Materials Science ★★★ Advanced New

🧲 Superconductivity

Below the critical temperature Tc, resistance drops to exactly zero and magnetic fields are expelled (Meissner effect). Explore BCS Cooper pairs, Type I/II phase diagrams, and Abrikosov flux vortices.

Cooper pairs in the crystal lattice
Resistance vs Temperature
T = 2.0 K
Tc = 4.2 K
State: SUPERCONDUCTING
R = 0.000 Ω
BCS gap: —

BCS Theory (Bardeen, Cooper, Schrieffer — 1957 Nobel Prize)

In a normal metal, electrons scatter off lattice vibrations (phonons), causing resistance. Below Tc, electrons form Cooper pairs via a phonon-mediated attraction: one electron distorts the lattice (leaving a positive polarization), which attracts a second electron. These pairs form a quantum condensate with a macroscopic wave function — they can flow without scattering.

The Meissner effect is the complete expulsion of magnetic flux from the interior of a superconductor. Surface currents spontaneously form to oppose any applied field. This is what levitates magnets above superconductors — it is not just perfect diamagnetism, but an active thermodynamic state.

Type I superconductors (like Hg, Pb) expel all flux below Hc. Type II superconductors (Nb, YBCO) allow flux to penetrate in quantized vortices between Hc1 and Hc2 — enabling high-field magnets and MRI. The BCS energy gap: 2Δ ≈ 3.52 k_B T_c.

About the Superconductivity Simulator

This simulation visualises the transition of a metal into the superconducting state. The left canvas animates Cooper pairs gliding through the crystal lattice, the Meissner expulsion of magnetic field, or Abrikosov flux vortices, while the right canvas plots resistance against temperature. Whether the sample superconducts is decided by the critical-field law H<Hc(1−(T/Tc)2), with the BCS energy gap estimated from 2Δ ≈ 3.52 kBTc.

Five material presets (mercury, lead, niobium, Nb₃Sn and YBCO) set the critical temperature and field. The temperature slider sweeps from 0.1 K to well above Tc, and the magnetic-field slider applies an external field H. Toggling between BCS Cooper Pairs, Meissner Effect and Type II Vortices reveals each phenomenon. Superconductors carry current without loss, enabling MRI scanners, particle-accelerator magnets and maglev transport.

Frequently Asked Questions

What is superconductivity?

Superconductivity is a state in which a material conducts electricity with exactly zero resistance and expels magnetic fields from its interior. It appears below a material-specific critical temperature, T sub c. The simulation shows resistance collapsing to zero as the temperature drops below T sub c for the chosen material.

What does the temperature slider do?

The temperature slider sets the sample temperature from 0.1 K up to several times the critical temperature. When the value falls below T sub c and the applied field is low enough, the state chip flips to SUPERCONDUCTING and the resistance reads 0.000 ohms. Above T sub c the metal returns to its normal, resistive state.

What is the magnetic field slider for?

The H slider applies an external magnetic field. Superconductivity survives only while H stays below the critical field, which itself falls as temperature rises. In Type II presets a strong enough field drives the material into the mixed state, where quantised flux vortices appear in the Type II Vortices view.

What are Cooper pairs?

A Cooper pair is two electrons bound together by an attractive interaction mediated by lattice vibrations, or phonons. One electron distorts the positively charged lattice, and that distortion attracts a second electron. The paired electrons form a quantum condensate with a single macroscopic wave function, so they flow without scattering and therefore without resistance.

What is the Meissner effect?

The Meissner effect is the active expulsion of magnetic flux from the interior of a superconductor. Surface screening currents spontaneously arise to cancel the field inside, keeping B equal to zero. It is more than perfect diamagnetism because it occurs even for a field already present before cooling, and it is what allows a magnet to levitate above a superconductor.

What is the difference between Type I and Type II superconductors?

Type I superconductors, such as mercury and lead, expel magnetic flux completely until the field reaches the critical field H sub c, then abruptly become normal. Type II superconductors, such as niobium, Nb3Sn and YBCO, have two critical fields and allow flux to thread through as quantised vortices between H sub c1 and H sub c2, which lets them remain superconducting in very strong fields.

What is the BCS energy gap shown on the panel?

The BCS energy gap is the minimum energy needed to break a Cooper pair into two free electrons. The simulation estimates it from the relation 2 delta is approximately 3.52 times k sub B times T sub c, displaying the result in millielectronvolts. A higher critical temperature gives a larger gap, which is why YBCO has a far bigger gap than mercury.

What are Abrikosov vortices?

Abrikosov vortices are tiny tubes of magnetic flux that penetrate a Type II superconductor in its mixed state. Each vortex carries exactly one flux quantum, phi nought equals h divided by 2e, and is encircled by a swirling supercurrent. The Type II Vortices view draws these cores and their circulating currents when the field lies between H sub c1 and H sub c2.

Is the simulation physically accurate?

The qualitative physics is faithful: the critical-field temperature dependence, the zero-resistance transition, the BCS gap ratio and the distinction between Type I and Type II behaviour all follow standard theory. However, the animation is a simplified visual model. The particle motion, vortex count and resistance are illustrative rather than the output of a full quantum-mechanical calculation.

Why do high-temperature superconductors like YBCO matter?

YBCO superconducts up to about 93 K, above the boiling point of liquid nitrogen at 77 K, so it can be cooled cheaply without liquid helium. That makes practical applications such as power cables, fault-current limiters and high-field research magnets far more affordable. This simulator includes YBCO so you can compare its high T sub c against conventional metals like mercury and lead.