Abstract
The spin Hall effect of light attracted enormous attention in the literature due to the ongoing progress in developing of new optically active materials and metamaterials with non-trivial spin-orbit interaction. Recently, it was shown that rotating fermionic systems with relativistic massless spectrum may exhibit a 3-dimensional analogue of the spin Hall current — the chiral vortical effect (CVE). Here we show that CVE is a general feature of massless particles with an arbitrary spin. We derive the semi-classical equations of motion in rotating frame from the first principles and show how by coordinate transformation in the phase space it can be brought to the intuitive form proposed in [1]. Our finding clarifies the superficial discrepancies in different formulations of the chiral kinetic theory for rotating systems. We then generalize the chiral kinetic theory, originally introduced for fermions, to an arbitrary spin and study chirality current in a general rotating chiral medium. We stress that the higher-spin realizations of CVE can be in principle observed in various setups including table-top experiments on quantum optics.
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References
M.A. Stephanov and Y. Yin, Chiral Kinetic Theory, Phys. Rev. Lett. 109 (2012) 162001 [arXiv:1207.0747] [INSPIRE].
K.Y. Bliokh, Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium, J. Opt. 11 (2009) 094009 [arXiv:0903.1910] [INSPIRE].
K.Y. Bliokh, F.J. Rodr´ıguez-Fortuño, F. Nori and A.V. Zayats, Spin-orbit interactions of light, Nature Photon. 9 (2015) 796 [arXiv:1505.02864] [INSPIRE].
V.S. Liberman and B.Y. Zel’dovich, Spin-orbit interaction of a photon in an inhomogeneous medium, Phys. Rev. A 46 (1992) 5199 [INSPIRE].
K.Y. Bliokh and Y.P. Bliokh, Topological spin transport of photons: The Optical Magnus Effect and Berry Phase, Phys. Lett. A 333 (2004) 181 [physics/0402110] [INSPIRE].
M. Onoda, S. Murakami and N. Nagaosa, Hall Effect of Light, Phys. Rev. Lett. 93 (2004) 083901 [INSPIRE].
C. Duval, Z. Horvath and P.A. Horvathy, Fermat principle for spinning light, Phys. Rev. D 74 (2006) 021701 [cond-mat/0509636] [INSPIRE].
D.E. Kharzeev, J. Liao, S.A. Voloshin and G. Wang, Chiral magnetic and vortical effects in high-energy nuclear collisions — A status report, Prog. Part. Nucl. Phys. 88 (2016) 1 [arXiv:1511.04050] [INSPIRE].
X.-G. Huang, Electromagnetic fields and anomalous transports in heavy-ion collisions — A pedagogical review, Rept. Prog. Phys. 79 (2016) 076302 [arXiv:1509.04073] [INSPIRE].
K. Hattori and X.-G. Huang, Novel quantum phenomena induced by strong magnetic fields in heavy-ion collisions, Nucl. Sci. Tech. 28 (2017) 26 [arXiv:1609.00747] [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: π 0 → γγ in the σ model, Nuovo Cim. A 60 (1969) 47 [INSPIRE].
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].
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].
J.-W. Chen, S. Pu, Q. Wang and X.-N. Wang, Berry Curvature and Four-Dimensional Monopoles in the Relativistic Chiral Kinetic Equation, Phys. Rev. Lett. 110 (2013) 262301 [arXiv:1210.8312] [INSPIRE].
V. Dwivedi and M. Stone, Classical chiral kinetic theory and anomalies in even space-time dimensions, J. Phys. A 47 (2013) 025401 [arXiv:1308.4576] [INSPIRE].
M. Stone and V. Dwivedi, Classical version of the non-Abelian gauge anomaly, Phys. Rev. D 88 (2013) 045012 [arXiv:1305.1955] [INSPIRE].
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].
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].
N. Mueller and R. Venugopalan, Worldline construction of a covariant chiral kinetic theory, Phys. Rev. D 96 (2017) 016023 [arXiv:1702.01233] [INSPIRE].
