Topological Insulator — Spin-Momentum Locking
Helical Dirac cone · Surface states · Z₂ topological invariant
Band Structure Parameters
Dirac velocity vF:
1.00
Gap Δ (trivial if Δ > 0):
0.00
Warping term λ:
0.00
View angle φ (°):
30
2D cut
3D cone
Surface Hamiltonian:
H = vF(kx σy − ky σx) + Δσz + λ(k+³+k−³)σz
Spin-momentum locking:
spin direction is locked perpendicular to momentum — backscattering by non-magnetic impurities is forbidden.
Z₂ invariant ν=1:
odd number of Dirac points on surface BZ. Δ=0 is the topological phase; Δ≠0 opens gap and destroys topology.
Warping (hexagonal) distorts circle → snowflake at higher k — observed in Bi₂Te₃.