  We investigate the lattice structure of heterostructures comprising of
ferroelectric BaTiO$_3$ (BTO) thin films and BaBiO$_3$ (BBO), the insulating
parent-compound of the high Tc superconductor. Motivated by theoretical
predictions of exotic phenomena in BBO-based heterostructures including
interfacial conductivity, superconductivity and topologically-protected states,
we synthesize BTO/BBO heterostructures by molecular beam epitaxy and
characterize their structural properties by in-situ reflection high energy
electron diffraction and ex-situ high-resolution synchrotron X-ray diffraction,
Raman spectroscopy and piezoforce microscopy. For heterostructures with 4 uc
BBO layers, reciprocal space maps indicate strain relaxation relative to the
SrTiO$_3$ substrate. We observe a strong tetragonal distortion for
heterostructures with 2 unit cells BBO coherently strained to the BTO layers.
Raman spectroscopy measurements indicate a suppression of the breathing mode
distortion associated with the charge density wave in bulk BBO. The
ferroelectric properties of the system are confirmed by piezoforce microscopy
measurements. The coupling between the ferroelectric polarization and the
electronic states in BBO may potentially serve as a starting point for tunable
electrostatic doping to realize the novel predicted states in the
atomically-thin BBO layers.
