The First Principle Study Of Topological Matters

In recent years,as a new quantum state,topological materials have become one of the current hot research fields.Since the discovery of the quantum Hall effect,topological theories and experiments have made great progress,and a large number of topological materials have been theoretically predicted and experimentally discovered.At the same time,the family members of the topological states are growing,such as topological insulators,Dirac/Weyl semimetals,nodal-line semimetal,triple-point semimetal,topological（crystal）Kondo insulator,topological superconductor,etc.These topological states protected by crystal symmetry are particularly robust to external perturbations,which provides an important guarantee for stable existence in the crystal and also for industrial applications in the future.Density functional theory and group theory play a very important role in the theoretical study of topological states,prompting people to discover a large number of topological materials and novel quantum states.In fact,people use density functional theory to calculate various types of topological states,and then use group theory to analyze the symmetry required for the existence of topological states.By destroying the symmetry and applying the external field,the realization of topological phase transition and topological state regulation has become a popular research method.The main contents and conclusions of this paper are listed below:In chapter one,we firstly review the development of several topological states,namely the family of quantum Hall effect,topological insulators,and topological semimetals.In chapter two,we introduce in detail the basic theories and calculation methods,including density functional theory and Wannier function.These theories and calculation methods provide the basis for the implementation of our work.Then we briefly introduce the theory of topological invariants.Topological invariants are an efficient way of characterizing these topological states,helping people to accurately identify the topological properties of materials.In chapter three,we study the Dirac semimetals（DSMs）in the magnetic space groups（MSGs）,and generalize the concept of DSMs to centrosymmetric type-IV MSGs,demonstrate the feasibility of the DSMs in this type of magnetic space group,and systematically study the symmetry requirements and distribution of Dirac points.According to the symmetry requirements provided by theoretical analysis and first-principle cal-culations,we propose that the interlayer AFM EuCd₂As₂is a candidate for such an AFM DSM.Many exotic topological states can be derived from the AFM DSMs.For example,when threefold rotation symmetry is broken,it can evolve into the AFM TI discussed by Moore et al,where the half-quantum Hall effect can be realized on the intrinsically gapped（001）face.If P is broken,it can result in a triple-point semimetal phase,rather than a Weyl semimetal.Our results extend the range of DSMs,and provide a platform to study the topological phase transition and the exotic properties of AFM topological states.In chapter four,we study the topological properties of three-dimensional material NaCdAs.By using first-principle calculations,we find that the Pnma NaCdAs is a topological nodal-line semimetal when the spin-orbit coupling（SOC）effect is not considered.This topological nodal-line semimetal has only a single nodal loop in the bulk,which exhibits a nearly flat band dispersion in momentum space.Moreover,a drumheadlike surface state appears on the（100）surface of this material.Its single nodal loop is protected by the glide mirror symmetryˉM₁₀₀,which can be stably present in the NaCdAs crystal.When the SOC effect is introduced,the system undergoes a topological phase transition from a topological nodal-line semimetal to a topological insulator.The SOC effect causes a huge change in the band struture of the system,and all the nodes on the nodal loop open a gap,and the system evolves in the topological insulator phase.Therefore,the Pnma NacdAs provides an alternative way to achieve the topological phase transition of the system by adjusting the SOC strength.In chapter five,we predict that a new topological Dirac semimetal can survive in the hexagonal ABC crystals,which has only one pair of Dirac points in bulk and exhibits nontrivial topological surface state,similar to Na3Bi.The hexagonal ABC compound NaCdAs has an inverted band structure with a band inversion around 0.5 eV in the presence of SOC.Its topological invariant Z₂=1,and this is zero-gap semimetal with a pair of Dirac points on their rotation axis.The finding of the Dirac semimetal phase in NaCdAs may intrigue further research on the topological properties of hexagonal ABC materials and promote future applicationsIn the last Chapter,we make a conclusion of this paper and give some future prospects for our work.