Optical activity of solids from first principles

Within the framework of independent particle approximation, the optical activity tensor of solids is formulated as from different contributions: the magnetic dipole, electric quadrupole, and band dispersion terms. The first two terms have similar counterparts in the theory of finite systems, whereas the last term is unique for crystals. The magnetic dipole and electric quadrupole transition moments are calculated with a sum-over-states formulation. We apply the formulation to calculate and analyze the optical rotation of elemental tellurium and the circular dichroism of the (6,4) carbon nanotube. Decomposed optical activity into different contributions is discussed. The calculated spectra agree well with experiments. As a showcase of achiral crystals, we calculate the optical activity of wurtzite GaN.

Figure 1

$\mathbf{k}$-resolved OR of Te (a) along $\mathrm{\Gamma }A$ and (b) in the two-dimensional (2D) hexagonal BZ calculated at $\hslash \omega$ of 0.3 eV. The arrows and dashed lines indicate the enlargement of the BZ around the $H$ point.

Figure 2

(a) Comparison of the calculations on uniform and adaptive $k$ meshes. (b) Convergence of OR on the adaptive $k$ mesh.

Figure 3

Comparison of the calculated OR dispersion with experiments for Te.

Figure 4

OR of Te for the light propagating (a) along (${\rho }_{\parallel }$) and (b) perpendicular to (${\rho }_{\perp }$) the optic axis.

Figure 5

(a) Comparison of the calculated CD spectra with experiment for (6,4) CNT. (b) The imaginary part of the dielectric function.

Figure 6

CD of (6,4) CNT for light propagating (a) perpendicular to (${\theta }_{\perp }$) and (b) along (${\theta }_{\parallel }$) the tube axis.

Figure 7

Optical activity of wurtzite GaN.