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Pyrochlore oxides $A_2B_2$O$_7$ have been a fruitful playground for condensedmatter 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), recenttheoretical studies predict the emergence of the "quasi-flat band" structure asa result of the strong hybridization between filled $A$-n$s$ and O-2$p$orbitals. In this work, we have established the growth conditions ofSn$_2$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 toelucidate their optical properties. Absorption-edge energies, both for directand 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 canbe well explained by considering the energy level of the constituent elements.A comparison of the difference between direct and indirect bandgaps revealsthat Pb$_2B_2$O$_7$ tends to have a less dispersive valence band thanSn$_2B_2$O$_7$. Our findings are consistent with the theoretical predictionsand are suggestive of the common existence of the hybridized states in thisclass of compounds.

apl materials

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