Chiral magnetic effect and natural optical activity in metals with or without Weyl points

Abstract

We consider the phenomenon of natural optical activity, and related chiral magnetic effect in metals with low carrier concentration. To reveal the correspondence between the two phenomena, we compute the optical conductivity of a noncentrosymmetric metal to linear order in the wave vector of the light wave, specializing to the low-frequency regime. We show that it is the orbital magnetic moment of quasiparticles that is responsible for the natural optical activity, and thus the chiral magnetic effect. While for purely static magnetic fields the chiral magnetic effect is known to have a topological origin and to be related to the presence of Berry curvature monopoles (Weyl points) in the band structure, we show that the existence of Berry monopoles is not required for the dynamic chiral magnetic effect to appear; the latter is thus not unique to Weyl metals. The magnitude of the dynamic chiral magnetic effect in a material is related to the trace of its gyrotropic tensor. We discuss the conditions under which this trace is non-zero; in noncentrosymmetric Weyl metals it is found to be proportional to the energy-space dipole moment of Berry curvature monopoles. The calculations are done within both the semiclassical kinetic equation, and Kubo linear response formalisms, with coincident results.

Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals

“…The semiclassical equations can be derived systematically to linear order in applied electric and magnetic fields, under certain assumptions that we review more fully in Section II below. In several cases, such as the anomalous Hall effect 7 and the gyrotropic or "transport limit" of the chiral magnetic effect 8,9 , the semiclassical approach (SCA) fully reproduces the results obtained from quantum-mechanical calculations based on the Kubo formula.…”

“…The quantum treatment may be feasible for two band systems as we employed to deduce quantum formula for CPGE and SHG, while it should become very complicated in cases of a general number of bands. In particular, it will be interesting to see how the Berry curvature and orbital magnetic moment arise in the quantum mechanical treatment, as is possible for linear responses for an arbitrary number of bands 8,9 , and what the corrections from the semiclassical formulas look like. These issues are left as future problems.…”

“…In particular, we focus on the current response J ∝ EB 2 and study how the Berry curvature and the orbital magnetic moment contribute to magnetoresistance in Weyl semimetals, since the interplay of these two quantities in transport properties of Weyl semimetals has not been fully investigated except for a few studies 8,9,23,24 . The obtained angle-dependence of magnetoresistance is compared with recent magneto-transport experiments for Dirac semimetals 10,11 .…”

Magnetic-field-induced nonlinear optical responses in inversion symmetric Dirac semimetals

“…It is interesting to note that the product b × E * is similar in form to the natural optical activity in dielectrics: ε ij ∼ k × E * that has been discussed in time reversal breaking Weyl semimetals 19,20 . As we discussed in the previous sections, we can obtain from (26) and (27) the result that one would get if the model of linearly dispersing Weyl fermions were used.…”

“…From other side, natural optical activity, a phenomenon similar to the magnetic optical activity but with the momentum of the light playing the role of the magnetic field, (ε ij ∼ ijl k l ) has been predicted to occur in Weyl semimetals 19,20 (but not in Dirac semimetals), appearing to be the same manifestation as the chiral magnetic effect 21 , when time dependent electromagnetic fields are considered. Since the natural optical activity is equivalent to the chiral magnetic effect in virtue of the Faraday's Law 19 , it is hard to justify a term of the form B · k in the dielectric tensor, at least in the linear regime.…”