CND-00 · laboratory
Drude, Bloch, BCS snapshot, Wiedemann–Franz and phonon heat.
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25 governing sheets
κ/σ = L T. The Lorenz number L links electronic heat and charge transport.
Electrons in solidsT_c = 1.14 ħω_D exp(−1/N(0)V). Weak-coupling BCS snapshot.
Superconductivityk = n π / a in 1-D, E = ħ² k² / (2 m*). A free-electron parabolic snapshot.
Electrons in solidsU = ħω / (e^{ħω/kT} − 1). Mean energy of one Bose mode (zero-point omitted).
PhononsC_V = (12 π⁴ / 5) N k_B (T/θ_D)³ at T ≪ θ_D. The phonon T³ law.
PhononsE_F = (ħ² / 2m) (3π² n)^{2/3}. Fermi energy of a 3-D free-electron gas.
Electrons in solidsg(E) = (V / 2π²) (2m/ħ²)^{3/2} √E. Spin-degenerate 3-D DOS.
Electrons in solidsR_H = 1 / (n e) for a single carrier of charge +e. Sign flips for electrons.
Electrons in solidsλ_L = √(m / (μ₀ n_s e²)). How far a magnetic field sneaks into a superconductor.
Superconductivityω_p = √(n e² / ε₀ m). The metal becomes transparent above ω_p.
Electrons in solidsU = − N α k e² / r. Ionic lattice energy with Madelung constant α.
Electrons in solidsC_V = 3 N k_B (θ_E/T)² e^{θ_E/T} / (e^{θ_E/T}−1)². Independent oscillators.
Phononsn_i = √(N_c N_v) exp(−E_g / 2 k T). Semiconductor law of mass action.
Electrons in solidsμ = e τ / m*. Drift mobility from a mean free time.
Electrons in solidsS = − (π² k_B² T) / (3 e E_F) for a free-electron metal. Thermopower.
Electrons in solidsΔρ/ρ = (μ B)² for a simple two-carrier sketch at low field.
Electrons in solidsχ = C / (T − θ). Mean-field magnet above a Curie (or Néel) temperature.
Electrons in solidsB(x) = B₀ e^{−x/λ}. Field expulsion at a superconducting surface.
Superconductivityκ_ph ~ T⁻¹ exp(θ_D / α T) with α ~ 2. Phonon heat that dies by Umklapp.
PhononsJ = A T² exp(−φ / k T). Thermionic emission over a work function φ.
Electrons in solidsC = 3 n R. Classical high-temperature heat capacity of a solid.
Phononsρ = ρ₀ + A T⁵. Low-temperature phonon resistivity of a pure metal.
Electrons in solidsv_F = ħ k_F / m, k_F = (3π² n)^{1/3}. Speed at the Fermi surface.
Electrons in solidsf = 2 e V / h = V / Φ₀. Voltage-to-frequency of a superconducting junction.
SuperconductivityFree-electron metal.
Condensed