Theoretical Model on the Interplay of Disorder and Electron Correlations

Abstract

In the present review paper we discuss a general theoretical treatment to investigate the interplay between the effects of disorder and electron-electron interaction in the Anderson-localized regime. In constructing the model Hamiltonian, the behaviour of Anderson-localized states with envelope function is explicitly taken into account. It is shown that, in the approximation of neglecting the interstate interactions, the rival effects of disorder and electron correlation can be described by two fundamental quantities: the average intrastate interaction energy and the distribution width of one-electron energies. On the basis of this model the spin susceptibility and electronic specific heat as well as density of states are calculated. It is shown that the intrastate interaction gives rise to the occurrence of singly-occupied states below the Fermi energy and that this results in a Curie-type spin susceptibility at low temperatures. It is shown that the configuration interaction which is one of the effects of interstate interactions gives rise to a kinetic type exchange interaction between singly-occupied states which favours spin-singlet states and that the competition between direct and kinetic exchanges leads to the spin pair model in which each localized spin of singly occupied state forms a ferromagnetic or antiferromagnetic pair with its nearest neighbour. Specific heat anomaly, in particular its magnetic field dependence, and magnetic susceptibility at very low temperatures are calculated by taking into account the coexistence of ferromagnetic and antiferromagnetic interactions within a spin pair model. It is shown that the experimental results on Si:P can be well explained by the present treatment. Finally the effects of electron-electron interactions on the magnetoresistance of the variable range hopping conduction are investigated. It is shown that magnetoresistance is positive as far as the change of localization length due to a magnetic field is neglected Taking into account the latter effect which is responsible for negative magneto-resistance, the total magnetoresistance is calculated for the systems of 1T-TaS2 and their observed peculiar features of magnetoresistance can be explained well by the present theory.