Theoretical Study On Topological Quantum State And Iron - Based High Temperature Superconductivity In Condensed Matter Physics

The past decade of progress in the frontiers of condensed matter physics has seen a period of unprecedented experimental discovery of exotic materials as well as appli-cations oriented developments. Most notably are the related studies on new topolog-ical states of matter, for instances, the discovery of graphene in2004, the discovery of quantum spin Hall effects in2006, and the subsequent discovery of three dimen-sional topological insulators. The combination of the topological effects with strong electron correlations may lead to a new discovery of fractional topological Chern in-sulator. On the other hand, the discovery of iron based superconductors in2008gave tremendous impact on the superconductivity research. Important developments in both experiments and theory have deepened our understanding of the mechanism of mag-netism and superconductivity in high temperature superconductors. In this thesis we will give a comprehensive study both on the topological quantum states and iron-based superconductivity.In the first part, we will focus on the topological quantum states in condensed matter physics. A brief introduction to this field will be presented in the first chapter.In the second chapter, the electronic properties of graphene and the quantum spin Hall effect as well as its transport properties will be addressed. We show that some new extra edge states can be created and controlled by an edge field. The Rashba-type spin-orbit coupling plays a vital role in depressing the band energy gap and destroying the topological insulating phase. The topological phase of the quantum spin Hall effects in bilayer graphene can be destroyed completely by introducing the interlayer Rashba-type spin-orbit coupling.In the third chapter, we will firstly discuss the topological quantum states both in two dimensional HgTe/CdTe heterostructure and three dimensional Bi2Se3family com-pounds. Then we will demonstrate that there is a topological quantum phase transition occurring from a trivial topological insulating phase to a non-trivial strong topological insulating one in Sb2Se3by tuning the pressure. Moreover, we will study the topologi-cal extended state, topological Anderson insulator, and its finite size effect. Our results show that the edge states on the two sides can be coupled, leading to enhancement of backscattering as the width of the nanoribbon decreases, thus destroying the perfect quantization phenomena in the topological Anderson insulator.Most of the developments in this field have focused on the effects of the topolog-ical properties, without taking the important electron correlations into account. The combination of the topological effects with strong electron correlations may lead to the emergence of fractional Hall states or a new discovery of fractional topological Chern insulator. We will address the fractional topological (spin) Chern insulator and its pos-sible realization in two dimensional organic metal materials in the fourth chapter.In the second part, we will study both the magnetic and superconducting properties of the iron-based superconductors. An introduction to high temperature superconduc-tivity will be given in the fifth chapter.In the sixth chapter, we will mainly study the magnetism of the parent compound in iron-based materials and its microscopic theory and show that the K1-xFe2-ySe2without iron vacancies should approach a checkerboard phase in which each of the four Fe sites group together in a tetragonal structure. The checkerboard phase is the ground state with a block antiferromagnetic order and a small charge density wave order in the absence of superconductivity. The physical mechanism in the parent compounds with different magnetic ordering is also presented and shown that the magnetic order in Fe layer of iron-based materials is closely related to the As-Fe-As bond angle.Next we move to study the superconductivity in iron-based superconductors, as shown in the seventh chapter. In particular, we will discuss the pairing symmetry in KFe2As2and show the pairing symmetry is s+s-wave in KFe2As2using a strong cou-pling approach and unify in relation with the pairing symmetry s±-wave in iron-based superconductor at the optimal doping. Our theoretical predictions can be tested by further experiments.In the concluding part, the eighth chapter, we will give a brief summary and out-look on the study of the topological quantum states and iron-based superconductivity.