Optical conductivities and signatures of topological insulators with hexagonal warping

In this work we study the effect of the hexagonal warping term on the optical conductivities of topological insulators (TIs). The possible optical signatures in the spectra are also discussed in detail. We begin with systematical analyses of the optical conductivities of the TIs by using Kubo's formula. Then, based on the features of the optical conductivities, we study the possible optical signatures due to the warping term. We explore the reflection spectra from a TI thin film growing on a metamaterial. We find that by properly tuning the refraction index of the metamaterial, all features of the warping effect on the conductivities can be detected and identified from the reflection spectra at an experimentally accessible level. Finally, we discuss the possibility of using the Goos-Hanchen effect and the Brewster angle measurement to determine the possible optical signatures of the warping term on the imperfectly quantized optical Hall conductivity.