Phenomenological theory of phase transitions with quantum-mechanical order parameters

Abstract

The phenomenological Landau theory of phase transitions (PT) is generalized for systems with degenerate atomic states. A new approach is based on the formalism of a matrix density constructed on the wave functions of a degenerate level. The space of the order parameter (OP) consists of density matrix components averaged over the Gibbs statistic assembly. A method to introduce a multicomponent OP is suggested for such systems. The multicomponent OP is determined as the mixing coefficients of the basis functions of the irreducible representation of a crystal group. The OP, introduced in such a way, characterises primarily an electronic spectrum rearrangement at the PT and the variation of the set of properties (atomic displacements, magnetic moment occurrences, polarization, etc.) accompanying the PT is expressed by the type of OPs. The suggested approach describes a wide range of PTs such as Jahn-Teller, magnetic (for magnetics with a finite magnetic spin) and orientation (those of order-disorder type in molecular crystals) transitions. Purely electronic PTs such as the snperconductor-normal metal and those with charge density waves can be ascribed to this approach as well. It is shown that all these phase transitions in systems with an OP of quantum-mechanical origin can be described by the unique scheme of the canonical Landau theory. The specificity of separate systems is revealed in constructing the order parameter from density matrix components.