Thermoelectric properties of Weyl and Dirac semimetals
Open accessAbstract
We study the electronic contribution to the thermal conductivity and the thermopower of Weyl and Dirac semimetals using a semiclassical Boltzmann approach. We investigate the effect of various relaxation processes including disorder and interactions on the thermoelectric properties, and also consider doping away from the Weyl or Dirac point. We find that the thermal conductivity and thermopower have an interesting dependence on the chemical potential that is characteristic of the linear electronic dispersion, and that the electron-electron interactions modify the Lorenz number. For the interacting system, we also use the Kubo formalism to obtain the transport coefficients. We find exact agreement between the Kubo and Boltzmann approaches at high temperatures. We also consider the effect of electric and magnetic fields on the thermal conductivity in various orientations with respect to the temperature gradient. Notably, when the temperature gradient and magnetic field are parallel, we find a large contribution to the longitudinal thermal conductivity that is quadratic in the magnetic field strength, similar to the magnetic field dependence of the longitudinal electrical conductivity due to the presence of the chiral anomaly when no thermal gradient is present.
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With interactions, the longitudinal thermal conductivity has a quadratic temperature dependence, in contrast to a linear dependence on the temperature for either charged impurities or short-range disorder.
“With interactions they find that the longitudinal thermal conductivity has a quadratic temperature dependence, in contrast to a linear dependence on the temperature for either charged impurities or short-range disorder (similar to normal metals).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Lundgren et al. , 2014
With the temperature gradient perpendicular to the magnetic field, the transverse thermal conductivity is linear in magnetic field and the longitudinal thermal conductivity has a negative contribution that goes as the square of the magnetic field.
“With the temperature gradient perpendicular to the magnetic field the transverse thermal conductivity is linear in magnetic field and the longitudinal thermal conductivity has a negative contribution that goes as the square of the magnetic field.”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Lundgren et al. , 2014
The presence of finite electric field is predicted to not change these dependences as long as there is no internode scattering.
“The presence of finite electric field is predicted to not change these dependences as long as there is no internode scattering.”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Lundgren et al. , 2014
For kBT ≫ EF, both Boltzmann transport and Kubo formalism calculations give a Lorenz number enhanced by interactions from the Fermi liquid value.
“For k B T ≫ E F , both Boltzmann transport (Lundgren et al. , 2014) and Kubo formalism (Tabert et al. , 2016) calculations give a Lorenz number enhanced by interactions from the Fermi liquid value.”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Lundgren et al. , 2014
When the temperature gradient is in the direction of the magnetic field there is an increasing quadratic magnetic field dependence for the longitudinal thermal conductivity and zero transverse thermal conductivity.
“When the temperature gradient is in the direction of the magnetic field there is an increasing quadratic magnetic field dependence for the longitudinal thermal conductivity and zero transverse thermal conductivity.”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Lundgren et al. , 2014
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Weyl and Dirac semimetals in three-dimensional solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015001 · Cited by 4,528 · see citing works
“Lundgren et al., 2014 also considered the effect of electric and magnetic fields on the thermoelectric coefficients.”
BackgroundMethodInfluentialThe chiral anomaly and thermopower of Weyl fermions in the half-Heusler GdPtBi
Hirschberger, M., Kushwaha, S., Wang, Z., Gibson, Q., Liang, S., Belvin, C. A., Bernevig, B. A., Cava, R. J., & Ong, N. P. (2016) · Nature Materials · doi:10.1038/nmat4684 · Cited by 576 · see citing works
Chiral Anomaly as the Origin of the Planar Hall Effect in Weyl Semimetals
Nandy, S., Sharma, G., Taraphder, A., & Tewari, S. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.176804 · Cited by 355 · see citing works
Predicted Unusual Magnetoresponse in Type-II Weyl Semimetals
Yu, Z.-M., Yao, Y., & Yang, S. A. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.077202 · Cited by 262 · see citing works
Helicity-protected ultrahigh mobility Weyl fermions in NbP
Wang, Z., Zheng, Y., Shen, Z., Lu, Y., Fang, H., Sheng, F., Zhou, Y., Yang, X., Li, Y., Feng, C., et al. (2016) · Physical Review B · doi:10.1103/physrevb.93.121112 · Cited by 201 · see citing works
Chiral anomaly and longitudinal magnetotransport in type-II Weyl semimetals
Sharma, G., Goswami, P., & Tewari, S. (2017) · Physical Review B · doi:10.1103/physrevb.96.045112 · Cited by 98 · see citing works
Weyl and Dirac Semimetals in Three Dimensional Solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2017) · arXiv
“Lundgren et al., 2014 also considered the effect of electric and magnetic fields on the thermoelectric coefficients.”
BackgroundMethodInfluential
- Authors
- Lundgren, R., Laurell, P., & Fiete, G. A.
- Affiliations
- The University of Texas at Austin (US)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2014-10-13
- Volume
- 90
- Issue
- 16
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2242977001
- Cited by
- 234
- References
- 8
- Citations by year
- 2026: 7 · 2025: 15 · 2024: 19 · 2023: 17 · 2022: 20 · 2021: 20 · 2020: 31 · 2019: 31 · 2018: 18 · 2017: 26 · 2016: 20 · 2015: 10
- FWCI
- 9.29
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- European Research Council (ERC-StG-Thomale-2013-336012)
- Army Research Office (W911NF-09-1-0527)
- National Science Foundation (2012115499, DMR-0955778)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Materials Science › Materials Chemistry › Advanced Thermoelectric Materials and Devices
- Physical Sciences › Materials Science › Materials Chemistry › Thermal properties of materials
- Keywords
- Weyl semimetals, Dirac semimetal, thermoelectric properties, thermal conductivity, Seebeck coefficient, Lorenz number, electron-electron interaction, disorder scattering, Kubo formalism, Boltzmann transport, chiral anomaly, chemical potential dependence
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