Charge Transport in Weyl Semimetals
Open accessAbstract
We study transport in Weyl semimetals with $N$ isotropic Weyl nodes in the presence of Coulomb interactions or disorder at temperature $T$. In the interacting clean limit, we determine the conductivity $\ensuremath{\sigma}(\ensuremath{\omega},T)$ by solving a quantum Boltzmann equation within a ``leading log'' approximation and find it to be proportional to $T$, up to logarithmic factors arising from the flow of couplings. In the noninteracting disordered case, we compute the Kubo conductivity and show that it behaves differently for $\ensuremath{\omega}\ensuremath{\ll}T$ and $\ensuremath{\omega}\ensuremath{\gg}T$: in the former regime we recover a previous result, of a finite dc conductivity and a Drude width vanishing as $N{T}^{2}$; in the latter, we find that $\ensuremath{\sigma}(\ensuremath{\omega},T)$ vanishes linearly with $\ensuremath{\omega}$ with a leading term as $T\ensuremath{\rightarrow}0$ equal to the clean, free-fermion result: ${\ensuremath{\sigma}}_{0}^{(N)}(\ensuremath{\omega},T=0)=N\frac{{e}^{2}}{12h}\frac{|\ensuremath{\omega}|}{{v}_{F}}$. We compare our results to transport data on ${\mathrm{Y}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$ and comment on the possible relevance to recent experiments on ${\mathrm{Eu}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$.
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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 Hosur et al., 2012
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Experimental — accuracy not yet measured3D Dirac and Weyl systems are predicted to have a number of interesting semi-classical transport and optical effects that are diagnostic for this state of matter.
“As mentioned above, 3D Dirac and Weyl systems are predicted to have a number of interesting semi-classical transport and optical effects that are diagnostic for this state of matter (Burkov and Balents, 2011; Hosur et al. , 2012)”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Hosur et al. , 2012
The opening summary (p. 1) predicts temperature-dependent and finite-frequency conductivity in 3D Weyl semimetals, and the Conclusions (p. 4) describe distinctive frequency-dependent behavior that further measurements could test. The paper does not establish the same transport and optical predictions for 3D Dirac systems; it mentions earlier Dirac-point studies only as a comparison (p. 2). (LLM, conf=0.84)
Experimental — accuracy not yet measuredIn the absence of impurities and interactions, the free fermion result for the conductivity in the low energy limit that arises from interband transitions across the Weyl or Dirac node when the chemical potential is at the Weyl or Dirac point is given by Eq. 40.
“In the absence of impurities and interactions the free fermion result for the conductivity in the low energy limit (where quadratic or higher order terms in the dispersion can be neglected) that arises from interband transitions across the Weyl or Dirac node when the chemical potential (E F ) is at the Weyl or Dirac point is”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Hosur et al. , 2012
A quantum Boltzmann calculation gives the expression for the optical conductivity Eq. 44.
“A quantum Boltzmann calculation (Hosur et al. , 2012) gives the expression for the optical conductivity”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Hosur et al. , 2012
In the opposite ω≫T limit the calculation gives Eq. 43.
“In the opposite ω ≫ T limit the calculation (Hosur et al. , 2012) gives”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Hosur et al. , 2012
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“…across the Weyl or Dirac node when the chemical potential (EF ) is at the Weyl or Dirac point is σ1(ω) = N e2 12h |ω| vF (40) where vF is the Fermi velocity and N is number of nodes (Burkov and Balents, 2011; Hosur et al., 2012; Hosur and Qi, 2013; Tabert et al., 2016; Wan et al., 2011).”
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BackgroundInfluentialSelf-citation
- Authors
- Hosur, P., Parameswaran, S. A., & Vishwanath, A.
- Affiliations
- University of California, Berkeley (US)
- Lawrence Berkeley National Laboratory (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2012-01-24
- Volume
- 108
- Issue
- 4
- Pages
- 046602-046602
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1967379174
- Cited by
- 466
- References
- 2
- Citations by year
- 2026: 13 · 2025: 15 · 2024: 12 · 2023: 31 · 2022: 41 · 2021: 44 · 2020: 39 · 2019: 37 · 2018: 47 · 2017: 37 · 2016: 45 · 2015: 47 · 2014: 30 · 2013: 16 · 2012: 12
- FWCI
- 17.38
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Funders
- U.S. Department of Energy
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Physical Sciences › Materials Science › Materials Chemistry › 2D Materials and Applications
- Keywords
- Weyl semimetals, charge transport, Kubo conductivity, quantum Boltzmann equation, leading-log approximation, electrostatic interactions, disorder, DC conductivity, Eu2Ir2O7, Weyl points
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