A. Huang, S. Shi, Y. Jiang, J. Liao and P. Zhuang, Complete and Consistent Chiral Transport from Wigner Function Formalism, Phys. Rev. D 98 (2018) 036010 [arXiv:1801.03640] [INSPIRE].
A. Avkhadiev and A.V. Sadofyev, Chiral Vortical Effect for Bosons, Phys. Rev. D 96 (2017) 045015 [arXiv:1702.07340] [INSPIRE].
N. Yamamoto, Photonic chiral vortical effect, Phys. Rev. D 96 (2017) 051902 [arXiv:1702.08886] [INSPIRE].
M. Joyce and M.E. Shaposhnikov, Primordial magnetic fields, right-handed electrons and the Abelian anomaly, Phys. Rev. Lett. 79 (1997) 1193 [astro-ph/9703005] [INSPIRE].
A. Boyarsky, J. Fröhlich and O. Ruchayskiy, Self-consistent evolution of magnetic fields and chiral asymmetry in the early Universe, Phys. Rev. Lett. 108 (2012) 031301 [arXiv:1109.3350] [INSPIRE].
X.-G. Huang, Simulating Chiral Magnetic and Separation Effects with Spin-Orbit Coupled Atomic Gases, Sci. Rep. 6 (2016) 20601 [arXiv:1506.03590] [INSPIRE].
Q. Li et al., Observation of the chiral magnetic effect in ZrTe5, Nature Phys. 12 (2016) 550 [arXiv:1412.6543] [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].
A. Manjavacas and F.J. Garcia de Abajo, Vacuum Friction in Rotating Particles, Phys. Rev. Lett. 105 (2010) 113601 [arXiv:1009.4107].
R. Zhao, A. Manjavacas, F.J. Garcia de Abajo and J.B. Pendry, Rotational Quantum Friction, Phys. Rev. Lett. 109 (2012) 123604 [arXiv:1208.4232].
Z.V. Khaidukov, V.P. Kirilin, A.V. Sadofyev and V.I. Zakharov, On Magnetostatics of Chiral Media, Nucl. Phys. B 934 (2018) 521 [arXiv:1307.0138] [INSPIRE].
A. Avdoshkin, V.P. Kirilin, A.V. Sadofyev and V.I. Zakharov, On consistency of hydrodynamic approximation for chiral media, Phys. Lett. B 755 (2016) 1 [arXiv:1402.3587] [INSPIRE].
N. Yamamoto, Chiral transport of neutrinos in supernovae: Neutrino-induced fluid helicity and helical plasma instability, Phys. Rev. D 93 (2016) 065017 [arXiv:1511.00933] [INSPIRE].
Y. Hirono, D. Kharzeev and Y. Yin, Self-similar inverse cascade of magnetic helicity driven by the chiral anomaly, Phys. Rev. D 92 (2015) 125031 [arXiv:1509.07790] [INSPIRE].
Y. Hirono, D.E. Kharzeev and Y. Yin, Quantized chiral magnetic current from reconnections of magnetic flux, Phys. Rev. Lett. 117 (2016) 172301 [arXiv:1606.09611] [INSPIRE].
K. Tuchin, Spontaneous topological transitions of electromagnetic fields in spatially inhomogeneous CP-odd domains, Phys. Rev. C 94 (2016) 064909 [arXiv:1607.07481] [INSPIRE].
V.P. Kirilin and A.V. Sadofyev, Anomalous Transport and Generalized Axial Charge, Phys. Rev. D 96 (2017) 016019 [arXiv:1703.02483] [INSPIRE].
Y. Li and K. Tuchin, Electrodynamics of dual superconducting chiral medium, Phys. Lett. B 776 (2018) 270 [arXiv:1708.08536] [INSPIRE].
K. Hattori, Y. Hirono, H.-U. Yee and Y. Yin, MagnetoHydrodynamics with chiral anomaly: phases of collective excitations and instabilities, arXiv:1711.08450 [INSPIRE].
