Dynamic chiral magnetic effect and anisotropic natural optical activity of tilted Weyl semimetals

Urmimala Dey,S Nandy,A Taraphder

doi:10.1038/s41598-020-59385-6

Urmimala Dey, S Nandy + Show 1 more

Open Access

https://doi.org/10.1038/s41598-020-59385-6

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Abstract

We study the dynamic chiral magnetic conductivity (DCMC) and natural optical activity in an inversion-broken tilted Weyl semimetal (WSM). Starting from the Kubo formula, we derive the analytical expressions for the DCMC for two different directions of the incident electromagnetic wave. We show that the angle of rotation of the plane of polarization of the transmitted wave exhibits remarkable anisotropy and is larger along the tilt direction. This striking anisotropy of DCMC results in anisotropic optical activity and rotary power, which can be experimentally observed as a topological magneto-electric effect of inversion-broken tilted WSMs. Finally, using the low energy Hamiltonian, we show that the DCMC follows the universal frac{{bf{1}}}{{{boldsymbol{omega }}}^{{bf{2}}}} decay in the high frequency regime. In the low frequency regime, however, the DCMC shows sharp peaks at the tilt dependent effective chemical potentials of the left-handed and right-handed Weyl points. This can serve as a signature to distinguish between the type-I and type-II Weyl semimetals.

Highlights

From the relation between the real part of dynamic chiral magnetic conductivity (DCMC) and the optical activity, we show that DCMC can be experimentally detected by measuring the angle of rotation of the plane of polarization of the transmitted electromagnetic beam
It is found that an inversion broken tilted Weyl semimetal shows remarkable anisotropy in the optical activity and produces larger rotation in the direction of tilt of the energy spectrum, which could be regarded as a characteristic feature of an inversion-asymmetric tilted WSM
We have shown the frequency dependence of the dynamic chiral magnetic conductivity from a continuum model and calculated analytical expressions for the real part of DCMC

Summary

As r is

DFtp1iai =fgrfaue tmrr.eeCne1tute.tv rsaTvtlhuhaleeruoseeuonsgfeahrtshgtieyhnerd(aiaWts,ipboee)yrr.l s=Wpio otthn21ie.nsn(toasfr)atiTthsykelpez l=seas-t tI0tihWcaaennSHdMtahkmyew =ciiltr tπ4hiotni(tcc2iaa)=lnfvo0faro.l0tury0ekp9z(etr=-acI)n 0,adtnwwtdi1ot =(hnd pot),naf(or-bard)mettygyepeptneee-re-IsrIIaIkWt0We =SbS Maπ4Mnadunwssdiimnthδge =tet2ht =2ea,t s0fofa.o3mrut erand type-I Weyl points. The WPs start to tilt in the x-direction. When r is above rc = 0.01, the Weyl nodes tilt further and two pairs of type-II WPs are observed. The green dots indicate WPs. by tuning the ratio r, one can go from a type-I to a type-II model. Increased, the Weyl points start to tilt in the x-direction. As r increases beyond rc, the Weyl nodes tilt further and we get two pairs of type-II Weyl points. For a system preserving time-reversal symmetry, Ω(−k) = −Ω(k) and for a spatial inversion symmetric system, Ω(−k) = Ω(k). Berry curvature acquires a non-zero value only when the system breaks either time-reversal symmetry or spatial inversion symmetry or both. (4) and (6), the components of Berry curvature can be calculated as ( ) Ωx(k) =.

Dynamic Chiral Magnetic Conductivity in the Lattice Model

Anisotropy in Rotary Power

Continuum Model

Summary and Conclusion

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