Topological Insulators - GDR Meso

(Weak) Localization
• 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
B
• Phase coherent corrections
‣ loop contributions
O ⇤ C,C =2⇥ C,C / 0
➡Effective diffusion of «pseudo particles» Diffuson (same dir.) / Cooperon (opp. dir.)
0.2
0
-0.2
-0.4
-0.6
-0.8
2.10 - 5 690 mK
11.2
11
10.8
0 20 40 60 80 100
-2000 0 2000
Conductance, same sample, different spins config.
12.4
12.2
12
11.8
11.6
11.4
Flux Through the Sample
mardi 3 janvier 12