Superconducting And Topological Properties Of Quasi-two-dimensional Layered Correlated Systems

Two-dimensional(2d)strongly correlated electron systems(SCESs)have attracted much attention because of their unique properties,such as copper oxides with high-temperature superconductivity on the quasi-two-dimensional square lattice and graphene with high electron mobility on the quasi-two-dimensional honeycomb lattice.2d SCESs have an antiferromagnetic spin order in the half-filled case,and carrier doping weakens and often destroys this spin order.As a result,physical properties of the 2d SCESs are drastically changed,and various interesting phases are generated by carrier doping.In this dissertation,by taking the electron correlation and the orbital degree of freedom as the main lines,we employ the mean-field and Green's function methods to investigate the properties of some typical and interesting 2d SCESs,including the spin disordered phase on the honeycomb lattice,the two-dome superconducting phase and the orbital Kondo effect on the square lattice.The content of this thesis is described as follows:In chapter one,we give a brief introduction of the properties of the 2d SCESs firstly,then introduce some basic concepts and knowledge which will be used in the latter sections,including several commonly used models in the 2d SCESs,spin liquid,iron-based superconductor,topological insulator,impurity,etc.At the end of chapter one,the meaning of this thesis is introduced.In chapter two,we introduce the mean field and Green's function methods which are mainly used in this thesis.In chapter three,we investigate the topological properties of the J1-J2 Heisenberg model on the honeycomb lattice.Even for the simplest Heisenberg model on honeycomb lattice,the specific form and boundary of spin disordered ground state are controversial.We find that there exist in fact two topologically different phases in the well-known spin disordered regime:for 0.21?J2/J1?0.32,the system is a zero-flux spin liquid which is topological trivial and gapless;for 0.32<J2/J1?0.43,it is a ?/2-flux chiral spin liquid,which is topological nontrivial and gapped.In summary,we provide a special perspective for further understanding of spin liquids.In chapter four,we theoretically study the superconductivity in iron-based superconductors based on a three-orbital model.Two dome superconducting(SC)phase is an exotic physical phenomenon found in iron-based superconductors.With appropriate values of the exchange interactions J1?? and J2??,we find a two-dome structure in the Tc-n phase diagram:one dome in the range of n?3.9 where the superconducting state is mainly sx2y2 component contributed by inter-orbital pairing,the other dome in the range of 3.9?n?4.46 where the SC state is mainly sx2y2+sx2y2 components contributed by intra-orbital pairing.In summary,we show that the competition between different orbitals is one of the key factors leading to the two/multi dome SC phase.In chapter five,we study the two-orbital single-impurity Anderson model on the honeycomb lattice.We try to explain the zero energy peak observed at each interstitial iron impurity in Fe(Te,Se).The zero energy peak is robust again the external magnetic field,which cannot be explained by the traditional impurity theory.We show that a zero-energy state emerges at the impurity in the unconventional sign-changed s+--wave superconductor.Physically,we argue that the zero-energy state is an orbital Kondo state induced by the orbital Kondo effect,which is an orbital analogue of the classical Kondo bound state.We also analyze the effect of the orbital splitting and the spin-orbit coupling on the orbital Kondo state.In summary,we provide a possible explanation for the related experiments and extend the impurity theory in superconductors.In chapter six,we make a summary of the whole thesis,showing the results we have achieved and the still shortcomings.At the end,we present an outlook of the future studies.