K. Tuchin, Impact of domain walls on the chiral magnetic effect in hot QCD matter, Phys. Rev. C 97 (2018) 064914 [arXiv:1802.09629] [INSPIRE].
M.A. Nowak, M. Rho and I. Zahed, Spin factors and geometric phases in arbitrary dimensions, Phys. Lett. B 254 (1991) 94 [INSPIRE].
N. Yamamoto, Spin Hall effect of gravitational waves, Phys. Rev. D 98 (2018) 061701 [arXiv:1708.03113] [INSPIRE].
H. Bacry, A Set of Wave Equations for Massless Fields Which Generalize Weyl and Maxwell Equations, Nuovo Cim. A 32 (1976) 448 [INSPIRE].
B.S. Skagerstam, Localization of massless spinning particles and the Berry phase, hep-th/9210054 [INSPIRE].
C. Duval and P.A. Horvathy, Chiral fermions as classical massless spinning particles, Phys. Rev. D 91 (2015) 045013 [arXiv:1406.0718] [INSPIRE].
Y. Jiang, X.-G. Huang and J. Liao, Chiral vortical wave and induced flavor charge transport in a rotating quark-gluon plasma, Phys. Rev. D 92 (2015) 071501 [arXiv:1504.03201] [INSPIRE].
Ö.F. Dayi, E. Kilinçarslan and E. Yunt, Semiclassical dynamics of Dirac and Weyl particles in rotating coordinates, Phys. Rev. D 95 (2017) 085005 [arXiv:1605.05451] [INSPIRE].
G. Sundaram and Q. Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Phys. Rev. B 59 (1999) 14915 [INSPIRE].
D. Xiao, M.-C. Chang and Q. Niu, Berry Phase Effects on Electronic Properties, Rev. Mod. Phys. 82 (2010) 1959 [arXiv:0907.2021] [INSPIRE].
D.E. Kharzeev, M.A. Stephanov and H.-U. Yee, Anatomy of chiral magnetic effect in and out of equilibrium, Phys. Rev. D 95 (2017) 051901 [arXiv:1612.01674] [INSPIRE].
A. Vilenkin, Quantum field theory at finite temperature in a rotating system, Phys. Rev. D 21 (1980) 2260 [INSPIRE].
D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
A.V. Sadofyev, V.I. Shevchenko and V.I. Zakharov, Notes on chiral hydrodynamics within effective theory approach, Phys. Rev. D 83 (2011) 105025 [arXiv:1012.1958] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational Anomaly and Transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].
V.A. Zyuzin, Landau levels for electromagnetic wave, Phys. Rev. A 96 (2017) 043830 [arXiv:1610.08048].
A. Cortijo, D. Kharzeev, K. Landsteiner and M.A.H. Vozmediano, Strain induced Chiral Magnetic Effect in Weyl semimetals, Phys. Rev. B 94 (2016) 241405 [arXiv:1607.03491] [INSPIRE].
T. Hayata, Chiral magnetic effect of light, Phys. Rev. B 97 (2018) 205102 [arXiv:1705.09926] [INSPIRE].
F.W. Hehl and W.-T. Ni, Inertial effects of a Dirac particle, Phys. Rev. D 42 (1990) 2045 [INSPIRE].
H.-L. Chen, K. Fukushima, X.-G. Huang and K. Mameda, Analogy between rotation and density for Dirac fermions in a magnetic field, Phys. Rev. D 93 (2016) 104052 [arXiv:1512.08974] [INSPIRE].
Y.-C. Liu, L.-L. Gao, K. Mameda and X.-G. Huang, Chiral kinetic theory in curved spacetime, arXiv:1812.10127 [INSPIRE].
M.V. Berry, Quantal phase factors accompanying adiabatic changes, Proc. Roy. Soc. Lond. A 392 (1984) 45.
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Huang, XG., Sadofyev, A.V. Chiral vortical effect for an arbitrary spin. J. High Energ. Phys. 2019, 84 (2019). https://doi.org/10.1007/JHEP03(2019)084
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DOI: https://doi.org/10.1007/JHEP03(2019)084