Excitonic effects in two-dimensional massless Dirac fermions
Open accessAbstract
We study excitonic effects in two-dimensional massless Dirac fermions with Coulomb interactions by solving the ladder approximation to the Bethe-Salpeter equation. It is found that the general four-leg vertex has a power-law behavior with the exponent going from real to complex as the coupling constant is increased. This change of behavior is manifested in the antisymmetric response, which displays power-law behavior at small wave vectors reminiscent of a critical state, and a change in this power law from real to complex that is accompanied by poles in the response function for finite-size systems, suggesting a phase transition for strong enough interactions. The density-density response is also calculated, for which no critical behavior is found. We demonstrate that exciton correlations enhance the cusp in the irreducible polarizability at $2{k}_{F}$, leading to a strong increase in the amplitude of Friedel oscillations around a charged impurity.
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Electron-hole compensation has been proposed as a possible mechanism for unusually large MR in topological semimetals.
“Electron-hole compensation has been proposed to be a possible mechanism (46,48,171).”
From Transport of Topological Semimetals (2019) · cites this paper as [171]
The Conclusion (p. 13) discusses excitonic effects and a particle-hole response in massless Dirac fermions, not electron-hole compensation as a mechanism for magnetoresistance. Searches for electron-hole compensation and magnetoresistance found no passage addressing the claim. (LLM, conf=0.76)
Experimental — accuracy not yet measuredTransverse MR in WSMs/DSMs such as Cd3As2, PtBi2, WTe2, and NbP can reach up to 0.1-1 million percent at low temperatures (0.5-5 K) and 9 T, without saturation up to 30-100 T.
“The transverse MR, measured with the field perpendicular to the current direction, can reach up to 0.1-1 million percent at low temperatures (0.5-5 K) and a field of 9 T (see Table 1), without any sign of saturation up to 30-100 T in WSMs/DSMs such as Cd 3 As 2 , PtBi 2 , WTe 2 , and NbP (46,48,171,172).”
From Transport of Topological Semimetals (2019) · cites this paper as [171]
The paper’s Conclusion (p. 13) discusses density response and Friedel oscillations in two-dimensional Dirac-fermion models, not transverse magnetoresistance. Searches for magnetoresistance, the named materials, and the quoted field strengths and percentages found no passage addressing the claim. (LLM, conf=0.76)
Experimental — accuracy not yet measuredQuadratic or nearly-quadratic field dependence of ρxx has been observed in a number of topological semimetals, but linear or sublinear MR has also been observed in a variety of samples.
“Such a dependence has indeed been observed in a number of topological semimetals (48,183,(191)(192)(193), but linear or even sublinear MR has also been observed in a variety of samples (107, 171, 172, 174-180, 182, 183, 191, 194).”
From Transport of Topological Semimetals (2019) · cites this paper as [171]
The Introduction (p. 1) and Conclusion (p. 13) discuss Coulomb interactions, density response, and Friedel oscillations in two-dimensional massless Dirac fermions. Searches for magnetoresistance, ρxx, and quadratic, linear, or sublinear magnetic-field dependence found no passage addressing the claimed observations in topological semimetals. (LLM, conf=0.76)
Experimental — accuracy not yet measuredAdditional frequencies attributed to magnetic breakdown have been observed in high-field quantum oscillation studies on several topological semimetals.
“The additional frequencies ascribed to magnetic breakdown have been observed in high-field quantum oscillation studies on several topological semimetals (171,226,252).”
From Transport of Topological Semimetals (2019) · cites this paper as [171]
The paper’s opening summary (p. 1) describes theoretical calculations of excitonic effects, and its Conclusion (p. 13) discusses density response and Friedel oscillations. Searches for magnetic breakdown, high-field quantum oscillations, and topological semimetals found no passage reporting the claimed experimental observations. (LLM, conf=0.76)
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References 36 · Cited by 28
Research works printed but not linked: 4
- 13 D. Nelson, in Defects and Geometry in Condensed Matter Physics (Cambridge University Press, New York, 2002).
- 21 E. Merzbacher, Quantum Mechanics, 2nd Edition (Wiley, New York, 1970).
- 22 W. H. Press et al. , Numerical Recipes, 3rd Edition (Cam- bridge University Press, 2007).
- 24 E. M. Hazewinkel, The Wiener-Hopf Method (Springer, 2001).
- Authors
- Wang, J., Fertig, H. A., Murthy, G., & Brey, L.
- Affiliations
- Indiana University Bloomington (US)
- University of Kentucky (US)
- Consejo Superior de Investigaciones Científicas (ES)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2011-01-11
- Volume
- 83
- Issue
- 3
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2047085649
- Cited by
- 28
- References
- 36
- Citations by year
- 2025: 3 · 2021: 2 · 2019: 1 · 2018: 4 · 2017: 5 · 2016: 1 · 2015: 1 · 2014: 1 · 2013: 3 · 2012: 4
- FWCI
- 1.91
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Topics
- 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
- Physical Sciences › Materials Science › Materials Chemistry › 2D Materials and Applications
- Keywords
- excitons, massless Dirac fermions, two-dimensional Dirac systems, electrostatic interactions, Bethe-Salpeter equation, ladder approximation, power-law behavior, critical state, Friedel oscillations, charged impurities, phase transitions
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