Group-theoretical methods applied to surface problems

Abstract

This is a review of the application of the 17 two-dimensional space groups and their irreducible representations to the description of phase transitions in two-dimensional systems. The two-dimensional space groups and their irreducible representations are characterized. A recapitulation of Landau and Birman theories and their application to symmetry breaking of two-dimensional systems is given. Subsequently a method of constructing the LGW Hamiltonians is described, and the application of Landau theory to monolayer adsorption of atoms and to surface reconstruction is discussed. A comparison of the experimental results with the theories is also given.

Key Words:

• Group theory
• surfaces