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

Abstract

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 $\mathrm{Re}{\sigma }_{\perp }^{\mathrm{IB}}(\omega )\propto {\sigma }_0\sqrt{\omega }$ and $\mathrm{Re}{\sigma }_{\parallel }^{\mathrm{IB}}(\omega )\propto {\sigma }_0/\sqrt{\omega }$. By contrast, the intraband LOCs in 2D tilted SDBs depend on $\mu$ in the power-law scaling as $\mathrm{Re}{\sigma }_{\perp }^{\mathrm{D}}(\omega )\propto {\sigma }_0\mu \sqrt{\mu }$ and $\mathrm{Re}{\sigma }_{\parallel }^{\mathrm{D}}(\omega )\propto {\sigma }_0\mu /\sqrt{\mu }$. 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 $0<t\le 2$, 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.

19 pages, 5 figures