transient localisation ยท molecular crystal
One phonon bath, three observables
The soft intermolecular phonons fix the elastic constants, dress the transfer integral as dynamic disorder, and carry the lattice heat. Drive C₄₄, T and J below.
mechanistic chain
●
C₄₄ — shear elastic modulus
mechanical face · input
2.00GPa
↓
ℏωsh ∝ √(C₄₄/ρ)
soft shear phonon
5.00meV
↳
κL ≈ ⅓Cvvs²τph ∝ C₄₄/T
lattice heat · thermal face
0.50W m⁻¹K⁻¹
↓
⟨u²⟩ = kBT / (Mω²)
thermal displacement
0.050Ų
↓
σJ = |∂J/∂u|·√⟨u²⟩
dynamic disorder (off-diagonal e–ph)
25.0meV
↓
Δ = σJ / J
localisation parameter
0.31
↓
LT(Δ) — shrinks as Δ grows
transient localisation length
2.21nm
↓
μ = eLT² / (2kBTτ), τ∼ℏ/(ℏωsh)
charge mobility · electronic face
7.16cm²V⁻¹s⁻¹
Model. Semiclassical TLT (D = LT²/(2τ), μ = eD/(kBT)). Stiffening C₄₄ lifts μ and κL together — not independent. Prefactors representative; the dependences are the content. Regime σJ∼J.
shared lattice · ⟨u²⟩ and LT
⟨u²⟩ = 0.050 Ų
LT = 2.21 nm
band-like transport μ(T)
Log–log. Solid: current C₄₄. Dashed: the stiffest setting, C₄₄ = 5 GPa. Here μ ∝ T−1.6 — the band-like signature, no activated hopping.