Polaronic Transport

Self-trapped electrons and hopping conductivity in polar crystals

In ionic/polar crystals, an electron polarizes the surrounding lattice, creating a potential well that self-traps the electron — this composite particle is a polaron. The polaron mass m*= m(1 + α/6 + 0.025α²) is heavier than the bare electron. For large α (strong coupling), transport is by thermally activated hopping: σ ∝ T⁻¹exp(−E_a/k_BT) — conductivity increases with temperature (unlike metals). The activation energy E_a ≈ E_JT/2 = λ²/(4K). Famous in manganites, organic semiconductors, and MgB₂.