🧊 Condensed Matter (2D)

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🧊 Condensed Matter Physics (2D) — Lattice Cross-Section

About this simulation

Conduction electrons drift through a crystal lattice, scattering off atoms that jitter thermally (phonons). Below a critical temperature, electrons can bind into Cooper pairs that glide through the lattice without scattering at all — superconductivity. This 2D cross-section shows the same physics as the 3D lattice viewer, flattened to a plane so the scattering events are easy to watch directly.

How it works

• Lattice type — switches the atomic arrangement between a simple square grid, a centered (body-centered analogue) grid, and a close-packed triangular (face-centered analogue) grid.
• Temperature — increases phonon (lattice) vibration amplitude, which raises electron scattering probability and resistivity.
• Electron density — sets how many conduction electrons drift through the lattice.
• Cooper pairing — below the critical temperature Tc, pairs electrons together so they glide through the lattice with zero scattering and zero resistivity.

Key equations

ρ(T) ≈ ρ₀ + aT⁵ — Bloch–Grüneisen resistivity law.

E_g ≈ 3.5 k_B T_c — Cooper pair binding energy.

v ∝ eEτ/m — Drude model of electron drift velocity.

Controls

• Lattice buttons — rebuild the crystal with a different packing.
• Temperature slider — hotter lattice, more phonon jitter, more scattering.
• Electron density slider — more or fewer drifting carriers.
• Enable Cooper Pairing — toggle superconducting mode (only zero-resistance below Tc).
• Pause / Reset — freeze the animation or reseed the electrons.

Did you know?

The same electron-phonon scattering and Cooper pairing this simulation illustrates underlies the design of MRI magnets and maglev trains, which rely on superconducting wire carrying current with zero resistive loss.