Advertisement

Magneto-transport in a chiral fluid from kinetic theory

  • Navid AbbasiEmail author
  • Farid Taghinavaz
  • Omid Tavakol
Open Access
Regular Article - Theoretical Physics
  • 15 Downloads

Abstract

We argue that in order to study the magneto-transport in a relativistic Weyl fluid, it is needed to take into account the associated quantum corrections, namely the side-jump effect, at least to second order. To this end, we impose Lorentz invariance to a system of free Weyl fermions in the presence of the magnetic field and find the second order correction to the energy dispersion. By developing a scheme to compute the integrals in the phase space, we show that the mentioned correction has non-trivial effects on the thermodynamics of the system. Specifically, we compute the expression of the negative magnetoresistivity in the system from the enthalpy density in equilibrium. Then in analogy with Weyl semimetal, in the framework of the chiral kinetic theory and under the relaxation time approximation, we explicitly compute the magneto-conductivities, at low temperature limit (Tμ). We show that the conductivities obey a set of Ward identities which follow from the generating functional including the Chern-Simons part.

Keywords

AdS-CFT Correspondence Anomalies in Field and String Theories Gaugegravity correspondence Holography and quark-gluon plasmas 

Notes

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.

References

  1. [1]
    D.T. Son and P. Surówka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam and P. Surówka, Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  3. [3]
    J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    K. Landsteiner, E. Megias and F. Pena-Benitez, Anomalous Transport from Kubo Formulae, Lect. Notes Phys. 871 (2013) 433 [arXiv:1207.5808] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    D.E. Kharzeev and H.-U. Yee, Anomalies and time reversal invariance in relativistic hydrodynamics: the second order and higher dimensional formulations, Phys. Rev. D 84 (2011) 045025 [arXiv:1105.6360] [INSPIRE].
  6. [6]
    N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Jain, S. Minwalla and T. Sharma, Constraints on Fluid Dynamics from Equilibrium Partition Functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    K. Jensen, R. Loganayagam and A. Yarom, Thermodynamics, gravitational anomalies and cones, JHEP 02 (2013) 088 [arXiv:1207.5824] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational Anomaly and Transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].
  10. [10]
    R. Loganayagam and P. Surówka, Anomaly/Transport in an Ideal Weyl gas, JHEP 04 (2012) 097 [arXiv:1201.2812] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  11. [11]
    K. Landsteiner, E. Megias, L. Melgar and F. Pena-Benitez, Holographic Gravitational Anomaly and Chiral Vortical Effect, JHEP 09 (2011) 121 [arXiv:1107.0368] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  12. [12]
    N. Yamamoto, Chiral Alfvén Wave in Anomalous Hydrodynamics, Phys. Rev. Lett. 115 (2015) 141601 [arXiv:1505.05444] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    N. Abbasi, A. Davody, K. Hejazi and Z. Rezaei, Hydrodynamic Waves in an Anomalous Charged Fluid, Phys. Lett. B 762 (2016) 23 [arXiv:1509.08878] [INSPIRE].
  14. [14]
    M.N. Chernodub, Chiral Heat Wave and mixing of Magnetic, Vortical and Heat waves in chiral media, JHEP 01 (2016) 100 [arXiv:1509.01245] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    M.N. Chernodub, A. Cortijo and K. Landsteiner, Zilch vortical effect, Phys. Rev. D 98 (2018) 065016 [arXiv:1807.10705] [INSPIRE].
  16. [16]
    X.-G. Huang and A.V. Sadofyev, Chiral Vortical Effect For An Arbitrary Spin, arXiv:1805.08779 [INSPIRE].
  17. [17]
    D.T. Son and N. Yamamoto, Berry Curvature, Triangle Anomalies and the Chiral Magnetic Effect in Fermi Liquids, Phys. Rev. Lett. 109 (2012) 181602 [arXiv:1203.2697] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    M.A. Stephanov and Y. Yin, Chiral Kinetic Theory, Phys. Rev. Lett. 109 (2012) 162001 [arXiv:1207.0747] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    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].
  20. [20]
    E.V. Gorbar, V.A. Miransky, I.A. Shovkovy and P.O. Sukhachov, Anomalous transport properties of Dirac and Weyl semimetals (Review Article), Low Temp. Phys. 44 (2018) 487 [Fiz. Nizk. Temp. 44 (2018) 635] [arXiv:1712.08947] [INSPIRE].
  21. [21]
    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].
  22. [22]
    J.-Y. Chen, D.T. Son, M.A. Stephanov, H.-U. Yee and Y. Yin, Lorentz Invariance in Chiral Kinetic Theory, Phys. Rev. Lett. 113 (2014) 182302 [arXiv:1404.5963] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    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].ADSCrossRefGoogle Scholar
  24. [24]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
  26. [26]
    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].ADSCrossRefGoogle Scholar
  27. [27]
    J.A. Harvey, TASI 2003 lectures on anomalies, hep-th/0509097 [INSPIRE].
  28. [28]
    W.A. Bardeen and B. Zumino, Consistent and Covariant Anomalies in Gauge and Gravitational Theories, Nucl. Phys. B 244 (1984) 421 [INSPIRE].
  29. [29]
    L. Lanadau and E. Lifshitz, Physical Kinetics: Volume 10 (Course of Theoretical Physics S), Pergamon (1981).Google Scholar
