| Weyl semimetals?WSMs?have been paid great attention in the field of condensed matter physics in recent years.The existence of the bulk Weyl fermions and surface Fermi arcs endow WSMs with extraordinary properties,such as ultrahigh mobility[1],positive longitudinal magnetoconductivity?LMC?[2-13],planar Hall effect[14],non-local quantum oscillations of the Fermi arc surface states[15],and quantum Hall effect in three dimension[16-19].Recently,by integrating the Landau quantization with Boltzmann equation,Deng et al.developed a unified analytical theory[22]for the anomalous positive LMC in a WSM,which is found to exhibit periodic-in-1/B quantum oscillations,superposed on the positive LMC,which were proposed to be a remarkable fingerprint of a WSM phase with chiral anomaly.In fact,such quantum oscillations have already been observed by several experimental works,e.g.,see Figs.3?a,b?in Ref.[4],Fig.2?d?in Ref.[9],Fig.3?d?in Ref.[12],and Fig.3 in Ref.[13].According to the theories[20-22],the inter-valley transport relaxation time ?inter and the intravalley transport relaxation time ?intra can be extracted from the measured zero-field conductivity and LMC in the dc regime indirectly by use of those theories.However,the calculation will involve the material parameters,Fermi energy EF,carrier density ne,Fermi velocity vF,etc.,which are of-ten not exactly known,or even unavailable.Therefore,it is highly desirable to find an experimental way to measure the two relaxation times directly,which is useful for the verification of the existing theories of the anomalous LMC,as well as for deepening our understanding of the effect of the chiral anomaly on the electron transport prop-erties in WSMs.So far,several theories related to the optical conductivity of WSMs have been proposed with the purpose of revealing the unusual transport properties of the materials,such as optical conductivity of multi-Weyl semimetals[23],nonlinear optical conductivity of Weyl semimetals in the terahertz regime[24],magneto-optical conductivity of Weyl semimtals with quadratic term in momentum[25],and universal optical conductivity of a disordered Weyl semimetal[26].In these papers,the charge pumping between the opposite chiralities driven by parallel electric and magnetic fields due to the chiral anomaly was not taken into account.In this paper,we generalize the theory of Deng et al.[22]of the anomalous LMC in a WSM to the ac regime.We propose that the intervalley and intravalley relaxation times governing the anomalous LMC can be directly obtained by measuring the ac con-ductivity as a function of the angular frequency.It is found that In the low-frequency regime,??inter<<1,the chiral chemical potential ?? can keep up with the oscillation of the ac field,and oscillates synchronically,so that the LMC induced by the chiral anomaly still happens,just as in the dc case,with its the real part??1?B,????dc and imaginary part ??2?B,???0.With increasing ? to the transitional region??inter???1,the real part of the LMC decreases from a finite value to vanishing,and the imaginary part of the LMC peaks at ?=/?inter.In the high-frequency regime,??inter>>1,there is no enough time for ?? to build up and relax each cycle,and so the complex LMC vanishes.We can apply almost the same discussion to the zero-field Drude conductivity ?D???.For low frequencies ??intra<<1,the real part of the zero-field conductivity is roughly a constant value,and the imaginary part vanishes,namely,?D1?????dc and ?D2????0.With the frequency increasing to a transitional region,??intra?1,the real part ?D1???shows a sharp decrease towards zero,while the imaginary part ?D2???exhibits a peak centered at the relaxation rate ?=1/?intra,which indicates that the current lags behind the electric field,because the electrons need roughly a time ?intra to accelerate in response to a change in the electric field.For higher frequencies,??intra>>1,the electrons can no longer catch up with the driving ac electric field,such that both the real and imaginary parts of the zero-field conductivity vanish,in the manner ?D1?????-2 and ?D2?????-1.Owing to the obvious transitional changes of the zero-field Drude conductivity ?D???and the LMC???B,??at different frequencies ??1/?intra and ??1/?inter,the total conductiv-ity Re[??B,??]displays two transitions,one transition occurring around ????1/?inter and the other transition occurring around ????1/?intra.As a result,by observing the two distinct transitions of the LMC and the zero-field conductivity,one can measure experimentally the intervalley and intravalley relaxation times directly. |
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