Theoretical Study Of Diagonal Conductivity Of Weyl Semimetal

Since 1929 the Weyl equation was proposed,the Weyl fermion predicted by Weyl equation hasn't been discovered in high-energy physics until now.However,with the con-cepts of quasiparticle and elementary excitation,the“Weyl fermion”under the meaning of quasiparticle was discovered in condensed matter physics.Now,a bunch of materials con-tain such“Weyl fermion”are called Weyl semimetal.The“Weyl fermion”existed in Weyl semimetal not only exhibits the properties which are predicted in quantum field theory,such as chiral anomalous effect,but also possesses unique properties such as Fermi arc.Weyl semimetal has already become spotlight in condensed matter physics research just like others topological materials.Its unique properties have been drawing much research interest.On the one hand,people screen out lots of candidate materials by the first princi-ple calculation which can be Weyl semimetal.Also,by ARPES technology,some materials are confirmed to be Weyl semimetal.On the other hand,theoretical study of transport phenomena of Weyl semimetal becomes a meaningful research subject naturally.Such as diagonal conductivity,Hall conductivity and thermo-electrical properties,etc.In this work,the diagonal conductivity of Weyl semimetal was investigated by semi-classical transport theory and linear response theory.The effects to conductivity from car-rier doping and tilt of Weyl cone are also considered.Types of impurities'potential include scalar potential and pseudospin potential.Following aspects are contained in this work:?1?Conspicuous discrepancies in results which are given by two methods are found via numerical computation.By analysis of Kubo formula and numerical verification,it's testified that these discrepancies are originated from quantum effect.Especifically,this quantum effect is brought out by inter band scattering in electron's motion,or called,inter band interference.Via comparison between Kubo formula and Boltzmann equation,it's understood that the quantum effect can't be counted in Boltzmann equation by considering high order scattering process in scattering rate.?2?Because absence of back scattering on z-direction and tilt of Weyl cone induce that electrons process extra velocity and more electrons participate in transport,is severe growing with increasing of Fermi energy.However,on x-direction,absence of back scat-tering doesn't exist in this situation.Therefore,is going to be flat with increasing of Fermi energy,which is similar with Boltzmann equation's results.As for inter valley scat-tering,because of another valley's complement,is also going to be flat.?3?In pseudospin potential scattering situation,the impurities bring out back scatter-ing.Therefore,bothandcalculated by Kubo formula are going to be flat with increasing of Fermi energy,which are behaved as Boltzmann equation's results.?4?Except thesubject to intra valley scattering of scalar potential impurities,the others results calculated by two methods have similar behavior at large Fermi energy.But numerical discrepancies exist in two methods'results which are caused by inter band in-terference.Inter band interference will be pretty weak when strength of impurities become weak,which leads to the disappearance of numerical differences.