Effect of electron-hole asymmetry on optical conductivity in 8-Pmmn borophene

TL;DR

This paper provides an exact theoretical analysis of the anisotropic optical conductivity and Drude weight in 8-Pmmn borophene with tilted Dirac cones, revealing nonmonotonic behavior influenced by tilt and universal conductivity properties.

Contribution

It offers analytical expressions for optical properties of 8-Pmmn borophene, highlighting the effects of tilt and anisotropy, and proposes optical measurements to determine tilt parameters.

Findings

Optical conductivity exhibits nonmonotonic behavior with photon energy.

Maximum optical conductivity components are independent of carrier density and tilt.

Product of maximum conductivities has a universal value $(e^2/4 ext{hbar})^2$.

Abstract

We present a detail theoretical study of the Drude weight and optical conductivity of 8-$Pmmn$ borophene having tilted anisotropic Dirac cones. We provide exact analytical expressions of $xx$ and $yy$ components of the Drude weight as well as maximum optical conductivity. We also obtain exact analytical expressions of the minimum energy ($\epsilon_1$) required to trigger the optical transitions and energy ($\epsilon_2$) needed to attain maximum optical conductivity. We find that the Drude weight and optical conductivity are highly anisotropic as a consequence of the anisotropic Dirac cone. The optical conductivities have a nonmonotonic behavior with photon energy in the regime between $\epsilon_1$ and $\epsilon_2$, as a result of the tilted parameter $v_t$. The tilted parameter can be extracted by knowing $\epsilon_1$ and $\epsilon_2$ from optical measurements. The maximum values of the components of the optical conductivity do not depend on the carrier density and the tilted parameter. The product of the maximum values of the anisotropic conductivities has the universal value $(e^2/4\hbar)^2$. The tilted anisotropic Dirac cones in 8-$Pmmn$ borophene can be realized by the optical conductivity measurement.