---
title: "Ginzburg–Landau theory: describe how superconducting order varies"
description: "How could a phenomenological field predict interfaces and magnetic response before microscopic pairing was known?"
canonical_url: "https://sandboxphysics.com/stories/condensed-matter/ginzburg-landau-order/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/condensed-matter/ginzburg-landau-order/"
last_modified: "2026-10-23"
---

[Cold liquids and superconducting order](https://sandboxphysics.com/stories/condensed-matter/#collective)

Materials · Measurements · Explanation

# Ginzburg–Landau theory: describe how superconducting order varies

How could a phenomenological field predict interfaces and magnetic response before microscopic pairing was known?

Sandbox Physics · 2026-10-23

Nobel contribution: 2003-1

1. Introduce a complex order parameter
2. Write a free-energy expansion
3. Include gradients and magnetic coupling
4. Compare length scales and response

The controlled expansion is near a continuous transition; its coefficients describe a specified material and approximation.

## The 1950 theory began from observable symmetry

Ginzburg and Landau introduced a complex field describing superconducting order and expanded the free energy in its amplitude and spatial variation. The theory preceded the microscopic BCS account.

It connected macroscopic spatial behavior to a compact set of effective coefficients. Those coefficients require physical input; the framework does not generate every material’s properties from its chemical name.

Sources: [1]

## Two lengths describe different spatial changes

The coherence length characterizes recovery of the order parameter after a disturbance. The penetration depth characterizes magnetic screening. Their ratio organizes the distinction between type-I and type-II behavior in the simplest isotropic theory.

$$
\kappa=\frac{\lambda}{\xi},\qquad \kappa_{\mathrm c}=\frac{1}{\sqrt{2}}
$$

Sources: [1] [3]

## Interfaces carry physical information

A boundary between normal and superconducting regions has a free-energy cost that depends on the length-scale ratio. This made the spatial theory essential for understanding magnetic structures. A uniform order parameter alone would miss that interface physics.

Sources: [1] [2]

## The new Lab keeps the near-transition scope

The critical-field Lab links the length scales to magnetic-state changes in a synthetic isotropic material. The 2003 award to Ginzburg, Abrikosov and Leggett covered related but distinct theoretical achievements. This scalar model does not include helium-three’s spin structure.

Sources: [1] [3] [4]

Continue with the physics

## Try the related models

### [Superconducting critical fields](https://sandboxphysics.com/labs/superconductor-critical-fields/)

Compare flux exclusion, vortex entry and destruction of superconductivity.

The isotropic Ginzburg–Landau model applies near the transition and is not a quantitative cuprate phase diagram.

## Sources and reading notes

1. [Ginzburg: On superconductivity and superfluidity (2003)](https://www.nobelprize.org/uploads/2018/06/ginzburg-lecture.pdf)

   The phenomenological order parameter, its effective charge and its range of validity.

2. [Abrikosov: Type-II superconductors and the vortex lattice (2003)](https://www.nobelprize.org/uploads/2018/06/abrikosov-lecture.pdf)

   Magnetic flux enters a type-II superconductor through quantized vortices.

3. [2003 Nobel scientific background: superconductors and superfluids](https://www.nobelprize.org/uploads/2018/06/advanced-physicsprize2003.pdf)

   Separates the theories of Ginzburg, Abrikosov and Leggett and their experimental setting.

4. [Nobel Prize in Physics 2003: official award](https://www.nobelprize.org/prizes/physics/2003/summary/)

   Official attribution and award year. The observation or theoretical paper may be much earlier.

[Condensed matter: from a material to its evidence](https://sandboxphysics.com/stories/condensed-matter/) [Liquid helium: building access to a new temperature range](https://sandboxphysics.com/stories/condensed-matter/liquid-helium-onnes/) [Landau’s helium: describe the liquid’s excitations](https://sandboxphysics.com/stories/condensed-matter/landau-superfluid-helium/) [Kapitsa’s helium flow: viscosity depended on how it was tested](https://sandboxphysics.com/stories/condensed-matter/kapitsa-helium-flow/) [BCS theory: one paired state had to explain several experiments](https://sandboxphysics.com/stories/condensed-matter/bcs-pairing-evidence/) [Giaever’s junction: current revealed the superconducting gap](https://sandboxphysics.com/stories/condensed-matter/giaever-gap-spectroscopy/) [Josephson’s prediction: phase could drive a zero-voltage current](https://sandboxphysics.com/stories/condensed-matter/josephson-phase-current/) [Cuprate superconductivity: a ceramic changed the temperature scale](https://sandboxphysics.com/stories/condensed-matter/cuprate-superconductivity/) [Helium-three: a pressure anomaly changed its interpretation](https://sandboxphysics.com/stories/condensed-matter/helium-three-superfluid/) [Abrikosov vortices: magnetic flux entered without ending superconductivity](https://sandboxphysics.com/stories/condensed-matter/abrikosov-vortex-lattice/) [Leggett’s helium-three: resonance identified the pairing order](https://sandboxphysics.com/stories/condensed-matter/leggett-helium-three/)