One of the most dramatic effects occurs when θ θ = π π and time-reversal symmetry is present, i.e. non-magnetic topological insulator. Since σ σ AHC surf is a pseudovector on the surface of the crystal, it must respect the surface symmetries, and T is one of them, but T σ σ AHC surf = − − σ σ AHC surf resulting in σ σ AHC surf = 0 . This forces ϕ ϕ = π π on every surface resulting in a Dirac cone (or more generally an odd number of Dirac cones) on every surface and therefore making the boundary of the material conducting.