The Research Of Beam Shifts In Weyl Semimetals

Since the discovery of Dirac fermion excitations in graphene materials,the idea of using condensed low-energy excitations as equivalent particles has been open.Weyl fermions are consistent with massless solutions of the Dirac equation,which have aroused great interest.With the observation of Fermi arc surface states and negative magnetoresistance effects in the nonmagnetic material Ta As,this particle that has existed only in theory,was brought to light for the first time in the form of quasiparticle excitations.Due to topological conservation,the energy gapless topological phase of Weyl fermions is very stable.And the energy gap keeps open only when two Weyl fermions close to each other and merge into a Dirac fermion.Meanwhile,Weyl semimetals are known as three-dimensional graphene due to their special electronic excitation patterns at the energy band crossings.In addition,Weyl semimetals possess many peculiar physical phenomena,such as linear magnetoresistance effect,anomalous Hall effect and special quantum oscillation responses.At present,researches related to Weyl semimetals have been widely reported,but little literature reported the study on optical aspects of Weyl semimetals.Interestingly,the chiral anomaly of Weyl fermion would provide a Chern-Simon topological term to Maxwell’s equations describing the electromagnetic wave transmission behavior,which means that there is an indirect correlation between the optical response of the Weyl semimetal and its intrinsic topological properties.Therefore,theoretically,the information on the intrinsic topology of the Weyl semimetal can be obtained by measuring the its optical response.Based on the above assumption,we have developed an optical response model for the interface of Weyl semimetals,and detailedly studied the Photonic Spin Hall effect,Goos-H(?)nchen effect and Imbert-Fedorov effect of this model with reference to the conventional optical study of graphene.Furthermore,the optical phenomena based on the above mentioned are effectively amplified by introducing the quantum weak measurement amplification technique,which provides a referentially theoretical model for obtaining the intrinsic topological properties of Weyl semimetallic materials through practical optical measurements.The related research work is as follows:1.Based on the previous work,the corresponding optical characteristic parameters of Weyl semimetallic materials are derived theoretically through the relationship between the distance between the Weyl point in momentum space and the conductivity of material itself,and a mathematical model is established on this basis.By studying the Goos-H(?)nchen(GH)effect of the model under the excitation of different beam polarization states,incident angles,and refractive indices of the substrate materials,it is found that in some special cases,the GH effect is very sensitive to the distance of the Weyl point in the momentum space of the Weyl semi-metal.Moreover,we obtained the corresponding optical characteristic parameters with practical significance.For example,when the incident beam is incident at an angle of 56°of horizontal polarization,the system can obtain the maximum GH spatial displacement value,and the GH angular shift is zero at the moment,indicating that the Weyl point distance is directly related to the GH spatial displacement.Furthermore,the GH spatial displacement value of system approaches zero when the GH angular shift is at maximum.2.We established an Imbert-Fedorov(IF)effect model based on the Weyl semi-metal,and found that when the beam is incident with left and right rotational circular polarization,there is almost no dependence between the IF displacement and the distance change of Weyl point.However,the IF displacement of horizontally polarized incidence or vertically polarized incidence is very sensitive to the change of the Weyl point,especially at the Weyl point distance b ranging of 0～0.1.Without considering the cross component of the reflection coefficient,the spatial displacement of the IF effect reaches a maximum of about 8000 nm at an incidence angle of 60degrees for both horizontally and vertically linearly polarized beams.In addition,we found that the conventional Artmann formula cannot provide an accurate description for the GH or IF effect of Weyl semi-metal through theoretical analysis.3.Based on the spin-orbit interaction of photons,we calculated the transverse and longitudinal spin shifts of the beam occurring at the interface of Weyl semi-metal.By tuning the Weyl point distance and related parameters,it is observed that the spin Hall effect of photons incident at Brewster angle is the most obvious when the two Weyl points are close together,and the transverse spatial displacement of the beam as well as the longitudinal angular shift is very sensitive to the change of the Weyl point distance.In addition,there are positive and negative maximum values for both transverse and longitudinal spin shifts,which both occurs in a small interval range.After that,there is almost no impact on the system spin shift with the continuous increase of Weyl point distance.4.We analyzed the study of quantum weak measurement based on GH effect as well as photon spin Hall effect.By introducing purely weak values,the photon spin space bits are effectively amplified with an amplification factor of 8×10~4,the displacement amplification of which is 300 times of the real weak values.This work makes it possible to upgrade the displacement of the beam directly from the previous nanometer scale to the micron scale,reaching the scope of practical optical measurement.