Glossary · Fundamentals
Coherence length links superconducting order to spatial structure
Coherence length describes a spatial scale of the superconducting state. It connects microscopic pairing to the distance over which superconducting order can vary. Together with magnetic penetration depth, it organizes the physics of interfaces, vortices, and superconducting types. [1][2]
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- DefinitionCoherence length
- A characteristic length associated with superconducting correlations. Microscopic pairing descriptions relate it to Cooper-pair size, while Ginzburg-Landau theory uses it for spatial changes in the magnitude of superconducting order, including vortex cores.
Pair size is a useful microscopic starting point
In a conventional microscopic description, a Cooper pair is a correlated electronic state spread over a characteristic distance. The associated pair-size scale depends on electronic velocity and the superconducting energy gap. The pairs can overlap extensively. They should not be pictured as isolated, compact molecules occupying separate positions in the material. [1]
The phrase coherence length also appears in phenomenological theories. Those theories need a scale for changes in collective superconducting order, rather than a direct image of an individual pair. The microscopic and Ginzburg-Landau lengths are related under appropriate assumptions, but their definitions and temperature dependence should remain explicit when comparing quoted values. [1][2]
Ginzburg-Landau theory describes spatial recovery
Ginzburg-Landau theory represents the superconducting state with a complex order parameter. Its magnitude describes the strength of superconducting order, while its phase controls coherent current behavior. A gradient of the order parameter carries an energy cost. Coherence length is the characteristic spatial scale arising from that balance. [2]
Near an interface or vortex core, the order parameter can be suppressed and recover toward its bulk value over a coherence-length scale. This is a smooth spatial variation rather than an abrupt boundary between independent electron pairs. The standard Ginzburg-Landau description applies most directly near the superconducting transition temperature. [2]
The length ratio distinguishes superconducting types
The Ginzburg-Landau parameter is penetration depth divided by coherence length. Nobel Prize’s explanation places the type I to type II boundary near 0.71 in the simple Ginzburg-Landau theory [3]. Values below the boundary correspond to type I behavior; values above it allow the type II mixed state. [2][3]
The distinction follows from the energy of an interface between superconducting and normal regions. Type II materials can admit quantized vortices while superconductivity remains around their cores. This classification concerns the magnetic response. It does not by itself identify the microscopic pairing mechanism or establish a practical current rating for a conductor. [2]
A length is different from a coherence time
Coherence length concerns spatial structure within the material. A qubit’s coherence time concerns how long a controlled quantum state retains its useful phase relationships. These quantities share a word but describe different measurements. Selecting a material by pair size alone cannot predict the coherence time of a fabricated superconducting circuit. [1][2]
When reading a reported coherence length, ask whether it is a microscopic pair-size estimate or a Ginzburg-Landau parameter inferred from magnetic measurements. Temperature, disorder, and direction can affect the interpretation. The value becomes useful when its definition and measurement conditions are given alongside penetration depth and the relevant superconducting model. [1][2]
Sources
- Solid State Physics: Superconductivity II, A. H. HarkerUniversity College London
- Type II Superconductors and the Vortex LatticeNobel Prize, 2003
- The Nobel Prize in Physics: Popular informationNobel Prize, 2003
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