Goos–H?nchen and Imbert–Fedorov shifts in tilted Weyl semimetals

We establish the beam models of Goos–H?nchen(GH)and Imbert–Fedorov(IF)effects in tilted Weyl semimetals(WSMs),and systematically study the influences of Weyl cone tilting and chemical potential on the GH and IF shifts at a certain photon energy 1.96 eV.It is found that the GH and IF shifts in tilted type-Ⅰand type-ⅡWSMs are both almost symmetric about the Weyl cone tilting.Meanwhile,the GH and IF shifts in type-I WSMs almost do not change with the tilt degree of Weyl cones,while those in type-ⅡWSMs are extremely dependent on tilt degree.These trends are mainly due to the nearly symmetric distribution of WSMs conductivities,where the conductivities keep stable in type-I WSMs and gradually decrease with tilt degree in type-II WSMs.By adjusting the chemical potential,the boundary between type-I and type-II WSMs widens,and the dependence of the beam shifts on the tilt degree can be manipulated.Furthermore,by extending the relevant discussions to a wider frequency band,the peak fluctuation of GH shifts and the decrease of IF shifts occur gradually as the frequency increases,and the performance of beam shifts at photon energy 1.96 eV is equally suitable for other photon frequencies.The above findings provide a new reference for revisiting the beam shifts in tilted WSMs and determining the types of WSMs.