A Research For A New Candidate For Unconventional Superconductors BaCoSO And A Series Of Topological Materials With ZrBeSi Structure

In recent years,unconventional superconductivity and topological states in mate-rials have been two most active research fields in condensed matter physics.Since the discovery of unconventional superconductivity,it has been one of the most important challenges to understand its micro pairing mechanism,which is helpful for the search and design of room temperature superconductors.In turn,if a new unconventional superconductor can be found or designed,it will help to understand the micro pairing mechanism of unconventional superconductors.The discovery of topological states in materials has greatly enlarged our knowledge about new phases and the theory of phase transition.Different from the conventional Landau phase transition theory,topo-logical phase transitions are not necessarily accompanied by the change of symmetry.It is of great significance for fundamental theoretical studies and potential applications to find new topological materials.This thesis mainly consists of two parts:in the first part,we predict BaCoSO to be a new candidate for unconventional superconductors,based on the knowledge of the unconventional superconductors discovered until now;in the second part,the topological phases in a series of ternary compounds which have ZrBeSi type structure,are systematically studied.For BaCoSO,we obtain it pairing symmetry in the strong and weak coupling limit respectively,based on the band structures given by the first principle calculations.It is found that,the bands are mainly contributed by the three t2g orbitals of the Co atoms near the Fermi level.In spite of the absence of the C4 rotational symmetry,the system still carries a d-wave like pairing symmetry state with gapless nodes and sign changed superconducting order parameters on the Fermi surfaces.The three t2g orbitals have very different superconducting form factors in momentum space:the intra-orbital pairing of the dxz and dyz orbitals both have d-wave like pairing form factors,while the intra-orbital pairing of the dx2-y2 orbital has a s-wave like pairing form factor.The above results are largely doping insensitive.However,The two methods predict very different pairing strength on different parts of Fermi surfaces.Therefore,BaCoSO and related materials can be a new ground to test and establish fundamental principles for unconventional superconductivity.In the part of topological materials,we study a spinless model which has time re-versal symmetry at first.We find that in the model a topological Weyl semimetal phase with four or eight Weyl points can be realized,and the semimetal phase for different symmetry classes can be viewed as an intermediate phase between the normal insulat-ing phase and the topological insulating phase,which is characterized by the so-called bent mirror Chern number.Then,a series of ternary compounds which have ZrBeSi type structure,including KZnP,BaAgAs,NaAuTe and KHgSb,are studied system-atically.It is found that,various topological insulating states and semimetal states can be realized in these materials.The states are highly tunable as the realization of these topological states depends on the competition between several energy scales,includ-ing the energy of atomic orbitals,the energy of crystal splitting,the energy difference between bonding and antibonding states,and the strength of spin-orbit coupling.The clear physical picture in this series of materials,is of great help for the experimental realization of different topological phases.