Phase Diagram Of2D Kondo Lattice Systems

Strongly correlated heavy fermion materials play a significant role in our understanding of the strongly correlated systems. As a basic model to describe the physical properties of heavy fermion compounds, the Kondo lattice model has caused much interest among condensed matter community. In this thesis, we use the mean-field approach to study and summarize the phase diagram of the Kondo lattice type theoretical models. The thesis is divided into five chapters. In chapter one, we introduce certain theoretical models in strongly correlated systems, especially the Kondo lattice model, which contains two main compet-itive interactions:the Kondo screening energy scale and the RKKY interaction. The energy scales of them are TK and TRKKY respectively, the Doniach phase diagram is introduced by comparison of these two energy scales. In chapter two, the bond-operator mean-field method is used to deal with the Kondo necklace model, we calculated the ground state and the finite temperature phase diagram for this model defined on the square and the honeycomb lattice. The phase di-agram is just consistent with the Doniach’s arguments, which means that the phase diagram contains the Kondo insulator phase and the antiferromagnetic phase (AFM) depending on the parameters in the Hamiltonian, and there is a quantum critical point to separate these two phases. In chapter three, we direct-ly study the Kondo lattice Hamiltonian. It is found that the Kondo insulator phase and the AFM phase can coexist with each other at the mean field level. This result suggests that there may be a coexistence zone of these two phas-es, instead of the quantum critical point. In chapter four, we concentrate our attention to the Kondo-Heisenberg model on the triangular lattice, where the intermoment interaction is included in the Hamiltonian due to the frustration. It is found that two Lifshitz transition points emerge in the heavy fermion liquid phase, quite different from the standard Kondo lattice model. In addition, we also find the heavy fermion liquid phase is unstable to superconductivity, and calculate some properties of the superconducting phase in order to compare with the experiments. In the last chapter, we summarize some related works on the global phase diagram of the heavy fermion materials and propose some problems which can be investigated in the near future.