Quantum Disordered Magnetism And Superconductivity In 3D Frustrated System In₃Cu₂VO₉

As a strongly correlated system with frustration,three-dimensional layered honeycomb compound In₃Cu₂VO₉ shows some new low-temperature quantum disordered magnetism,which is distinctly different from expected antiferromagnetism.Moreover,It behaves very similar electronic states and electronic structures to those in high-temperature cuprate superconductors,thus it may well demonstrate the superconducting properties upon doping.In this paper,we first study the ground-state and finite-temperature magnetic properties of an interlayer frustrated J1-J2-Jc Heisenberg model on three-dimensional honeycomb lattice by employing the Schwinger boson mean-field theory,focusing on the low-energy physics in In₃Cu₂VO₉.Then we present the zero-and finite-temperature superconducting properties and the superconducting symmetry of a modified t-J1-J2-Jc model on three-dimensional In₃Cu₂VO₉ by employing the mean-field approach and the Slave Boson mean-field theory.According to these results,we find that the magnetic ground state of the undoped system may be an exotic spin disordered phase,and on this basis the superconducting ground state in doped system supports a dx2-y2+idxy pairing symmetry.We can understand the mechanism of high-Tc superconductivity better through further exploring the competition and coexistence of the quantum magnetic and superconducting phase.The content of each chapter is addressed as follows:In first chapter,we first briefly introduce the origin of material magnetism and its history,the main magnetic structures and the Heisenberg exchange interaction model.Then we outline the experimental and theoretical development of the conventional superconductivities,the discovery of high-Tc superconductivities and their unique properties,existing problems and possible solutions.Afterwards,the high-profile spin liquid phase is described.And then,we summarize the experimental and theoretical research status of anomalous magnetic and superconducting properties in layered material In₃Cu₂VO₉,and put forward the unsolved questions,adopted theoretical methods and significance of the present study.In second chapter,we mainly study the anomalous magnetism of the three-dimensional strongly correlated and frustrated In₃Cu₂VO₉.We first describe the Hamiltonian of the interlayer fustrated J1-J2-Jc Heisenberg model on this honeycomb lattice by employing the Schwinger boson mean-field theory,and then obtain the self-consistent equations for the ordered parameters.Solving these self-consistent equations,we could obtain the energy dispersion relations,the phase diagram with J2 and Jc dependences of interlayer order parameter Q3 and the spin-spin correlation functions between the four sublattice sites in the ground state,as well as the temperature dependence of the order parameters,the specific heat and the static magnetic susceptibility.We find that with the increase of interlayer coupling Jc from 0 to 3.6 meV,the interlayer frustrated system transits from an antiferromagnetic?AFM?phase to a state with interlayer disorder and intralayer AFM order.This particular spin disordered phase explains not only the intralayer phase transition at TN=38 K,but also the qualitative behaviors of the intermediate-temperature specific heat and magnetic susceptibility in In₃Cu₂VO₉.In third chapter,we focus on the superconducting properties of doped In₃Cu₂VO₉.We first present an effective Hamiltonian of the generalized t-J1-J2-Je model,employ the conventional mean-field and strongly correlated Slave Boson theory,respectively,to acquire the zero-and finite-temperature superconducting properties.We find that the highest superconducting transition temperature Tc = 4 K occurs at the optimum doping hole concentration x = 0.03.The superconducting phase disappears at doping concentration of x=0.06.The superconducting ground state in doped In₃Cu₂VO₉ supports a dx2-y2+ idxy pairing symmetry when the interlayer coupling Jc varies from 1.2 to 5.2 meV.Our theoretical results suggest that doped In₃Cu₂VO₉ is a possible superconducting honeycomb system.In the final chapter,we summarize our results and point out the possible research direction in further study.