Study of localization and correlation effects in disordered electronic systems

This thesis describes attempts to study the effects of localization and electronic correlation in disordered electronic systems so as to see their role in bringing about or affecting, independently or in combination, such features as the metal-insulator transition, response functions like the frequencydependent conductivity and the magnetic susceptibility, and diffusion of charge-and spin-density fluctuations, for example. We have also investigated the effects of localization in the vicinity of magnetic instabilities on the Stoner criterion, Stoner excitations and the spin-wave mode. A macroscopic renormalization group study of the Anderson localization transition is described in chapter 2. The critical behavior of the localization transition and effects of short-ranged interactions on the stability of the localization fixed point are discussed. We find the Hubbard interaction to be relevant whereas the triplet interaction (in the particle-particle channel) is found to be irrelevant. This indicates that the critical behavior of spinless fermions is identical to that of noninteracting fermions. Chapter 3 describes a study of the disordered-antiferromagnetic instability in a lattice system with a half-filled band using exact eigenstates of the noninteracting part of the Hamiltonian. The phase diagram for the 1 -d and 3 -d systems has been obtained. The interacting fixed point which describes the metal-insulator transition lies on the critical line which separates the paramagnetic and the disordered-antiferromagnetic phases. The electron-gas system which has been studied in chapter 4 undergoes a ferromagnetic instability, in contrast. A generalized N-orbital model for electrons is introduced and studied within the liN-expansion technique. This method is well suited for studying the combined effects of disorder and interaction because it systematizes the terms in perturbation theory. We obtain typical Fenni-liquid behavior, generalized to the ferromagnetic phase, in the N -+ 00 limit with two separate diffusion constants for spin-and charge-density fluctuations. The dc conductivity in the ferromagnetic phase and the spin-diffusion constant associated with Stoner excitations acquire a localization correction but the spin-wave stiffness constant does not. This suggests that the system can exist in an Anderson-insulating state and still exhibit long-range magnetic ordering. The effects of spin-dependent impurity scattering is studied in chapter 5 by introducing random spin-orbit coupling. There is indication of competing interactions in a lattice system with a half-filled band in the ultra-localized limit suggesting the possibility of having frustration. Spin flipping due to the spin-orbit term introduces damping in spin-density fluctuations, Stoner excitations and the spin-wave mode. Also, the spin-dependence of impurity scattering leads to different localization corrections to the diffusion constants for spin-and charge-density fluctuations.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2011

Author dc:creator

• Singh, Avinash

Contributors dc:contributor

• Fradkin, Eduardo H.

• localization
• correlation effects
• disordered electronic systems
• magnetic instabilities
• Stoner criterion
• Stoner excitations
• spin-wave mode

Statement dc:rights

• 1988 Avinash Singh

Language dc:language

en

Identifier

3476292

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23903