Transport Properties Of Topological Materials Tuned By Magnetic Field And Magnetism

Topological physics is one of the greatest advancements made in the study of condensed matter physics since this century.The introduction of topology concepts has taken the classification and understanding of matter to a new level.The first topological material derived from the concept of topology is the topological insulator,which is also the most representative one among topological materials.The bulk energy band structure of topological insulators is topologically different from that of the outside;therefore,the topological transition happens at the interface,giving the topological insulator stable interface states.The topologically protected interface states are the most known feature of the topological materials.After the discovery of topological insulators,many other topological materials have been proposed and experimentally realized,including Dirac semimetals,Weyl semimetals,nodal-line semimetals,and so on.In recent years,researchers have started to investigate magnetic topological materials and higher-order topological materials,and design and manufacture topological systems in classical systems such as optical systems,acoustic systems,and electric circuits.Because their energy band structures are topologically different from those of traditional materials,topological materials often exhibit various novel physical properties.This makes them the ideal platform for investigating a new class of transport phenomena.This dissertation will study the transport properties of topological materials from the following aspects.Starting from the quantum theory,we have studied the magnetoresistance in various directions in several low-energy effective models,and the effect of different types of impurities has been considered.By the analytical derivation and calculations of the magnetoresistance,we have obtained two important results:first,the longitudinal magnetoresistance in the quantum limit is inversely proportional to the magnetic field strength,independent of impurity scattering,in materials with a single Dirac cone dispersion;second,linear magnetoresistance in the quantum limit is not exclusive to systems with linear energy dispersion,but can also occur in systems with quadratic energy dispersion.In addition,calculations show that the long-range Gaussian-type impurity can induce both linear longitudinal and transverse magnetoresistance,but the screened-Coulomb-type impurity can only induce linear transverse magnetoresistance.The above results reveal the scattering mechanisms and the corresponding physical meaning in the quasi-one-dimensional systems with Landau bands,and explain the linear longitudinal magnetoresistance observed in experiments.The investigation of magnetoresistance in this dissertation brings new insights into the transport properties of topological semimetals and advances research progress in the field of linear magnetoresistance.We have developed the theory of the charge density wave under the magnetic field.Calculations show that the electron-phonon interactions in ZrTe₅ are responsible for the form of the charge density wave,and the three-dimensional quantum Hall effect of ZrTe₅is supported by a fixed-Fermi-wavevector commensurate charge density wave.The three-dimensional quantum Hall effect supported by the charge density wave is special in that the magnetic field strength simultaneously governs the order parameter phase transition of the system along the magnetic field direction and the topological phase transition perpendicular to the magnetic field direction.Theoretical analysis and calculations in this dissertation can explain the three-dimensional quantum Hall effect observed in ZrTe₅ and help to further promote the dissipationless transport into practical applications.We have proposed using the nonlocal measurement to distinguish the axion insulators and normal insulators,and comparatively investigated the nonlocal resistance in the ideal axion insulator and the antiferromagnetic Mn Bi₂Te₄.Numerical calculations show that there exists non-quantized nonlocal transport in Mn Bi₂Te₄,which is robust against Fermi energy change,impurities,and electrode thickness.Additionally,this dissertation discovers that Mn Bi₂Te₄ devices of even-number-layer and odd-number-layer can be distinguished based on the nonlocal resistance measured in different ways.The above results provide a practical approach to measuring the nonlocal transport of Mn Bi₂Te₄ in experiments and search for axion insulators.