Correlated electronic structure and optical response of rare-earth based semiconductors

The coexistence of Mott localized $f$ states with wide conduction and valence bands in $f$-electron semiconductors results, quite generically, in a complex optical response with the nature of the absorption edge difficult to resolve both experimentally and theoretically. Here, we combine a dynamical mean-field theory approach to localized $4f$ shells with an improved description of band gaps by a semilocal exchange-correlation potential to calculate the optical properties of the light rare-earth fluorosulfides $Ln\mathrm{SF}$ ($Ln=\mathrm{Pr}$, Nd, Sm, Gd) from first principles. In agreement with experiment, we find the absorption edge in SmSF to stem from $\mathrm{S}\text{−}3p$ to $\mathrm{Sm}\text{−}4f$ transitions, while the Gd compound behaves as an ordinary $p\text{−}d$ gap semiconductor. In the unexplored PrSF and NdSF systems we predict a rather unique occurrence of strongly hybridized $4f\text{−}5d$ states at the bottom of the conduction band. The nature of the absorption edge results in a characteristic anisotropy of the optical conductivity in each system, which may be used as a fingerprint of the relative energetic positions of different states.

Figure 1

Many-body spectral functions compared to experimental XPS spectra. While the $\mathrm{F}\text{−}2p$ (blue), the $\mathrm{S}\text{−}3p$ (green), and the rare-earth $5d$ (orange) spectral weight remain almost unchanged from PrSF to GdSF (a)–(d), the rare-earth $4f$ states show a significant evolution which defines the absorption-edge optical transitions. The position of the peaks in the total broadened spectral function of the occupied states (dotted black lines, broadening = 0.4 eV ) compares well to the experimental XPS spectra (solid black lines, taken from Ref. [14].)

Figure 2

$\mathbf{k}$-resolved spectral functions of the rare-earth fluorosulfides $Ln\mathrm{SF}$. (a) PrSF and (b) NdSF show an optical gap of 2.5 eV formed between the $\mathrm{S}\text{−}3p$ band (highest occupied bands) and a strongly hybridized rare-earth $5d\text{−}4f$ band. (c) In SmSF, the optical absorption edge can clearly be attributed to transitions from $\mathrm{S}\text{−}3p$ to $\mathrm{Sm}\text{−}4f$ (flat bands around 2.3 eV ). (d) In GdSF, the Gd-$4f$ states are not involved in the optical transitions and the optical gap is a pure $\mathrm{S}\text{−}3p$ to Gd-$5d$ band gap.

Figure 3

Anisotropic optical conductivities. (a) Comparison of the polarization-averaged optical conductivities. (b)–(e) The conductivities for two different orientations of the light polarization, [100] (in red) and [001] (in blue). The strong anisotropy allows us to distinguish between $p\text{−}f$ (in SmSF) and $p\text{−}d$ (in GdSF) absorption edges. In PrSF and NdSF one has a $p\text{−}d$ absorption edge, which is immediately followed by $p\text{−}f$ transitions above 3 eV.