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Developing a phenomenological theory of phase transitions driven by quasi-particle interactions

We have developed a phenomenological theory of phase transitions which are driven by quasi-particle interactions and have attempted to unify the various mechanisms in melting, superconductivity and the Peierls instabilities.

An underlying idea is that the opening of a gap at the Fermi level stabilizes the structure, both, in superconductors at low temperatures and in Peierls distorted systems as the energy levels close to the Fermi energy are displaced downwards. We have been able to show that the transition temperature is related to some characteristic energy of the system (related to the elastic constants) and to the quasi-particle interaction energy.

We have made some progress in our investigations of the solid-liquid transition by relating the characteristic energy to the bulk modulus and the quasi-particle interaction energy to Gruneisen's constant. It is our intention to apply first-principles theory to calculate both, the characteristic energy pre-factors and the quasi-particle interaction energies and so determine the transition temperatures in the different phase transitions. We will re-examine the BCS superconductors in this context before focussing on the high TC superconductors.