Theoretical Studies On Kondo Lattice Model With Spin-orbit Coupling

Exploring novel phases and the associated phase transition is a major subject of condensed matter physics.Quantum phase transition is phase transition at zero temper-ature under the thermodynamic limit.It plays a central role in the study of the electrical and magnetic properties of numerous important solid state materials.We are concerned with the theoretical description of the different types of quantum phases and phase tran-sitions that are possible within heavy fermion metals.Motivated by the growing interest in seeking novel quantum phases in materi-als with strong electron correlations and spin-orbit coupling,we study the interplay of the spin-orbit coupling,Kondo interaction,and magnetic frustration in a Kane-Mele-Kondo-Heisenberg model on a two-dimensional honeycomb lattice.By using a fermionic representation of the spin operators,we calculate the renormalized electronic struc-ture and correlation functions within a mean-field approximation.We find the global ground-state phase diagram of the model at half-filling contains a variety of phases due to the competing interactions.In addition to a Kondo insulator,there is a topological insulator with valence bond solid correlations in the spin sector,and two novel antifer-romagnetic phases.Interestingly,in the antiferromagnetic phases,the direction of the magnetic moments can be either within or perpendicular to the lattice plane,determined by the competition between the spin-orbit coupling and the Kondo interaction.We show that the latter antiferromagnetic state is topologically nontrivial for moderate and strong spin-orbit couplings.Recent years have seen extensive studies about the effect of a fine spin-orbit cou-pling?SOC?on the electronic bands.In topological insulators?TIs?,the bulk band gap opens due to a nonzero SOC,and there exist gapless surface states.The nontrivial topol-ogy of the band structure is protected by the time reversal symmetry?TRS?.In general,these TIs and TAFIs can be tuned to topologically trivial insulators via topological quan-tum phase transitions.But how the strong electron correlations influence the properties of these symmetry dictated topological phases and related phase transitions is still under active discussion.Here we investigate the global phase diagram of a spin orbit-coupled Kondo lattice model on the honeycomb lattice at half-filling.We show that the competing interactions in this model give rise to a very rich phase diagram containing a TI,a KI,and two AFM phases.We focus on discussing the influence of magnetic frustration on the phase diagram.In the TI,the local moments develop a VBS order.In the two AFM phases,the moments are ordered,respectively,in the plane of the honeycomb lattice(denoted as AFM_xy)and perpendicular to the plane?AFM_z?.Particularly in the AFM_zphase,the conduction electrons may have a topologically nontrivial band structure,although the TRS is explicitly broken.This T-AFM_zstate connects to the trivial AFM_zphase via a topological phase transition as the SOC is reduced.This thesis is consist of six chapters.We start by introducing the model and our theoretical procedure in Chapter I and Chapter II.In Chapter III we consider the Kondo lattice J1-J2 model with half filling.Next we obtain the global phase diagram of the full model in Chapter IV.In Chapter V we discuss the magnetic phase diagram of the Heisenberg model for the local moments.We examine the nature of the conduction-electron band structures in the AFM states,with a focus on their topological characters.We discuss the implications of our results in Chapter VI.