Local electronic properties in the superconducting and the normal phase in the disordered film of titanium nitride

We present in this paper the conductance maps at 100 mK in the disordered polycrystalline film of titanium nitride (TiN). At 5 nm, the film is close to quasi-two dimensional limit and exhibits features pertaining to the superconductor to insulator transition. We measured conductance maps at zero field and at 4 T, which represent the superconducting and the normal phase, respectively. The conductance map at 4 T is uniform, in which the conductance behavior, with logarithmic variation, resembles to the disorder enhanced electron-electron interaction in the two dimensional metallic phase. At low fields we observe the spatial variations of the conductance in the superconducting phase. At several places the superconducting energy gap fluctuates to an extent that the quasi-particle peaks are absent in the conductance curves. The conductance map over a region encompassing only few crystallites suggests that the inhomogeneities in the superconducting phase related to the spatial variations of the electronic density are across the crystalline boundaries.