Disorder, Quantum Phase Transition And Topological States In Correlated Electron Systems

Strong correlations play an important role in various fields of condensed matter. In recent years, magnetism, impurity induced quantum phase transition and quantum Hall effects remain the central themes in strongly correlated systems. Motivated by various exotic phenomena on experimental side, we start from the microscopic model, employ various many-body techniques to investigate the strong interacting systems and discuss the possible role of strong correlations. The complex of the microscopic model results in the rich interplay between both external condi-tions (e.g. applied electromagnetic field and charge current) and intrinsic correlation strength and disorder effects.In the first chapter, we briefly introduce the research background and history in high-Tc cuprate superconductors, iron-based superconductors and quantum Hall systems. The rest of dis-sertation mainly covers the following topics:(1) Motivated by recent experiments on Zn-doped122-type iron pnictides Ba(Fe1-x-yCoyZnx)2As2, we investigate the disorder effects of nonmagnetic Zn impurities in the strong scattering limit on various properties of the system in the s±-wave superconducting pairing state. The lattice Bogoliubov-de Gennes equation is solved self-consistently based on a minimal two-orbital mod-el with an extended range of impurity concentrations. We find that Zn impurity is best modeled as a defect, where charge is mainly localized, but scattering is extended over a few lattice sites. With increasing Zn concentration the density of states shows a gradual filling of the gap, revealing the impurity-induced pair breaking effect. Moreover, both the disorder configuration-averaged su-perconducting order parameter and the superfluid density are dramatically suppressed towards the dirty limit, indicating the violation of the Anderson theorem for conventional s-wave superconduc-tors and the breakdown of the Abrikosov-Gorkov theory for impurity-averaged Green’s functions. Furthermore, we find that the superconducting phase is fully suppressed close to the critical impu-rity concentration of roughly nimp≈10%, in agreement with the recent experiments.(2) In the chapter three, we study two species of fermions with short-range intra-species re- pulsion in the presence of opposite magnetic field, each at Landau level filling factor1/3. In the absence of inter-species interaction, the ground state is simply two copies of the1/3Laughlin state, with opposite chirality, representing the fractional topological insulator phase(FTI). We show this phase is stable against moderate inter-species interactions. However strong enough inter-species repulsion leads to phase separation, while strong enough inter-species attraction drives the system into a superfluid phase. We obtain the phase diagram through exact diagonalization calculations. The FTI-superfluid phase transition is shown to be in the (2+1)D XY universality class, using an appropriate Chem-Simons-Ginsburg-Landau effective field theory.(3) In the chapter four, we study an Anderson impurity embedded in a d-wave superconductor carrying a supercurrent. The low-energy impurity behavior is investigated by using the numerical renormalization group method developed for arbitrary electronic bath spectra. The results explic-itly show that the local impurity state is completely screened upon the non-zero current intensity. The impurity quantum criticality is in accordance with the well-known Kosterlitz-Thouless transi-tion.(4) In the chapter five, we study quasiparticle tunneling in the Moore-Read state, which is proposed as the ground state of fractional quantum Hall systems at filling factor v=5/2. We find that quasiparticles of charge e/4(non-Abelian) and e/2(Abelian) may co-exist and both contribute to edge transport. On a disk geometry, we calculate the matrix elements for e/2and e/4quasiholes to tunnel through the bulk of the Moore-Read state, in an attempt to understand their relative importance. We find the tunneling amplitude for charge e/2quasihole is exponentially smaller than that for charge e/4quasihole, and the ratio between them can be partially attributed to their charge difference. We also find that including long-range Coulomb interaction only has a weak effect on the ratio. We finally discuss briefly the relevance of these results to recent tunneling and interferometry experiments at filling factor v=5/2.(5) In the last chapter, we study the phase diagram of a square lattice Hubbard model with a perfect vacancy superstructure. The model can be also defined on a new bipartite lattice with each building blocks consisting of a minimal square. The non-interacting model is exactly solved and a mid-band gap opens at the Fermi energy in the weak inter-block hopping regime. Increasing the Coulomb interaction will develop the Neel antiferromagnetic order with varying block spin moments. The metal-insulator transition with UMI smaller than the one without vacancies occurs above the magnetic instability UM. The emergent intermediate magnetic metal phase develops substantially in the moderate inter-block hopping regime. Drastic increases in the ordered moment and the gap magnitude are observed on the verge of tight-binding band insulator with increasing U. The implications of these results for the recent discovered (A,T1)yFe2-xSe2compounds are discussed.