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We report a characterization of surfaces of the dichalcogenide TaSe$_2$ usingscanning tunneling microscopy and spectroscopy (STM/S) at 150 mK. When the toplayer has the 2H structure and the layer immediately below the 1T structure, wefind a singular spatial dependence of the tunneling conductance below 1 K,changing from a zero bias peak on top of Se atoms to a gap in between Se atoms.The zero bias peak is additionally modulated by the commensurate $3a_0 \times3a_0$ charge density wave of 2H-TaSe$_2$. Multilayers of 2H-TaSe$_2$ show aspatially homogeneous superconducting gap with a critical temperature also of 1K. We discuss possible origins for the peculiar tunneling conductance in singlelayers.

Scanning tunneling spectroscopy of layers of superconducting 2H-TaSe$_\textbf{2}$: Evidence for a zero bias anomaly in single layers