Critical behavior of disordered degenerate semiconductors. II. Spectrum and transport properties in mean-field theory.
Abstract
The critical behavior of disordered degenerate semiconductors is studied within a mean-field theory valid when the number of degeneracy points is large. I show that above two dimensions there is a semimetal-metal transition at a critical impurity concentration. The mean free path and the one-particle density of states exhibit scaling behavior with universal exponents. The transition is smeared at nonzero temperature. An equation of state, relating temperature, disorder, and bare conductivity, is presented. In two dimensions, the semimetallic phase is unstable. I show that a localization transition follows except in two dimensions where all states are localized. The bare conductivity appears to be a universal number in two dimensions. Applications to zero-gap semiconductors and other systems are discussed.
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There is broad theoretical consensus that a 2D gas of Dirac fermions should exhibit a minimum conductivity of about e^2/h.
“Although there is a broad theoretical consensus [18-23,10,11] that a 2D gas of Dirac fermions should exhibit a minimum conductivity of about e 2 / h”
From Two-dimensional gas of massless Dirac fermions in graphene (2005) · cites this paper as [23]
Analogous calculations for 3D semimetals show a vanishing density of states persisting up to a finite value of disorder strength (Fradkin, 1986; Goswami and Chakravarty, 2011; Hosur et al., 2012; Pixley et al., 2016a) beyond which a metallic state is expected.
“Analogous calculations for 3D semimetals show a vanishing density of states persisting up to a finite value of disorder strength (Fradkin, 1986; Goswami and Chakravarty, 2011; Hosur et al. , 2012; Pixley et al. , 2016a) beyond which a metallic state is expected.”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Fradkin, 1986
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References 7 · Cited by 396
- Authors
- Fradkin, E.
- Affiliations
- University of Illinois Urbana-Champaign (US)
- Corresponding author
- Fradkin, Eduardo
- ORCID
- Fradkin, Eduardo
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1986-03-01
- Volume
- 33
- Issue
- 5
- Pages
- 3263-3268
- ISSN
- 0163-1829 (ISSN-L)
- OpenAlex
- W2018317672
- Cited by
- 396
- References
- 7
- Citations by year
- 2026: 5 · 2025: 9 · 2024: 8 · 2023: 16 · 2022: 16 · 2021: 19 · 2020: 34 · 2019: 23 · 2018: 32 · 2017: 31 · 2016: 27 · 2015: 19 · 2014: 19 · 2013: 10 · 2012: 14
- FWCI
- 0.64
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. B, Condensed matter (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Science Foundation
- University of California, Santa Barbara
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Keywords
- critical behavior, mean-field theory, critical impurity concentration, mean free path, density of states, scaling exponents, equation of state, localization transition, two-dimensional localization, zero-gap semiconductors, Anderson localization
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