Electronic structure studies on competing phases of Aurivillius Bi$_4$Ti$_3$O$_{12}$ using first-principles calculations

The low temperature ferroelectric to high temperature paraelectric phase transition in bismuth titanate (Bi$_4$Ti$_3$O$_{12}$) has been experimentally observed at Curie temperature (T$_C$) around 675 $^{\circ}$C. The first-principles calculations using density functional theory as implemented in the Vienna \textit{ab initio} simulation package (VASP) with generalized gradient approximation (GGA) for the exchange-correlation interaction are performed to investigate this monoclinic (\textit{b}1\textit{a}1) to tetragonal (\textit{I}4/\textit{mmm}) crystal structural transition. We further, provide discussion of the band structure and the Ti--O orbital hybridization, in addition to the frequency dependent dielectric and optical properties of Bi$_4$Ti$_3$O$_{12}$ due to the potential applications in the electronic devices.