Topological Insulators - GDR Meso
Topological Insulators - GDR Meso 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
Anisotropic Scattering of Dirac states P. Adroguer, D. Carpentier, J. Cayssol and E. Orignac, unpublished H 0 = ~v F ẑ ⇥ (~ ⇥ ~ k) +V (~r ) H W = 2 z k 3 + + k 3 k ± = k x ± ik y Diagrammatic Boltzmann equation b w = ‣ Double perturbation E2 F 2~ 3 v 3 F ‣ Anisotropic scattering ‣ warped Fermi surface e ~ E.@ ~k ñ = Z ~ k 0 |h ~ k 0 | ~ ki| 2 (E ~k E ~k 0) ñ ~k 0 ñ ~k L i = p D⌧ i k min kmax H C Γ C ( ⃗ Q) Classical Conductivity ‣ Renormalized density of states ‣ Renormalized Transport time + Univ. Class (AII) : ‣ Various quantum contributions ‣ All dephasing lengths depends on bw mardi 3 janvier 12
- Page 1 and 2: Some Transport properties of Topolo
- Page 3 and 4: Surface States of 3D Topological In
- Page 5 and 6: Transport measurement on TI Bi2Se3
- Page 7 and 8: Transport measurement on TI Bi2Se3
- Page 9 and 10: Transport measurement on TI ‣ Bi2
- Page 11 and 12: 2D Dirac Matter A B H = ~v F ( y .k
- Page 13 and 14: Diffusion of 2D Dirac states • Tr
- Page 15 and 16: Study of diffusion of 2D Dirac stat
- Page 17 and 18: (Weak) Localization • Probability
- Page 19 and 20: (Weak) Localization / Quantum trans
- Page 21 and 22: Weak localization : Universality cl
- Page 23 and 24: Weak localization : Universality cl
- Page 25 and 26: Anderson Univ. classes and Topologi
- Page 27 and 28: Anderson Univ. classes and Topologi
- Page 29: Anisotropic Scattering of Dirac sta
- Page 33: Conclusion ‣ New playground for u
Anisotropic Scattering of Dirac states<br />
P. Adroguer, D. Carpentier, J. Cayssol and E. Orignac, unpublished<br />
H 0 = ~v F ẑ ⇥ (~ ⇥ ~ k) +V (~r ) H W = 2<br />
z k 3 + + k 3<br />
k ± = k x ± ik y<br />
Diagrammatic<br />
Boltzmann equation<br />
b w =<br />
‣ Double perturbation<br />
E2 F<br />
2~ 3 v 3 F<br />
‣ Anisotropic scattering<br />
‣ warped Fermi surface<br />
e ~ E.@ ~k ñ =<br />
Z<br />
~ k 0<br />
|h ~ k 0 | ~ ki| 2 (E ~k E ~k 0) ñ ~k 0 ñ ~k<br />
L i = p D⌧ i<br />
k min<br />
kmax<br />
H C<br />
Γ C ( ⃗ Q)<br />
Classical Conductivity<br />
‣ Renormalized density of states<br />
‣ Renormalized Transport time<br />
+ Univ. Class (AII) :<br />
‣ Various quantum contributions<br />
‣ All dephasing lengths depends on bw<br />
mardi 3 janvier 12
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