Abstract
We consider as a model of Weyl semimetal thermoelectric transport a (3 + 1)-dimensional charged, relativistic and relaxed fluid with a U(1)V × U(1)A chiral anomaly. We take into account all possible mixed energy, momentum, electric and chiral charge relaxations, and discover which are compatible with electric charge conservation, Onsager reciprocity and a finite DC conductivity. We find that all relaxations respecting these constraints necessarily render the system open and violate the second law of thermodynamics. We then demonstrate how the relaxations we have found arise from kinetic theory and a modified relaxation time approximation. Our results lead to DC conductivities that differ from those found in the literature opening the path to experimental verification.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N.P. Armitage, E.J. Mele and A. Vishwanath, Weyl and Dirac Semimetals in Three Dimensional Solids, Rev. Mod. Phys. 90 (2018) 015001 [arXiv:1705.01111] [INSPIRE].
A.A. Burkov, Weyl Metals, Ann. Rev. Condens. Mat. Phys. 9 (2018) 359 [arXiv:1704.06660] [INSPIRE].
P. Hosur and X. Qi, Recent developments in transport phenomena in Weyl semimetals, Comptes Rendus Physique 14 (2013) 857 [arXiv:1309.4464] [INSPIRE].
H.B. Nielsen and M. Ninomiya, Absence of Neutrinos on a Lattice. I. Proof by Homotopy Theory, Nucl. Phys. B 185 (1981) 20 [Erratum ibid. 195 (1982) 541] [INSPIRE].
H.B. Nielsen and M. Ninomiya, No Go Theorem for Regularizing Chiral Fermions, Phys. Lett. B 105 (1981) 219 [INSPIRE].
S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [INSPIRE].
J.S. Bell and R. Jackiw, A PCAC puzzle: π0 → γγ in the σ model, Nuovo Cim. A 60 (1969) 47 [INSPIRE].
H.B. Nielsen and M. Ninomiya, Adler-Bell-Jackiw anomaly and Weyl fermions in crystal, Phys. Lett. B 130 (1983) 389 [INSPIRE].
K. Landsteiner, Notes on Anomaly Induced Transport, Acta Phys. Polon. B 47 (2016) 2617 [arXiv:1610.04413] [INSPIRE].
K. Landsteiner, Y. Liu and Y.-W. Sun, Negative magnetoresistivity in chiral fluids and holography, JHEP 03 (2015) 127 [arXiv:1410.6399] [INSPIRE].
K. Landsteiner, Anomalous transport of Weyl fermions in Weyl semimetals, Phys. Rev. B 89 (2014) 075124 [arXiv:1306.4932] [INSPIRE].
M.N. Chernodub et al., Thermal transport, geometry, and anomalies, Phys. Rept. 977 (2022) 1 [arXiv:2110.05471] [INSPIRE].
S. Wang et al., Quantum transport in Dirac and Weyl semimetals: a review, Adv. Phys. X 2 (2017) 518 [INSPIRE].
P.O. Sukhachov and B. Trauzettel, Anomalous Gurzhi effect, Phys. Rev. B 105 (2022) 085141 [arXiv:2112.00781] [INSPIRE].
A. Lucas, R.A. Davison and S. Sachdev, Hydrodynamic theory of thermoelectric transport and negative magnetoresistance in Weyl semimetals, Proc. Nat. Acad. Sci. 113 (2016) 9463 [arXiv:1604.08598] [INSPIRE].
N. Abbasi, A. Ghazi, F. Taghinavaz and O. Tavakol, Magneto-transport in an anomalous fluid with weakly broken symmetries, in weak and strong regime, JHEP 05 (2019) 206 [arXiv:1812.11310] [INSPIRE].
N. Abbasi, F. Taghinavaz and O. Tavakol, Magneto-Transport in a Chiral Fluid from Kinetic Theory, JHEP 03 (2019) 051 [arXiv:1811.05532] [INSPIRE].
E.V. Gorbar, V.A. Miransky, I.A. Shovkovy and P.O. Sukhachov, Nonlocal transport in Weyl semimetals in the hydrodynamic regime, Phys. Rev. B 98 (2018) 035121 [arXiv:1804.01550] [INSPIRE].
D.T. Son and B.Z. Spivak, Chiral Anomaly and Classical Negative Magnetoresistance of Weyl Metals, Phys. Rev. B 88 (2013) 104412 [arXiv:1206.1627] [INSPIRE].
