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We propose the design of low strained and energetically favourable mono andbilayer graphene overlayer on anatase TiO$_2$ (001) surface and examined theelectronic structure of the interface with the aid of first principlecalculations. In the absence of hybridization between surface TiO$_2$ andgraphene states, dipolar fluctuations govern the minor charge transfer acrossthe interface. As a result, both the substrate and the overlayer retain theirpristine electronic structure. The interface with the monolayer grapheneretains its gapless linear band dispersion irrespective of the inducedepitaxial strain. The potential gradient opens up a few meV bandgap in the caseof Bernal stacking and strengthens the interpenetration of the Dirac cones inthe case of hexagonal stacking of the bilayer graphene. The difference betweenthe macroscopic average potential of the TiO$_2$ and graphene layer(s) in theheterostructure lies in the range 3 to 3.13 eV, which is very close to theTiO$_2$ bandgap ($\sim$ 3.2 eV). Therefore, the proposed heterostructure willexhibit enhanced photo-induced charge transfer and the graphene component willserve as a visible light sensitizer.

Electronic Structure of Graphene/TiO$_2$ Interface: Design and Functional Perspectives