Trends in Bandgap of Epitaxial $\textit{A}$$_2$$\textit{B}$$_2$O$_7$ ($\textit{A}$ = Sn, Pb; $\textit{B}$ = Nb, Ta) Films Fabricated by Pulsed Laser Deposition

Pyrochlore oxides $A_2B_2$O$_7$ have been a fruitful playground for condensed matter physics because of the unique geometry in the crystal structure. Especially focusing on the $A$-site tetrahedral sub-lattice, in particular, pyrochlore oxides $A_2B_2$O$_7$ ($A$ = Sn, Pb and $B$ = Nb, Ta), recent theoretical studies predict the emergence of the "quasi-flat band" structure as a result of the strong hybridization between filled $A$-n$s$ and O-2$p$ orbitals. In this work, we have established the growth conditions of Sn$_2$Nb$_2$O$_7$, Sn$_2$Ta$_2$O$_7$, Pb$_2$Nb$_2$O$_7$, and Pb$_2$Ta$_2$O$_7$ films by pulsed laser deposition on Y-stabilized ZrO$_2$ (111) substrates to elucidate their optical properties. Absorption-edge energies, both for direct and indirect bandgaps, increase in the order of Sn$_2$Nb$_2$O$_7$, Sn$_2$Ta$_2$O$_7$, Pb$_2$Nb$_2$O$_7$, and Pb$_2$Ta$_2$O$_7$. This tendency can be well explained by considering the energy level of the constituent elements. A comparison of the difference between direct and indirect bandgaps reveals that Pb$_2B_2$O$_7$ tends to have a less dispersive valence band than Sn$_2B_2$O$_7$. Our findings are consistent with the theoretical predictions and are suggestive of the common existence of the hybridized states in this class of compounds.