Highly anisotropic optical conductivities in two-dimensional tilted semi-Dirac bands

Within linear response theory, the absorptive part of highly anisotropic optical conductivities are analytically calculated for distinct tilts in two-dimensional (2D) tilted semi-Dirac bands (SDBs). The transverse optical conductivities always vanish. The interband longitudinal optical conductivities (LOCs) in 2D tilted SDBs differ qualitatively in the power-law scaling of omega as Re sigma(IB)(perpendicular to)(omega)proportional to sigma(0)root omega and Re sigma(IB)(parallel to)(omega)proportional to(sigma)/root omega. By contrast, the intraband LOCs in 2D tilted SDBs depend on mu in the power-law scaling as Re sigma(D)(perpendicular to)(omega)proportional to sigma(0)mu/root mu and Re sigma(D)(parallel to)(omega)proportional to sigma 0 mu root mu. The tilt-dependent behaviors of LOCs could qualitatively characterize distinct impact of band tilting in 2D tilted SDBs. In particular, for arbitrary tilt t satisfying 0<t <= 2, the interband LOCs always possess a robust fixed point at omega=2 mu. The power-law scalings and tilt-dependent behaviors further dictate significant differences in the asymptotic background values and angular dependence of LOCs. Our theoretical predictions should be valid for a broad class of 2D tilted SDB materials, and can also be used to fingerprint 2D tilted SDB from 2D untilted SDB as well as tilted Dirac bands.