Ab initio intraband contributions to the optical properties of metals

We introduce a method, based on the linearization of the band dispersion, to include intraband contributions in ab initio calculations of the optical spectra of metals. We illustrate its application to cubic iron and hexagonal magnesium, by analyzing the contributions of interband and intraband transitions to the dielectric function and the optical conductivity. These calculations demonstrate a way to compute the conductivity anisotropy of noncubic metals without the need to resort to phenomenological parametrizations. In particular, we introduce a method to recover the correct asymptotic trend of the response functions in the $\omega \to 0$ limit and hence compare directly with the experimental static conductivity.

Figure 1

(Color online) The path followed by the complex frequency ${\omega }^{+}$, Eq. (10), to have Eq. (9) generate the correct Drude behavior of metallic solids.

Figure 2

(Color online) The spin-resolved DOS (left) and band structure of BCC iron computed along the standard high symmetry directions of the BZ, as depicted inside the BZ of a bcc crystal drawn in the inset. Majority electrons: solid lines; minority: dashed lines. The energy reference is taken at the Fermi level.

Figure 3

(Color online) Imaginary (top) and real (bottom) parts of the computed dielectric function (solid) of iron, resolved in its interband (dot-dashed line) and intraband (dashed line) contributions. Experimental data from Ref. 15 (crosses) and 19 (dots) are reproduced for comparison. Inset: the infrared region in a log-log scale, displaying the $\propto {\omega }^{-1}$ and $\propto {\omega }^{-3}$ power-law behaviors of ${\epsilon }_2$ in the far- and near-infrared regions.

Figure 4

(Color online) Comparison between optical conductivity measurements (Refs. 15, 19) and the present calculation (RPA with the inclusion of CLF and intraband transitions). Inset: a log-log blowup of the low-energy region with the experimental static conductivity values at three temperatures (Ref. 64). For conductivity we use traditional inverse-second units but regular SI units ${\left(\Omega \text{m}\right)}^{-1}$ are retrieved immediately by multiplication by $4\pi {\epsilon }_0=1.11\times {10}^{-10}\text{s}/\left(\Omega \text{m}\right)$.

Figure 5

(Color online) The DOS (left) and band structure of hcp magnesium computed along the path in the BZ, depicted in the inset. The energy reference is taken at the Fermi level.

Figure 6

(Color online) Imaginary (top) and real (bottom) parts of the computed dielectric function of magnesium in the basal plane (solid) and along the $c$ axis (dashed). Experimental data from Ref. 15 (dots) and 22 (crosses and squares) are reproduced for comparison. Inset: the infrared region in a log-log scale, displaying the $\propto {\omega }^{-1}$ and $\propto {\omega }^{-3}$ power-law behaviors of ${\epsilon }_2$ in the far- and near-infrared regions.

Figure 7

(Color online) Computed optical conductivity in the basal plane (solid) and along the $c$ axis (dashed), compared to measurements on polycrystalline magnesium samples (Ref. 15). Inset: a log-log blowup of the infrared region with the experimental static conductivity at two temperatures (Ref. 64). Units are like in Fig. 4.