Anticrossing energy and symmetry-broken spin angular momentum of the surface states on Au(111)

The surface states on Au(111) are demonstrated for the anticrossing energy and the symmetry-broken spin angular momentum on the basis of first-principles calculations. The surface states are described as two anticrossing nondegenerate states in the single group and two anticrossing degenerate states in the double group. The surface states are also described as the finite and symmetry-broken spin angular momentum in the x-, y-, and z-axes and the finite and symmetry-broken spin angular momentum in the in-plane [2¯11]- and [01¯1]-axes and the infinitesimal spin angular momentum in the out-of-plane [111]-axis. The energy splitting is then attributed to the crystal potential and electron–electron interaction terms rather than the spin–orbit coupling term.