Electronic structure and excitonic absorption in $\text{BaCu}Ch\text{F}$ ($Ch=\text{S}$, Se, and Te)

Double excitonic absorption peaks are observed in textured BaCuSF and BaCuSeF thin films. The excitonic doublet separation increases with increasing fraction of heavy chalcogen in the thin-film solid solutions, in good agreement with the spin-orbit splitting of the valence bands calculated by density-functional theory. In BaCuSF and BaCuSeF, the excitons have large binding energies (95 and 65 meV, respectively) and can be observed at room temperature. A three-dimensional Wannier-Mott excitonic absorption model gives good agreement between the experimental and theoretical optical properties. Band gaps of BaCuSF and BaCuSeF calculated using the GW approximation agree with experiment. In BaCuTeF, transitions across the lowest direct energy gap and excitonic absorption are suppressed, extending its transparent range.

Figure 1

(Color online) (a) Relativistic band structure of $\text{BaCu}Ch\text{F}$ calculated by GGA DFT. The spin-orbit split valence bands are labeled ${\text{VB}}_A$ and ${\text{VB}}_B$, while the conduction bands are labeled ${\text{CB}}_{\text{I}}$, ${\text{CB}}_{\text{II}}$, ${\text{CB}}_{\text{III}}$, and ${\text{CB}}_{\text{IV}}$. (b) Schematic electronic structure of $\text{BaCu}Ch\text{F}$ compounds. The band gaps in (b) are calculated using the GW approximation.

Figure 2

(Color online) (a) Room-temperature experimental absorption spectra of $\text{BaCu}Ch\text{F}$. (b) Experimental absorption edge of $\text{BaCu}\left({Ch}_{1-x}{Ch}_x^{\prime }\right)\text{F}$ thin films (diamonds) and powders (squares). The lines are guides to the eye. (c) Theoretical absorption spectra of BaCuSF, BaCuSeF and BaCuTeF. The arrows in (a) and (c) indicate the electronic band gap as estimated by GW and GGA DFT calculations, respectively.

Figure 3

(Color online) Experimental absorption spectra of (a) BaCuSF, (b) BaCuSeF and (c) BaCuTeF at 80–250 K. The dotted lines are fits based on the analysis described in the text. The spectra are offset on the vertical axis for clarity. Insets: schematic interpretation of the absorption spectra.

Figure 4

(Color online) Experimental absorption spectra of (a) $\text{BaCu}\left({\text{Se}}_{1-x}{\text{Te}}_x\right)\text{F}$ and (b) $\text{BaCu}\left({\text{S}}_{1-x}{\text{Se}}_x\right)\text{F}$ at 80 K. The dotted lines are fits to the data as discussed in the text. The spectra are offset on the vertical axis for clarity.

Figure 5

(Color online) (a and b) Band gaps and (c and d) FWHM of the excitonic peaks in BaCuSF and BaCuSeF absorption spectra for spin-orbit split valence bands $A$ and $B$. The dotted lines are fits to the data as discussed in the text.

Figure 6

(Color online) Exciton binding energy as a function of band gap for materials with different crystal structures. Dashed lines are guides for the eye.

Figure 7

(Color online) (a) Band gaps and (b) spin-orbit splittings in $\text{BaCu}\left({\text{Se}}_{1-x}{\text{Te}}_x\right)\text{F}$ and $\text{BaCu}\left({\text{S}}_{1-x}{\text{Se}}_x\right)\text{F}$. Insets show schematic electronic bands and excitonic levels.