  In this study, we present the results of our first-principles calculations of
the band structure, density of states and the Born effective charge tensors for
the ferroelectric (ground state B1a1) and paraelectric (I4/mmm) phases of
bismuth titanate. The calculations are done using the generalized gradient
approximation (GGA) as well as the local density approximation (LDA) of the
density functional theory. In contrast to the literature, our calculations on
B1a1 structure using GGA and LDA yield smaller indirect band gaps as compared
to the direct band gaps, in agreement with the experimental data. The density
of states shows considerable hybridization among Ti 3d, Bi 6p and O 2p states
indicating covalent nature of the bonds leading to the ferroelectric
instability. The Born effective charge tensors of the constituent ions for the
ground state (B1a1) and paraelectric (I4/mmm) structures were calculated using
the Berry phase method. This is followed by the calculation of the spontaneous
polarization for the ferroelectric B1a1 phase using the Born effective charge
tensors of the individual ions. The calculated value for the spontaneous
polarization of ferroelectric bismuth titanate using different Born effective
charges was found to be in the range of 55+/-13 $\mu$C/cm2 in comparison to the
reported experimental value of (50+/-10 $\mu$C/cm2) for single crystals. The
origin of ferroelectricity is attributed to the relatively large displacements
of those oxygen ions in the TiO6 octahedra that lie along the a-axis of the
bismuth titanate crystal.
