Topological Insulator — Surface Dirac Cone

3D topological insulators host gapless surface states forming a Dirac cone: E = ±ℏv_F|k|, protected by time-reversal symmetry. Spin is locked perpendicular to momentum (spin-momentum locking). Backscattering from non-magnetic impurities is forbidden.

Band Structure

Fermi velocity v_F 1.0 Dirac mass m (gap) 0.0 Fermi energy E_F 0.5 Bulk gap Δ 1.0 Rotation 30°

Surface: E=±v_F|k|
Bulk gap: Δ = 1.0 eV
Z₂ invariant: ν=1
TRS protected
No backscattering