First Principles Study Of Electronic States And Topological Properties Of Correlated Materials

In contemporary condensed matter physics,the correlated electron system has attracted scientists in this field due to its unique quantum phenomena and many novel physics problems to be solved urgently.Recently,the research focuses on the space dimension with electronic correlation effect and non-trivial topological phase.Our research calculated the electronic structure of three kinds of materials by First-principles study,and combining the experimental data,try to analysis these electronic states and topological properties.The structure of this paper is as follows:In the first chapter,we introduce the background of this research,starting with the influence of the dimension on many-body system to the current research-s with topological materials.Then it briefly describes the calculation methods involved in this paper.The second chapter introduces the Density Functional Theory(DFT),pseu-dopotential method(PP),and Wannier function.It includes the adiabatic approx-imation,single electron approximation,and periodic potential approximation of the solid band theory,Hohenberg-Kohn theorem,Konh-Sham equation and some exchange correlation functionals like Local-Dens,ity Approximation(LDA),Generalized-Gradient Approximation(GGA).The pseudopotential method including Norm-Conserving Pseudopotential,Ultra Soft Pseudopotential,and Projector Augment-ed Wave Method.Finally Wannier function method is introduced.The third chapter is the study of the crystal structure,electron structure,magnetic order,density of states and fermi surface of quasi-one dimensional mag-netic material Tl2Fe6Te6.The calculated results compare to the experimental re-searchs shows that the crystal structure remain the symmetry after optimization,and the calculated crystal constants are similar to the experimental values.In the study of ground state magnetic configurations,several configurations,such as fer-romagnetic(FM),interlayer antiferromagnetic(AFM)and non-collinear,are con-sidered and self-consistent calculations are carried out.In the calculation of band structure,the band results of Tl2Fe6Te6 show a strong three-dimensional nature.The energy dispersion in all directions is very large,which is different from that of other quasi-one-dimensional materials with the same lattice structure.Finally,the Fermi surface and density of states of electrons are calculated by constructing tight-bound approximate Hamiltonian with Wannier function,and these results are discussed.In chapter four,the first-principles method is applied to a class of lanthanide phosphorous compounds LnPn(Ln-Ce,Pr,Sm,Gd,Yb;Pn=Sb,Bi)were stud-ied.In particular,we compare the electronic structure calculated by Perdew-Burke Ernzerhof(PBE),modified Becke-Johnson(mBJ),and Heyd-Scuseria-Ernzerhof hybrid(HSE06)functionals,and analyze the band inversion features correspond-ing Z2 indices.We find a good agreement between the mBJ/HSE06 results and quantum oscillation measurements,while PBE results usually yields substantially larger ? and ? band frequencies due to overestimation of band inversion.From Ce to Yb,it can be observed that the energy band inversion decreases gradual-ly due to the lanthanide contraction,and the topologically non-trivial to trivial transition takes place around SmSb for antimonides and DyBi for bismuthides,respectively.Finally,we find that,unlike lanthanide contraction,simple press'ure increases the band inversion gap of the system.In the last chapter,we have carried out a series of transport experiments on ?-Ga single crystals,and observed the maximum magnetoresistance of about 1.66×106%under the external magletic field of 2K and 9T.The experiments of dHvA(de Haas-van Alphen)and SdH(Shubinikov de Hass)quantum oscillations at low temperatures have yielded very high carrier mobility,very small cyclotron effective mass and non-trivial Berry phase.Combined with the band structure analysis,the above properties all show that ?Ga is a rare pure metal with topo-logical properties.Then by measuring the specific heat and resistance,we can see the superconducting phase of 0.9K.The above results show that ?-Ga is a unique pure metal material with non-trivial topology and superconductivity.In the end,we made a summary of the calculation results and talk about further expectation and prospect for the development of the future work.