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On the Surface States Associated with a Periodic Potential
Abstract
The wave functions and energy levels associated with a finite one-dimensional periodic potential field are investigated. In a plot of the energy spectrum versus interatomic distance the surface levels appear only at lattice constants so small that the boundary curves for the allowed energy bands have crossed. The levels appear in the "forbidden" region between allowed bands in pairs one coming from each of the adjoining bands. In three dimensions these surface levels give rise to surface bands. The surface bands probably exist and are half-filled for diamond. They exist for all metals and are entirely unoccupied only for the monovalent metals.
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Cited by
Electromagnetic propagation in periodic stratified media I General theory*
Yeh, P., Yariv, A., & Hong, C.-S. (1977) · Journal of the Optical Society of America · doi:10.1364/josa.67.000423 · Cited by 1,537
Topological protection of photonic mid-gap defect modes
Noh, J., Benalcazar, W. A., Huang, S., Collins, M. J., Chen, K. P., Hughes, T. L., & Rechtsman, M. C. (2018) · Nature Photonics · doi:10.1038/s41566-018-0179-3 · Cited by 630
Observation of unconventional edge states in ‘photonic graphene’
Plotnik, Y., Rechtsman, M. C., Song, D., Heinrich, M., Zeuner, J. M., Nolte, S., Lumer, Y., Malkova, N., Xu, J., Szameit, A., et al. (2014) · Nature Materials · doi:10.1038/nmat3783 · Cited by 389
Observation of optical Shockley-like surface states in photonic superlattices
Malkova, N., Hromada, I., Wang, X., Bryant, G., & Chen, Z. (2009) · Optics Letters · doi:10.1364/ol.34.001633 · Cited by 284
Observation of Discrete Surface Solitons
Suntsov, S., Makris, K. G., Christodoulides, D. N., Stegeman, G. I., Haché, A., Morandotti, R., Yang, H., Salamo, G., & Sorel, M. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.063901 · Cited by 271
Metadata
- Authors
- Shockley, W.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1939-08-15
- Volume
- 56
- Issue
- 4
- Pages
- 317-323
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2090782634
- Cited by
- 1,241
- References
- 0
- FWCI
- 1.00
- Type
- journal article
- Language
- en
- Open access
- closed
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- Shockley, W. (1939). On the Surface States Associated with a Periodic Potential. Physical Review. https://doi.org/10.1103/physrev.56.317
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
