Recent high-resolution angle-resolved photoemission spectroscopy experiments have given a reason to believe that pure bismuth is a topologically nontrivial semimetal. We derive an analytic theory of surface and size-quantized states of Dirac fermions in Bi(111) films taking into account the new data. The theory relies on a new phenomenological momentum-dependent boundary condition for the effective Dirac equation. The boundary condition is described by two real parameters that are expressed by a linear combination of the Dresselhaus and Rashba interface spin-orbit interaction parameters. In semi-infinite Bi(111), near the $\overline{\mathrm{M}}$ point the surface states possess anisotropical parabolic dispersion with very heavy effective mass in the $\overline{\mathrm{\Gamma }}\text{−}\overline{\mathrm{M}}$ direction order of ten free electron masses and light effective mass in the $\overline{\mathrm{M}}\text{−}\overline{\mathrm{K}}$ direction order of one hundredth of free electron mass. In Bi(111) films with equivalent surfaces, the surface states from top and bottom surfaces are not split. In such a symmetric film with arbitrary thickness, the bottom of the lowest quantum confinement subband in the conduction band coincides with the bottom of the bulk conduction band in the $\overline{\mathrm{M}}$ point.

中文翻译：

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铋（111）薄膜中狄拉克费米子的量子约束和重表面态：一种分析方法

最近的高分辨率角度分辨光发射光谱实验已经给出了一个理由，使人们相信纯铋是一种在拓扑上很重要的半金属。考虑到新数据，我们推导了Bi（111）薄膜中狄拉克费米子的表面和尺寸量子化状态的解析理论。该理论依赖于有效的狄拉克方程的一种新的现象学依赖于动量的边界条件。边界条件由两个真实参数描述，两个真实参数由Dresselhaus和Rashba界面自旋轨道相互作用参数的线性组合表示。在半无限Bi（111）中，在$\overline{\mathrm{中号}}$ 点的表面态具有各向异性的抛物线色散，在其中的有效质量非常重 $\overline{\mathrm{\Gamma }}\text{-}\overline{\mathrm{中号}}$ 十个自由电子质量和光有效质量的方向顺序 $\overline{\mathrm{中号}}\text{-}\overline{\mathrm{ķ}}$方向为自由电子质量的百分之一。在具有等效表面的Bi（111）膜中，顶部和底部表面的表面状态不会分裂。在这种具有任意厚度的对称膜中，导带中最低量子约束子带的底部与导带中体导电带的底部重合。$\overline{\mathrm{中号}}$ 观点。