Optical Conductivity In The Two-dimensional Tilted Dirac Materials

In recent years,a large number of two-dimensional Dirac materials with strange band structures have been studied theoretically and experimentally,such as graphene,silicene,8-pmmn borophene,1T’-MoS2 and so on.Among them,1T’-MoS2 is one of the monolayer T’-phase transition metal dichalcogenides 1T’-MX2 with M=(W,Mo)and X=(Te,Se,S),which has a valley-spin polarized band gap that can be controlled by a vertical electrostatic field,and it is also a typical two-dimensional tilted Dirac material.This article takes 1T’-MoS2 as the research object,under the framework of linear response theory,starting from the linearized Hamiltonian,using the Kubo formula,the method of combining analytical derivation and numerical calculation is used to study in detail its optical conductivity properties.We hope to use this research to illustrate the universal properties of the optical conductivity of the two-dimensional tilted Dirac material.Through theoretical analysis,we prove that the off-diagonal optical conductivity of 1T’-MoS2 is strictly equal to zero,and the longitudinal optical conductivity can be divided into two parts:intraband and interband.In the absence of doping,the longitudinal optical conductivities are entirely contributed by the inter-band transition of electrons.And,the characteristic that the resonance peak of the longitudinal optical conductivity changes with the applied vertical electric field can be used to determine whether the material is in the topological insulator phase or the band insulator phase.According to the relative size of the chemical potential and the band gap,we define the doping state of the energy band.The vertical electric field can change the doping state of the band by adjusting the gap,thereby changing the number of optical conductivity resonance peaks.When the energy band is doped,in addition to the interband transition of electrons,the inraband transition of electrons also contribute to the optical conductivity,which are manifested as a Drude peak in the optical conductivity curve.When the incident photon energy is large enough,we strictly prove through analytical derivation that the longitudinal optical conductivity will attenuate to a certain asymptotic value Reσjjasyp,which are not affected by the band gap,doping,temperature and tilt factor,and satisfy the universal relationship Reσxxasyp·Reσyyasyp=σ02.