Direction dependent giant optical conductivity in 2D \textit{semi}-Dirac materials

We show that the gap parameter in \textit{semi}-Dirac material induces a large degree of sensitivity for inter-band optical conductivity with respect to the polarization direction. The optical conductivity reveals an abruptly large value at a certain frequency for light along a particular polarization direction while it is significantly suppressed along the direction orthogonal to the former. The direction-dependent optical conductivity may, in turn, be used to uniquely predict the dispersive nature of the 2D \textit{semi}-Dirac materials, in addition to other possible applications in the field of transparent conductors.