T. Nag and S. Nandy, Magneto-transport phenomena of type-I multi-Weyl semimetals in co-planar setups, J. Phys. Condens. Matter 33 (2021) 075504 [arXiv:1812.08322] [INSPIRE].
J. Gooth, F. Menges, N. Kumar, V. Süß, C. Shekhar, Y. Sun et al., Thermal and electrical signatures of a hydrodynamic electron fluid in tungsten diphosphide, Nature Commun. 9 (2018) 4093.
D. Vu et al., Thermal chiral anomaly in the magnetic-field-induced ideal Weyl phase of Bi1−xSbx, Nature Mater. 20 (2021) 1525 [arXiv:1906.02248] [INSPIRE].
J. Xiong, S.K. Kushwaha, T. Liang, J.W. Krizan, M. Hirschberger, W. Wang et al., Evidence for the chiral anomaly in the dirac semimetal Na3Bi, Science 350 (2015) 413.
X. Huang et al., Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs, Phys. Rev. X 5 (2015) 031023 [arXiv:1503.01304] [INSPIRE].
J. Gooth et al., Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP, Nature 547 (2017) 324 [arXiv:1703.10682] [INSPIRE].
Z. Jia et al., Thermoelectric signature of the chiral anomaly in Cd3As2, Nature Commun. 7 (2016) 13013.
A. Amoretti, D.K. Brattan, L. Martinoia and I. Matthaiakakis, Leading order magnetic field dependence of conductivities in anomalous hydrodynamics, Phys. Rev. D 108 (2023) 016003 [arXiv:2212.09761] [INSPIRE].
A. Amoretti, D.K. Brattan, L. Martinoia and I. Matthaiakakis, Restoring time-reversal covariance in relaxed hydrodynamics, Phys. Rev. D 108 (2023) 056003 [arXiv:2304.01248] [INSPIRE].
E.V. Gorbar, V.A. Miransky, I.A. Shovkovy and P.O. Sukhachov, Consistent hydrodynamic theory of chiral electrons in Weyl semimetals, Phys. Rev. B 97 (2018) 121105 [arXiv:1712.01289] [INSPIRE].
R.M.A. Dantas, F. Peña-Benitez, B. Roy and P. Surówka, Magnetotransport in multi-Weyl semimetals: A kinetic theory approach, JHEP 12 (2018) 069 [arXiv:1802.07733] [INSPIRE].
P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].
A. Amoretti and D.K. Brattan, On the hydrodynamics of (2 + 1)-dimensional strongly coupled relativistic theories in an external magnetic field, Mod. Phys. Lett. A 37 (2022) 2230010 [arXiv:2209.11589] [INSPIRE].
A. Amoretti, D.K. Brattan, L. Martinoia and I. Matthaiakakis, Non-dissipative electrically driven fluids, JHEP 05 (2023) 218 [arXiv:2211.05791] [INSPIRE].
M. Rogatko and K.I. Wysokinski, Magnetotransport of Weyl semimetals with ℤ2 topological charge and chiral anomaly, JHEP 01 (2019) 049 [arXiv:1810.07521] [INSPIRE].
A.V. Sadofyev and Y. Yin, Drag suppression in anomalous chiral media, Phys. Rev. D 93 (2016) 125026 [arXiv:1511.08794] [INSPIRE].
M.A. Stephanov and H.-U. Yee, No-Drag Frame for Anomalous Chiral Fluid, Phys. Rev. Lett. 116 (2016) 122302 [arXiv:1508.02396] [INSPIRE].
K. Das and A. Agarwal, Thermal and gravitational chiral anomaly induced magneto-transport in Weyl semimetals, Phys. Rev. Res. 2 (2020) 013088 [arXiv:1909.07711] [INSPIRE].
B.Z. Spivak and A.V. Andreev, Magnetotransport phenomena related to the chiral anomaly in weyl semimetals, Phys. Rev. B 93 (2016) 085107.
G. Sharma, P. Goswami and S. Tewari, Nernst and magnetothermal conductivity in a lattice model of Weyl fermions, Phys. Rev. B 93 (2016) 035116 [arXiv:1507.05606] [INSPIRE].
