Universal infrared absorbance of two-dimensional honeycomb group-IV crystals

We show that the low-frequency absorbance of undoped graphene, silicene, and germanene has a universal value, only determined by the Sommerfeld fine-structure constant. This result is derived by means of ab initio calculations of the complex dielectric function for optical interband transitions applied to two-dimensional (2D) crystals with honeycomb geometry. The assumption of chiral massless Dirac fermions is not necessary. The low-frequency absorbance does not depend on the group-IV atom, neither on the sheet buckling nor on the orbital hybridization. We explain these findings via an analytical derivation of the relationship between absorbance and fine-structure constant for 2D Bloch electrons. The effect of deviations of the electronic bands from linearity is also discussed.