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Critical behavior of disordered degenerate semiconductors. I. Models, symmetries, and formalism
Abstract
A model that describes the qualitative properties of the electronic states of a disordered degenerate semiconductor with a finite number of degeneracy points is proposed. I introduce an effective Hamiltonian of the form of a Dirac operator coupled to randomly distributed fields. It is shown that there is a phase transition between the semimetal and metallic phases followed by a localization transition. The symmetry breaking associated with this transition is related to the nonsymmorphic character of the space group. The density of states plays the role of the order parameter and the elastic mean free path is the correlation length. A path-integral representation is introduced and used to characterize the universality class of this transition. The lower critical dimension is 2. A mapping of the two-dimensional case to one-dimensional self-interacting Fermi systems is presented. Applications to zero-gap semiconductors and other systems are discussed.
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Cites
Absence of Diffusion in Certain Random Lattices
Anderson, P. W. (1958) · Physical Review · doi:10.1103/physrev.109.1492 · Cited by 12,468
Cited by
The electronic properties of graphene
Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S., & Geim, A. K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.109 · Cited by 24,803
Burkov, A. A., Hook, M. D., & Balents, L. (2011) · Physical Review B · doi:10.1103/physrevb.84.235126 · Cited by 1,677
Electronic properties of disordered two-dimensional carbon
Peres, N. M. R., Guinea, F., & Castro Neto, A. H. (2006) · Physical Review B · doi:10.1103/physrevb.73.125411 · Cited by 1,445
Fradkin, E. (1986) · Physical Review B · doi:10.1103/physrevb.33.3263 · Cited by 396
Self-citationThermoelectric properties of Weyl and Dirac semimetals
Lundgren, R., Laurell, P., & Fiete, G. A. (2014) · Physical Review B · doi:10.1103/physrevb.90.165115 · Cited by 234
Metadata
- Authors
- Fradkin, E.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1986-03-01
- Volume
- 33
- Issue
- 5
- Pages
- 3257-3262
- ISSN
- 0163-1829 (ISSN-L)
- OpenAlex
- W2010862020
- Cited by
- 228
- References
- 1
- FWCI
- 0.85
- Type
- journal article
- Language
- en
- Open access
- closed
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- Fradkin, E. (1986). Critical behavior of disordered degenerate semiconductors. I. Models, symmetries, and formalism. Physical Review B. https://doi.org/10.1103/physrevb.33.3257
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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.
