  When an electron interacts with phonons, the electron can exhibit either free
electron-like or polaron-like properties. The latter tends to occur for very
strong coupling, and results in a phonon cloud accompanying the electron as it
moves, thus raising its mass considerably. We summarize this behaviour for the
Holstein model in one, two and three dimensions, and note that the crossover
occurs for fairly low coupling strengths compared to those attributed to real
materials exhibiting conventional superconductivity.
