Fröhlich Polaron — Electron-Phonon Coupling
An electron dresses itself with phonon cloud, gaining effective mass and losing mobility
Coupling α:
3.00
Phonon freq ω_LO:
1.00
Temperature kT:
0.20
H = p²/2m + Σ_k ω_LO a†a + V_k(a+a†)
Fröhlich coupling: α = (e²/ħ)(1/ε_∞−1/ε₀)√(m/2ω_LO)
Weak: α≪1 → m* ≈ m(1+α/6)
Strong: α≫1 → m* ~ α⁴ (Pekar)
Feynman path integral exact
Energy: E ≈ -αω_LO (weak)
GaAs: α≈0.07; SrTiO₃: α≈5