Topological Insulators - GDR Meso

Anisotropic Scattering of Dirac states
Consider Dirac surface states with
‣ phase coherence (small sample, low T)
‣ scalar disorder
‣ semi-classical limit
H 0 = ~v F ẑ ⇥ (~ ⇥ ~ k)
+V (~r )
(high doping in the gap)
Hexagonal warping :
L. Fu, PRL 103 (2009)
H W = z 2
k+ 3 + k 3 k ± = k x ± ik y
b w = E2 F
‣ allowed by Time Reversal Symmetry (same univ. class)
‣ experimentally extracted value in TI : bw=0.4-0.6
‣ important at high kF (weak localization regime)
‣ Perturbative parameter (deformation of Fermi surface) bw
➡ depends on EF
Anisotropic scattering :
‣ comes from pure (Dirac) Hamiltonian, not disorder
‣ strongly increased by warping term
k min
2~ 3 v 3 F
kmax
Scattering amplitude
bw=0.6 bw=0.0
f(✓, ✓ 0 ✓)=|h ~ k|V | ~ k 0 i|
✓ =0 ✓ = ⇡/6
mardi 3 janvier 12