The non - dissipative transport effects have been widely discussed recent years. These effects are to be observed in the non - central heavy ion collisions [1]. They have also been considered for the  Dirac and Weyl semimetals [2] and in $^3$He-A [3].
Among the other effects their family includes  the chiral separation effect (CSE) [4], the chiral vortical effect (CVE) [5], the anomalous quantum Hall effect (AQHE) [2]. All those phenomena have the same origin - the chiral anomaly.

In the present paper we  propose the new non - dissipative transport effect - the chiral torsional effect (CTE). Namely, we will discuss the emergence of  axial  current of thermal quasiparticles in the presence of torsion. It will be shown that this effect is intimately related to the chiral vortical effect [5], i.e. the latter may be considered as the particular case of the CTE. It is well  - known that in conventional general relativity  torsion vanishes identically, it appears only in its various extensions. However, the background (non - dynamical) gravity with torsion emerges in certain condensed matter systems.  For example, elastic deformations in graphene and in Weyl semimetals induce the effective torsion experienced by  the quasiparticles [6]. In $^3$He-A torsion appears dynamically when motion of the superfluid component is non - homogeneous.

 

[1] W. T. Deng and X. G. Huang, \Vorticity in Heavy-Ion Collisions," Phys. Rev. C 93, no. 6,
064907 (2016) [arXiv:1603.06117 [nucl-th]].
[2] A. A. Zyuzin and A. A. Burkov, \Topological response in Weyl semimetals and the chiral
anomaly," Phys. Rev. B 86 (2012) 115133 [arXiv:1206.1868 [cond-mat.mes-hall]].
[3] G.E. Volovik, The Universe in a Helium Droplet, Clarendon Press, Oxford (2003).
[4] \Anomalous Axion Interactions and Topological Currents in Dense Matter",Max A. Metlitski
and Ariel R. Zhitnitsky,Phys. Rev. D 72 (2005), 045011
[5] A. Vilenkin, Phys. Rev. D 22, 3080 (1980)
[6] G.E.Volovik, M.A.Zubkov, Annals of Physics 340/1 (2014), pp. 352-368, arXiv:1305.4665 [cond-mat.mes-hall].

 

 

Z.V.Khaidukov, M.A.Zubkov
JETP Letters 108, issue 10(2018)