where z ^ ^ is normal to the surface and σ σ is in the real spin basis. However, if we rotate spin by a unitary operator, U = d i a g [ 1 , i ] , we will end up with the standard notation of Dirac Hamiltonian, H = ℏ ℏ v D σ σ ⋅ ⋅ k . Such Dirac cones emerging on the surface of 3-dimensional crystals were observed in experiment, e.g.: bismuth selenide (Bi 2 Se 3 ), tin telluride (SnTe) and many other materials.