With the aid of Lang-Firsov transformation, a single particle Green's function describing the propagation of small Fröhlich polaron has been derived. One- and two-dimensional spectral functions are studied by expanding Green's function perturbatively. SIS tunnelling cuprates can also be described by some closely-related type of this Green's function. The theory allows us to determine the characteristic phonon frequencies, gap parameter, inverse-lifetime parameter and the electron-phonon coupling from the tunnelling data.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.