  The electronic properties of graphene on top of ferroelectric HfO$_2$
substrates in orthorhombic phase with space group Pca2$_1$ are investigated
using density functional theory calculations. The space group Pca2$_1$ was
recently identified as one of the two potential candidates for ferroelectricity
in hafnia, with the polarization direction oriented along [001] direction. Our
results indicate the appearance of sizable energy gaps in graphene induced by
the HfO$_2$ substrate, as a consequence of orbital hybridization and locally
deformed graphene structure. The gap sizes depend on the type of the HfO$_2$
terminations interacting with graphene, showing larger gaps for oxygen
terminated slabs compared to hafnium terminated ones. These observations may
prove to be highly significant for the development of graphene based field
effect transistors using high-k dielectrics.
