---
title: "Superconductors in a Magnetic Field Interactive Lab | Sandbox Physics"
description: "Why can a magnetic field enter one superconductor before it becomes normal? A type-II superconductor can admit flux in vortices while superconductivity survives between their cores. The first vortices enter near the lower critical field; only near the upper critical field does bulk superconductivity disappear. A type-I material has a single bulk transition field."
canonical_url: "https://sandboxphysics.com/labs/superconductor-critical-fields/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/superconductor-critical-fields/"
last_modified: "2026-10-24"
---

C-X5 · Exclusion, vortices and breakdown

# Superconductors in a Magnetic Field

**Why can a magnetic field enter one superconductor before it becomes normal?** A type-II superconductor can admit flux in vortices while superconductivity survives between their cores. The first vortices enter near the lower critical field; only near the upper critical field does bulk superconductivity disappear. A type-I material has a single bulk transition field.

Compare two synthetic materials near their transition temperature. Raise the field to move from magnetic exclusion to a vortex state or the normal state, then follow the corresponding critical-field curves.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

This near-transition Ginzburg–Landau teaching model uses synthetic penetration-depth and coherence-length amplitudes. The type-II sample has a ratio of six; its lower field uses a large-ratio London approximation. The type-I sample has a ratio of one quarter and uses the thermodynamic critical field. Applied induction is compared with bulk critical fields, with demagnetization neglected. The slab, flux markers and vortex lattice are qualitative schematics. Vortex density uses a disclosed interpolated induction proxy and is not a self-consistent GL solution. Pinning, transport current, hysteresis, finite geometry, thermal fluctuations and cuprate pairing mechanisms are omitted.

From the experiment

## Observe, then compare

Curves use synthetic GL amplitudes; the screening profile is a semi-infinite Meissner reference. The marker identifies the current setting.

Near-transition critical fields

Magnetic screening profile

Nobel · Condensed matter

## What did the original experiments establish?

Follow the apparatus, observations and interpretation in the historical evidence. Each article explains where this teaching model fits.

[Read the evidence 1](https://sandboxphysics.com/stories/condensed-matter/ginzburg-landau-order/) [Read the evidence 2](https://sandboxphysics.com/stories/condensed-matter/abrikosov-vortex-lattice/) [All six reading paths](https://sandboxphysics.com/stories/condensed-matter/)

Physics tutorial

## Two lengths set the magnetic response

**Background** The penetration depth describes magnetic screening. The coherence length describes how the superconducting order recovers after a disturbance.

**Why it matters** Their ratio separates the two bulk magnetic responses in Ginzburg–Landau theory.

Start with the essentials

- **Focus question**: Why can a magnetic field enter one superconductor before it becomes normal?
- **One-sentence intuition**: Vortices allow flux through a type-II material while superconductivity survives outside their cores.

### Core mathematical model

#### Characteristic lengths near transition

$$
\lambda=\lambda_* (1-T/T_c)^{-1/2},\quad\xi=\xi_* (1-T/T_c)^{-1/2}
$$

The starred quantities are synthetic GL amplitude parameters, not extrapolated zero-temperature measurements.

#### Upper critical induction

$$
B_{c2}=\frac{\Phi_0}{2\pi\xi^2}
$$

It decreases linearly with the distance below the transition temperature in this approximation.

#### Lower field for the large-ratio sample

$$
B_{c1}\simeq\frac{\Phi_0}{4\pi\lambda^2}(\ln\kappa+0.5),\quad\kappa=\lambda/\xi
$$

This London approximation is used only for the synthetic type-II sample with a length ratio of six.

### Common difficulties

#### Reading the model correctly

**Typical misconception** The plotted critical-field curves predict an arbitrary real superconducting material.

**Better mental model** The amplitudes were selected for teaching. Geometry, pinning and microscopic material physics require additional models and measurements.

### Run the experiment

1. 01

   #### Admit the first vortices

   Compare Exclude the field and Vortices enter.

   **What to observe:** The lower critical field marks the first thermodynamically allowed flux penetration in the ideal bulk picture.

2. 02

   #### Destroy the remaining order

   Select Destroy superconductivity.

   **What to observe:** Above the upper field, the sample is normal throughout.

3. 03

   #### Change material type

   Select Type-I comparison and raise Applied magnetic induction.

   **What to observe:** The bulk model switches directly from exclusion to normal at the thermodynamic field.

Physical conclusion

These synthetic near-transition curves explain bulk regimes, not measured material parameters or a high-temperature pairing mechanism.

Quantum & fields · Starter path

## Start from a single measurement

Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference.

[Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/)

1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/)
2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/)
3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/)
4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/)
5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/)
6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/)

[View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)