Strange Metal — Planckian Dissipation

Linear-in-T Resistivity: τ = ℏ/k_BT (Planckian scattering rate)
Resistivity ρ(T)
MFL Self-Energy Im Σ(ω,T)
α = 1.00 (Planckian)
ρ₀ = 0.050
TF = 20 T*
T* = 0.20
Planckian rate:
1/τ = α k_BT/ℏ
Strange metal ρ:
ρ = ρ₀ + A·T (exact)
Fermi liquid ρ:
ρ = ρ₀ + B·T²
MFL self-energy:
Σ''(ω,T) ∝ max(|ω|, πT)
Drude formula:
ρ = m*/ne²τ
α ≈ 1 in many materials!
Strange metals violate Fermi liquid theory: ρ ∝ T instead of T². The Planckian bound conjecture (Zaanen 2004, Hartnoll 2015): 1/τ ≤ k_BT/ℏ. Many strange metals saturate this bound exactly, suggesting a universal dissipation mechanism perhaps related to quantum chaos (Lyapunov exponent λ_L ≤ 2πk_BT/ℏ).