Electrons drift through a crystal lattice, scattering off thermally vibrating atoms (phonons). Below a critical temperature, electrons can bind into Cooper pairs that flow without scattering — superconductivity.
ρ(T) ≈ ρ₀ + aT⁵ (Bloch–Grüneisen)
Cooper pair binding: E_g ≈ 3.5 k_B T_c
Electron velocity ∝ eE·τ/m (Drude model)
- Lattice type — switches the atomic arrangement between simple cubic, BCC, and FCC packing.
- Temperature — increases phonon (lattice) vibration amplitude, raising scattering and resistivity.
- Electron density — sets how many conduction electrons drift through the lattice.
- Cooper pairing — pairs electrons together; below Tc they glide through the lattice with zero resistivity.
Real-world application: understanding electron-phonon scattering and Cooper pairing underlies the design of MRI magnets and maglev trains built from superconducting wire.