Physic Labs

Condensed matter physics

Superconductivity and BCS theory

Explore the BCS model: Cooper pairs (two opposite-spin electrons) condense and open an energy gap Δ\Delta in the excitation spectrum E(k)=ξ2+Δ2E(k)=\sqrt{\xi^2+\Delta^2}. Vary T/Tc and the pair density to watch Δ(T)\Delta(T) close at the transition temperature.

Research

Equipment

  • Virtual crystal lattice with opposite-spin electron pairs
  • Temperature slider T/Tc
  • Pair-density slider and model parameter
  • Excitation-spectrum plot $E(k)=\sqrt{\xi^2+\Delta^2}$ and readout $\Delta(T)/\Delta(0)$

Procedure

  1. Observe Cooper pairs and the gap

    Set T/Tc low (about 0.2): on the canvas, opposite-spin electron pairs appear stably, and the spectrum plot shows a forbidden region around the Fermi level — exciting a quasiparticle costs at least Δ\Delta.

  2. Raise temperature through the transition

    Drag T/Tc from 0 up through 1: the readout Δ(T)/Δ(0)\Delta(T)/\Delta(0) falls to 0 at Tc, pairs break apart, and the spectral gap closes — the metal returns to its normal state. Record a few points (T/Tc, Δ/Δ(0)) to sketch the gap curve.

  3. Change pair density and predict

    Hold T/Tc fixed below 1 and lower the pair-density slider: fewer pairs mean a shallower gap in the model. Predict the spectrum as the density → 0 and verify it returns to the free parabola E=∣ξ∣E=|\xi|.

Simulation

Experiment history

Heike Kamerlingh Onnes, after liquefying helium (1908), measured mercury's resistance in 1911 and found it dropping to zero near 4.2 K — he called the phenomenon 'superconductivity'. Walther Meissner and Robert Ochsenfeld showed in 1933 that superconductors also expel magnetic fields, a true state of matter rather than mere perfect conduction. A microscopic theory waited until 1957, when John Bardeen, Leon Cooper, and John Robert Schrieffer proved that a weak phonon-mediated attraction pairs electrons into a common Cooper-pair condensate — earning them the 1972 Nobel Prize. The predicted gap 2Δ(0)≈3,53 kBTc2\Delta(0)\approx3{,}53\,k_BT_c was soon confirmed by infrared spectroscopy and by Ivar Giaever's tunneling experiments (1960).

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