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Quantum Confinement and Heavy Surface States of Dirac Fermions in Bismuth (111) Films: an Analytical Approach
Mesoscale and Nanoscale Physics · Submitted 11 Dec 2017
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In semi-infinite Bi(111), near $\overline{\rm M}$-point the surface states possess anisotropical parabolic dispersion with very heavy effective mass in $\overline{\rm \Gamma}-\overline{\rm M}$ 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.
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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 $\overline{\rm \Gamma}-\overline{\rm M}$ 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recent high-resolution angle-resolved photoemission spectroscopy experiments have given a reason to believe that pure bismuth is topologically non-trivial semimetal. | background 1.00 | 0.04 | 0.05 | hedged possibility 0.99 |
| s1 | We derive an analytic theory of surface and size-quantized states of Dirac fermions in Bi(111) films taking into account the new data. | contribution 0.99 | 0.96 | 0.11 | asserted 1.00 |
| s2 | The theory relies on a new phenomenological momentum-dependent boundary condition for the effective Dirac equation. | method 0.95 | 0.84 | 0.06 | asserted 1.00 |
| s3 | 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. | method 0.96 | 0.79 | 0.06 | asserted 1.00 |
| s4 | In semi-infinite Bi(111), near $\overline{\rm M}$-point the surface states possess anisotropical parabolic dispersion with very heavy effective mass in $\overline{\rm \Gamma}-\overline{\rm M}$ 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. | result 1.00 | 0.73 | 0.24 | asserted 1.00 |
| s5 | In Bi(111) films with equivalent surfaces, the surface states from top and bottom surfaces are not splitted. | result 1.00 | 0.81 | 0.13 | asserted 1.00 |
| s6 | 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. | result 1.00 | 0.86 | 0.17 | asserted 1.00 |
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Original abstract
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 $\overline{\rm \Gamma}-\overline{\rm M}$ 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.
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Lately SS spectra in Bi(111) thick [ref] and thin [ref] films were also studied in frames of tight-binding models and first-principles density functional theory [ref] .
First-principles study of spin texture and Fermi lines in Bi(111) multi-layer nanofilm · Introduction · 0.86
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