The Study Of First-principles Calculations Of Topological Materials And Their Optical Effects

We introduce the development history of researches of topological materials in this paper,and summarize the topological properties and the calculation methods of topological invariants of typical topological materials.Then,we introduce develop-ment history of first-principles calculations methods and Wannier functions methods.Besides,we studied the topological properties of three kinds topological materials:We found the Ba3Cd2As4 family belong to topological crystalline insulators(TCIs),they host topological surface states and edge states induced by C2 rotation anomaly;We found a new kind of Dirac semimetal(DSM)BaHgSn,it hosts the hourglass-like sur-face states(HSSs);Combining with the measurements of optical spectra,we studied the temperature-dependent band structures and optical conductivity of ferromagnetic Weyl semimetal(WSM)Co3Sn2S2.These researches reveal the topological properties and optical effects of topological materials,and provide ideas for the prediction and researches of new topological materials.In the introduction chapter,we introduce the basic theories about quantum Hall effect(including the integer quantum Hall effect,quantized anomalous Hall effect and quantum spin Hall effect),topological insulators(TIs),TCIs and topological semimetals(TSMs),and summarize the definition and the detailed calculation methods of topolog-ical invariants.Then we introduce the way to identify the topological classification and the topological invariants by first-principles calculations and symmetry indicator theory,and the flowchart of the automatic search for topological materials.In the calculation methods chapter,we introduce the history of the development of first-principles calcu-lations,and detailly introduce the density functional theory.We also detailly introduce the widely used Wannier functions methods.We usually use the atomic orbital Wan-nier functions in the calculations of topological materials,which can help us calculate the topological properties such as surface states,Fermi surface,Wilson loop spectra,Quasiparticle interference(QPI)and so on.Based on first-principles calculations and symmetry-based indicator analysis,we found a class of TCIs protected by C2 rotation symmetry and time-reversal symmetry in a family of Zintl compounds,including Ba3Cd2As4,Ba3Zn2As4 and Ba3Cd2Sb4.There are nontrivial two-dimensional Dirac shaped surface states(surface Dirac cones)and one-dimensional helical hinge states,which are caused by C2 rotation anomaly.By calculations,we identify the precise position of the surface Dirac cones,and we prove the existence of them by the nested Wilson loop technique.We also calculate the hinge states and their distribution in real space.Finally,we studied the topological phase transitions of these materials.They can transform among TCIs,TIs and trivial insulators by tuning the external strain.We proposed that BaHgSn is a DSM which host HSSs as protected by nonsym-morphic glide symmetry.Compared to KHgSb,an isostructural TCI with the same HSSs,but BaHgSn has an additional band inversion induced by the stronger interlayer coupling at ? point.This band inversion leads to bulk Dirac nodes along the ?-A path.In addition,the mirror Chern number protected by the kz=0 mirror plane changes from 2 in KHgSb to 3 in BaHgSn.Therefore,when a compressive uniaxial strain is applied along the y axis to break the Dirac point,BaHgSn becomes a strong TI with strong topological invariant Z2=1,weak topological invariant(v1v2v3)=(000)which host the topological surface Dirac cone co-exists with HSSs on the(010)surface.The Wilson loop spectra have been calculated to verify these surface states.We also calcu-late the Fermi surfaces and QPI patterns,and these results will help the measurement and verification of these topological surface states in experiments.The discovery of ferromagnetic WSM Co3Sn2S2 has triggered great interest for fascinating properties in topological magnetic materials.Understanding how the mag-netization affects the band structure can give us a deeper comprehension of the topo-logical properties in ferromagnetic WSMs and provide a theoretical foundation for their future practical applications.We systematically study the temperature-dependent band structures and optical conductivity of ferromagnetic WSM Co3Sn2S2 by experiments and first-principles calculations.Comparing the results by experiments and calcula-tions,we find the many-body correlation effect due to Co 3d electrons leads to the renormalization of band structures.The renormalization factor of band is 1.33,and the renormalization factor of electronic kinetic energy is 0.43.These results indicate that the correlation effect is moderate,and the description within density functional theory is suitable.As the temperature drops down,the magnetic phase transforms from paramagnetic state to ferromagnetic state,and the magnetization drives the band shift through exchange splitting.The optical spectra can well show these results caused by band shifts,including the absorption peaks of inter-band transitions sensitive and insen-sitive to the magnetization,and absorption peak of transitions from the bands around the Weyl nodes.The results strongly support that Co3Sn2S2 is a ferromagnetic WSM,and its magnetization can be tuned by temperature changes.We detailly studied the topological properties of TCIs,DSMs and the optical effects of ferromagnetic WSM.At present,the researches about the topological properties are sophisticated,and the future researches will be extended to higher-order topological insulators,magnetic topological materials,topological superconductors and so on.On the other hand,the researches about transport properties,such as the anomalous Hall effect,the optical effects,the magnetic effects and so on,are also focused,so that these fields still need theoretical and experimental researches.