Potential applications of a scanning tunnelling microscope with a superconducting tip

We discuss the potential applications of the scanning tunnelling microscope (STM) with the superconducting tip. A number of set-ups are considered. The theoretical models are used to calculate the dependence of the measurable quantities on the bias voltage and other relevant parameters. Anticipated results include the position-resolved measurement of primary and secondary components of the superconducting order parameter on the surface, single-spin relaxation time measurements and, possibly, an effective spin-polarized STM. (author)