Matrix elements and selection rules for the two-band model of bismuth
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The valence and conduction bands at L are derived from antisymmetric (La) and symmetric (Ls) p-type orbitals, respectively, and the effective low-energy Hamiltonian at this point is described by the (3+1)-dimensional relativistic Dirac equation.
“The valence and conduction bands at L are derived from antisymmetric (L a ) and symmetric (L s ) p -type orbitals, respectively, and the effective low-energy Hamiltonian at this point is described by the (3+1)-dimensional relativistic Dirac equation (18).”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [18]
Cites
Motion of Electrons and Holes in Perturbed Periodic Fields
Luttinger, J. M., & Kohn, W. (1955) · Physical Review · doi:10.1103/physrev.97.869 · Cited by 3,088 · see citing works
Motion in a Constant Magnetic Field
Johnson, M. H., & Lippmann, B. A. (1949) · Physical Review · doi:10.1103/physrev.76.828 · Cited by 450 · see citing works
Energy Bands in the Bismuth Structure. I. A Nonellipsoidal Model for Electrons in Bi
Cohen, M. H. (1961) · Physical Review · doi:10.1103/physrev.121.387 · Cited by 282 · see citing works
Theg-factor and de haas-van alphen effect of electrons in bismuth
Cohen, M. H., & Blount, E. I. (1960) · Philosophical magazine · doi:10.1080/14786436008243294 · Cited by 248 · see citing works
Infrared Magnetoreflection in Bismuth. I. High Fields
Lax, B., Mavroides, J. G., Zeiger, H. J., et al. (1960) · Physical Review Letters · doi:10.1103/physrevlett.5.241 · Cited by 153 · see citing works
Brown, R. N., Mavroides, J. G., & Lax, B. (1963) · Physical Review · doi:10.1103/physrev.129.2055 · Cited by 121 · see citing works
Far Infrared Studies of Bismuth
Boyle, W. S., & Brailsford, A. D. (1960) · Physical Review · doi:10.1103/physrev.120.1943 · Cited by 102 · see citing works
Hybrid Resonance and "Tilted-Orbit" Cyclotron Resonance in Bismuth
Smith, G. E., Hebel, L. C., & Buchsbaum, S. J. (1963) · Physical Review · doi:10.1103/physrev.129.154 · Cited by 97 · see citing works
Size Effects for Conduction in Thin Bismuth Crystals
Friedman, A. N., & Koenig, S. H. (1960) · IBM Journal of Research and Development · doi:10.1147/rd.42.0158 · Cited by 83 · see citing works
Electronic Structure of Bismuth Type Crystals
Mase, S. (1958) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.13.434 · Cited by 82 · see citing works
Electrons and Holes in Bismuth
Jain, A., & Koenig, S. H. (1962) · Physical Review · doi:10.1103/physrev.127.442 · Cited by 79 · see citing works
Electronic Structure of Bismuth Type Crystals, II
Mase, S. (1959) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.14.584 · Cited by 54 · see citing works
Experimental Determination of Effective Masses in a Bismuth-Antimony Alloy
Smith, G. (1962) · Physical Review Letters · doi:10.1103/physrevlett.9.487 · Cited by 52 · see citing works
Electron Spin Resonance in Bismuth and Antimony
Smith, G., Galt, J. K., & Merritt, F. R. (1960) · Physical Review Letters · doi:10.1103/physrevlett.4.276 · Cited by 32 · see citing works
De Haas-van Alphen Type Oscillations in the Infrared Transmission of Bismuth
Boyle, W. S., & Rodgers, K. F. (1959) · Physical Review Letters · doi:10.1103/physrevlett.2.338 · Cited by 28 · see citing works
Interband Magnetoreflection in Bismuth. II. Low Fields
Brown, R. N., Mavroides, J. G., Dresselhaus, M. S., et al. (1960) · Physical Review Letters · doi:10.1103/physrevlett.5.243 · Cited by 24 · see citing works
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<i>Colloquium</i> : Topological insulators
Hasan, M. Z., & Kane, C. L. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.3045 · Cited by 19,930 · see citing works
A topological Dirac insulator in a quantum spin Hall phase
Hsieh, D., Qian, D., Wray, L., Xia, Y., Hor, Y. S., Cava, R. J., & Hasan, M. Z. (2008) · Nature · doi:10.1038/nature06843 · Cited by 3,523 · see citing works
“The valence and conduction bands at L are derived from antisymmetric (La) and symmetric (Ls) p-type orbitals, respectively, and the effective low-energy Hamiltonian at this point is described by the (3+1)-dimensional relativistic Dirac equation [14, 15, 16].”
BackgroundInfluentialTopological Insulator Materials
Ando, Y. (2013) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.82.102001 · Cited by 1,789 · see citing works
Teo, J. C. Y., Fu, L., & Kane, C. L. (2008) · Physical Review B · doi:10.1103/physrevb.78.045426 · Cited by 761 · see citing works
Phase Transitions of Dirac Electrons in Bismuth
Li, L., Checkelsky, J. G., Hor, Y. S., Uher, C., Hebard, A. F., Cava, R. J., & Ong, N. P. (2008) · Science · doi:10.1126/science.1158908 · Cited by 166 · see citing works
Chiral anomaly, dimensional reduction, and magnetoresistivity of Weyl and Dirac semimetals
Gorbar, E. V., Miransky, V. A., & Shovkovy, I. A. (2014) · Physical Review B · doi:10.1103/physrevb.89.085126 · Cited by 145 · see citing works
- Authors
- Wolff, P. A.
- Corresponding author
- Wolff, P.A.
- Venue
- Journal of Physics and Chemistry of Solids
- Publisher
- Elsevier BV
- Published
- 1964-10
- Volume
- 25
- Issue
- 10
- Pages
- 1057-1068
- ISSN
- 0022-3697 (ISSN-L)
- OpenAlex
- W1963552490
- Cited by
- 235
- References
- 16
- Citations by year
- 2026: 2 · 2025: 4 · 2024: 3 · 2023: 7 · 2022: 9 · 2021: 6 · 2020: 8 · 2019: 4 · 2018: 9 · 2017: 8 · 2016: 9 · 2015: 18 · 2014: 15 · 2013: 6 · 2012: 6
- FWCI
- 3.10
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Physics and Chemistry of Solids (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Semiconductor Quantum Structures and Devices
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Semiconductor materials and interfaces
- Keywords
- bismuth, two-band model, matrix elements, selection rules, Dirac Hamiltonian, interband transitions, intraband transitions, magneto-optics, electron wave functions
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