Quantum Confinement and Heavy Surface States of Dirac Fermions in Bismuth (111) Films: an Analytical Approach
Recent high-resolution angle-resolved photoemission spectroscopy experiments have given a reason to believe that pure bismuth is topologically non-trivial 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 $\overline{\rm M}$-point the surface states possess anisotropical parabolic dispersion with very heavy effective mass in $\overline{\rm Γ}-\overline{\rm M}$ direction order of ten free electron masses, and light effective mass in $\overline{\rm M}-\overline{\rm K}$ 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 splitted. In such symmetric film with arbitrary thickness, bottom of the lowest quantum confinement subband in conduction band coincides with the bottom of bulk conduction band in $\overline{\rm M}$-point.