R. Lundgren, P. Laurell and G.A. Fiete, Thermoelectric properties of Weyl and Dirac semimetals, Phys. Rev. B 90 (2014) 165115 [arXiv:1407.1435] [INSPIRE].
B.N. Narozhny, Hydrodynamic approach to two-dimensional electron systems, Riv. Nuovo Cim. 45 (2022) 661 [arXiv:2207.10004] [INSPIRE].
K. Huang, Statistical mechanics, Wiley (1987).
D. Tong, Kinetic theory, lecture notes [http://www.damtp.cam.ac.uk/user/tong/kinetic.html].
G.S. Denicol and D.H. Rischke, Microscopic Foundations of Relativistic Fluid Dynamics, Springer Cham (2021) [https://doi.org/10.1007/978-3-030-82077-0].
L.P. Pitaevskii and E.M. Lifshitz, Physical Kinetics. Volume 10 (Course of Theoretical Physics), Butterworth-Heinemann (1981).
H.K. Pal, V.I. Yudson and D.L. Maslov, Resistivity of non-galilean-invariant fermi- and non-fermi liquids, Lithuanian J. Phys. 52 (2012) 142.
D. Dash, S. Bhadury, S. Jaiswal and A. Jaiswal, Extended relaxation time approximation and relativistic dissipative hydrodynamics, Phys. Lett. B 831 (2022) 137202 [arXiv:2112.14581] [INSPIRE].
B.N. Narozhny and I.V. Gornyi, Hydrodynamic approach to electronic transport in graphene: Energy relaxation, Front. Phys. 9 (2021) .
C. Cercignani, Mathematical methods in kinetic theory, Springer New York (1990) [https://doi.org/10.1007/978-1-4899-7291-0].
M. Ochi, Electron-hole dichotomy for thermoelectric transport in a two-valley system with strong intervalley scattering, arXiv:2306.04075.
D.T. Son and N. Yamamoto, Kinetic theory with Berry curvature from quantum field theories, Phys. Rev. D 87 (2013) 085016 [arXiv:1210.8158] [INSPIRE].
E.V. Gorbar, V.A. Miransky, I.A. Shovkovy and P.O. Sukhachov, Consistent Chiral Kinetic Theory in Weyl Materials: Chiral Magnetic Plasmons, Phys. Rev. Lett. 118 (2017) 127601 [arXiv:1610.07625] [INSPIRE].
K. Pongsangangan, T. Ludwig, H.T.C. Stoof and L. Fritz, Hydrodynamics of charged two-dimensional Dirac systems. I. Thermoelectric transport, Phys. Rev. B 106 (2022) 205126 [arXiv:2206.09687] [INSPIRE].
C. Bianca and C. Dogbé, On the Boltzmann gas mixture equation: Linking the kinetic and fluid regimes, Commun. Nonlinear Sci. Numer. Simul. 29 (2015) 240.
J.A. Fotakis et al., Multicomponent relativistic dissipative fluid dynamics from the Boltzmann equation, Phys. Rev. D 106 (2022) 036009 [arXiv:2203.11549] [INSPIRE].
V.A. Zyuzin, Magnetotransport of Weyl semimetals due to the chiral anomaly, Phys. Rev. B 95 (2017) 245128 [arXiv:1608.01286] [INSPIRE].
P.L. Bhatnagar, E.P. Gross and M. Krook, A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems, Phys. Rev. 94 (1954) 511 [INSPIRE].
G.S. Rocha, G.S. Denicol and J. Noronha, Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation, Phys. Rev. Lett. 127 (2021) 042301 [arXiv:2103.07489] [INSPIRE].
D.K. Brattan and G. Lifschytz, Holographic plasma and anyonic fluids, JHEP 02 (2014) 090 [arXiv:1310.2610] [INSPIRE].
D.K. Brattan, A strongly coupled anyon material, JHEP 11 (2015) 214 [arXiv:1412.1489] [INSPIRE].
Acknowledgments
A.A. and I.M. have been partially supported by the “Curiosity Driven Grant 2020” of the University of Genoa and the INFN Scientific Initiative SFT: “Statistical Field Theory, Low-Dimensional Systems, Integrable Models and Applications”. This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 101030915.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2309.05692
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Amoretti, A., Brattan, D.K., Martinoia, L. et al. Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory. J. High Energ. Phys. 2024, 71 (2024). https://doi.org/10.1007/JHEP02(2024)071
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2024)071