Decay length of surface-state wave functions on Bi(1 1 1).
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 [Formula: see text] along the [Formula: see text] 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 [Formula: see text], while it remains less than 5 Bi bilayers when [Formula: see text] is away from [Formula: see text] and [Formula: see text]. At [Formula: see text], 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 [Formula: see text] is less than 10 Bi bilayers due to the large effective mass (small curvature) of the highest valence band in the surface normal direction.
College of Humanities and Sciences, Nihon University, Sakura-josui, Tokyo 156-8550, Japan. Center for Materials Research by Information Integration, National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan.
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Ishida