Topological Insulators - GDR Meso

(Weak) Localization / Quantum transport
• Probability to diffuse from ⇥r to ⇥r
⇥
P (⌅r ⌅r ⇥ ) ⇥
path C ⇥r
• Phase variation along a diffusion path :
• Average interferences vanish,
except if ”C = C ” (reversed ring)
⇥r ⇥
A C
2
= ⇥ |A C | 2 + ⇥ A C A C ⇥
C
C⇤=C ⇥
⌅ C =2⇤ L C
⇥ F
Classical
Interferences
random in a metal
O ⇤ C,C =2⇥ C,C / 0
• Phase coherent corrections
‣ loop contributions
➡Effective diffusion of «pseudo particles» Diffuson (same dir.) / Cooperon (opp. dir.)
‣ Universality properties of (weak) localization
➡ numbers of Cooperon/Diffuson (symmetry)
mardi 3 janvier 12