  30. [30]
    N. Abbasi, F. Taghinavaz and K. Naderi, Hydrodynamic Excitations from Chiral Kinetic Theory and the Hydrodynamic Frames, JHEP 03 (2018) 191 [arXiv:1712.06175] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    V.I. Zakharov, Chiral Magnetic Effect in Hydrodynamic Approximation, Lect. Notes Phys. 871 (2013) 295 [arXiv:1210.2186] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    K. Landsteiner, Notes on Anomaly Induced Transport, Acta Phys. Polon. B 47 (2016) 2617 [arXiv:1610.04413] [INSPIRE].
  33. [33]
    J. Hernandez and P. Kovtun, Relativistic magnetohydrodynamics, JHEP 05 (2017) 001 [arXiv:1703.08757] [INSPIRE].
  34. [34]
    E. D’Hoker and P. Kraus, Charged Magnetic Brane Solutions in AdS 5 and the fate of the third law of thermodynamics, JHEP 03 (2010) 095 [arXiv:0911.4518] [INSPIRE].
  35. [35]
    K. Fukushima, D.E. Kharzeev and H.J. Warringa, The Chiral Magnetic Effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].
  36. [36]
    X.-G. Huang, A. Sedrakian and D.H. Rischke, Kubo formulae for relativistic fluids in strong magnetic fields, Annals Phys. 326 (2011) 3075 [arXiv:1108.0602] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  37. [37]
    A. Abrikosov, Introduction to the Theory of Normal Metals, Academic Press, New York U.S.A. (1972).Google Scholar
  38. [38]
    P. Romatschke, Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions, Eur. Phys. J. C 76 (2016) 352 [arXiv:1512.02641] [INSPIRE].
  39. [39]
    Y. Hidaka, S. Pu and D.-L. Yang, Relativistic Chiral Kinetic Theory from Quantum Field Theories, Phys. Rev. D 95 (2017) 091901 [arXiv:1612.04630] [INSPIRE].
  40. [40]
    N. Abbasi, R. Ghazi F. Taghinavaz and O. Tavakol, Magneto-transport in an anomalous fluid with weakly broken symmetries, in weak and strong regime, arXiv:1812.11310 [INSPIRE].
  41. [41]
    N.W. Ashcroft and N.D. Mermin, Solid State Physics, Holt, Rinehart and Winston, New York U.S.A. (1976).Google Scholar
  42. [42]
    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].
  43. [43]
    J.-Y. Chen, D.T. Son and M.A. Stephanov, Collisions in Chiral Kinetic Theory, Phys. Rev. Lett. 115 (2015) 021601 [arXiv:1502.06966] [INSPIRE].
  44. [44]
    K. Kim, Role of axion electrodynamics in Weyl metal: Violation of Wiedemann-Franz law, Phys. Rev. B 90 (2014) 121108(R) [arXiv:1409.0082] [INSPIRE].
  45. [45]
    N. Abbasi, F. Taghinavaz and O. Tavakol, Exact dispersion relation of the classical Weyl particles in the magnetic field, to appear.Google Scholar
  46. [46]
    K. Landsteiner, Y. Liu and Y.-W. Sun, Negative magnetoresistivity in chiral fluids and holography, JHEP 03 (2015) 127 [arXiv:1410.6399] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    D. Roychowdhury, Magnetoconductivity in chiral Lifshitz hydrodynamics, JHEP 09 (2015) 145 [arXiv:1508.02002] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    Y.-W. Sun and Q. Yang, Negative magnetoresistivity in holography, JHEP 09 (2016) 122 [arXiv:1603.02624] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    M. Rogatko and K.I. Wysokinski, Magnetotransport of Weyl semimetals with2 topological charge and chiral anomaly, JHEP 01 (2019) 049 [arXiv:1810.07521] [INSPIRE].
  50. [50]
    M. Rogatko and K.I. Wysokinski, Hydrodynamics of topological Dirac semi-metals with chiral and2 anomalies, JHEP 09 (2018) 136 [arXiv:1804.02202] [INSPIRE].
  51. [51]
    M. Buzzegoli and F. Becattini, General thermodynamic equilibrium with axial chemical potential for the free Dirac field, JHEP 12 (2018) 002 [arXiv:1807.02071] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].
  53. [53]
    J. Bhattacharya, S. Bhattacharyya, S. Minwalla and A. Yarom, A Theory of first order dissipative superfluid dynamics, JHEP 05 (2014) 147 [arXiv:1105.3733] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    Y. Neiman and Y. Oz, Relativistic Hydrodynamics with General Anomalous Charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  55. [55]
    M. Buzzegoli, E. Grossi and F. Becattini, General equilibrium second-order hydrodynamic coefficients for free quantum fields, JHEP 10 (2017) 091 [Erratum JHEP 07 (2018) 119] [arXiv:1704.02808] [INSPIRE].
  56. [56]
    N. Sadooghi and S.M.A. Tabatabaee, The effect of magnetization and electric polarization on the anomalous transport coefficients of a chiral fluid, New J. Phys. 19 (2017) 053014 [arXiv:1612.02212] [INSPIRE].
  57. [57]
    R.A. Davison, W. Fu, A. Georges, Y. Gu, K. Jensen and S. Sachdev, Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography, Phys. Rev. B 95 (2017) 155131 [arXiv:1612.00849] [INSPIRE].
  58. [58]
    A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    W. Li, S. Lin and J. Mei, Conductivities of magnetic quark-gluon plasma at strong coupling, Phys. Rev. D 98 (2018) 114014 [arXiv:1809.02178] [INSPIRE].
  60. [60]
    A. Mokhtari, S.A. Hosseini Mansoori and K. Bitaghsir Fadafan, Diffusivities bounds in the presence of Weyl corrections, Phys. Lett. B 785 (2018) 591 [arXiv:1710.03738] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.School of Particles and AcceleratorsInstitute for Research in Fundamental Sciences (IPM)TehranIran
  2. 2.Department of PhysicsSharif University of TechnologyTehranIran

Personalised recommendations