Decay length of surface-state wave functions on Bi(1 1 1)

Abstract

We calculate the decay length in surface normal direction of the surface-state wave functions on a clean Bi(1 1 1) surface as a function of two-dimensional (2D) wave vector along the line. For this purpose, we perform a first-principles density functional theory (DFT) calculation for semi-infinite Bi(1 1 1) by employing the surface embedded Green’s function technique. The decay length of the two surface bands is found to be ∼24 Bi bilayers at , while it remains less than 5 Bi bilayers when is away from and . At , the degenerate surface bands are split from the upper boundary energy of the projected bulk valence bands only by 5 meV. In spite of this, the decay length of these bands at is less than 10 Bi bilayers due to the large effective mass (small curvature) of the highest valence band in the surface normal direction.