled by pinning potentials and collective pinning theory developed by A. I. Larkin and Yu. N. Ovchinnikov. Thermal activation over pinning barriers yields flux creep, while quantum tunnelling of vortices (quantum creep) becomes relevant at low temperatures and in nanoscale systems. Vortex dynamics couples to electromagnetic environments and to normal quasiparticle reservoirs, influencing noise in superconducting qubits and performance of superconducting magnets.
The Abrikosov vortex lattice defines the mixed (Shubnikov) phase between the lower critical field Hc1 and the upper critical field Hc2. Phase diagrams of type-II materials include transitions from ordered vortex lattices to disordered vortex glasses and vortex liquids; these transitions are studied using scaling theories and renormalization-group approaches. Material parameters, thermal fluctuations, dimensionality (2D vs 3D), and anisotropy (as in YBCO and BSCCO) control melting lines and pinning regimes, which are crucial for high-field applications like MRI magnets and particle accelerator magnets developed at laboratories such as CERN and Brookhaven National Laboratory.
Abrikosov vortices have been visualized with many techniques: magnetic force microscopy (MFM), scanning tunneling microscopy (STM), scanning Hall probes, Lorentz transmission electron microscopy (LTEM), Bitter decoration, muon spin rotation (μSR), and small-angle neutron scattering (SANS). STM reveals core bound-state spectra; SANS and Bitter decoration image lattice symmetry (triangular, square) influenced by anisotropy and nonlocal electrodynamics. μSR measures internal field distributions and penetration depths, providing quantitative tests of theoretical models and material characterization used in research at institutions like National High Magnetic Field Laboratory.
Control of Abrikosov vortex behavior underpins performance limits of superconducting wires, tapes, and thin-film devices. Strong pinning enhances critical current density Jc in applications such as power transmission, maglev, and superconducting magnets. Conversely, vortex motion generates dissipation and flux noise that degrade superconducting qubits and detectors, motivating engineered pinning landscapes via irradiation, nanoparticle inclusions, and patterned arrays. Emerging areas explore hybrid structures combining vortices with topological insulators or magnetic textures to realize novel quantum states and potential components for quantum computing.
Category:Superconductivity Category:Quantum mechanics Category:Condensed matter physics