Topological Insulators - GDR Meso

Weak localization : Universality classes
Diagrammatic techniques
Kubo formula
↵ = ~
2⇡V Re Tr ⇥ j ↵ G R j G A⇤
Coherent Diffusive Regime
Perturbative expension in
1/k F l e
Correlate sequences of scatterers in same / opposite order
➡Diffusons / Cooperon propagators
Average conductance
H C
Γ C ( ⃗ Q)
Fluctuations of conductance
⃗ k
⃗ Q − ⃗ k, EF − Ω
Γ C (Ω, ⃗ Q)
⃗Q − ⃗K ′ ,
EF − Ω
⃗K ′
⃗ k
⃗ k − ⃗q, EF − Ω
Γ D (Ω, ⃗q)
⃗K ′ − ⃗q,
EF − Ω
⃗K ′
H C Γ C (−Ω, ⃗ Q)
H C
H D
H D
⃗k ′
⃗ Q − ⃗ k ′ ,EF − Ω
⃗Q − K, ⃗
EF − Ω
⃗K
⃗k ′
⃗ k ′ − ⃗q, EF − Ω
Γ D (−Ω, −⃗q)
⃗K − ⃗q,
EF − Ω
⃗K
Corrections of Hikami boxes (anisotropic scattering !)
⃗k ′ k ⃗′
⃗ k ⃗ k k ⃗′ k ⃗′
⃗ k
k ⃗′
⃗
⃗ k ⃗ k ⃗ k ⃗ k k ⃗ k
H D = + +
H0 D H1 D H2
D
⃗k ′
⃗ k
⃗k ′
⃗k ′
⃗ k
⃗ k
End Formula depends only on number of
Cooperons / Diffusons : How many Singlet / Triplets ?
Based on microscopic Hamiltonian
mardi 3 janvier 12
See e.g. Book by Akkermans and Montambaux