Magnetic Transport Studies In Topological Weyl Semimetals

Topological quantum materials have become a research hotspot in the field of condensed matter physics in the past ten years.Topological semimetal,as one of many topological quantum materials,has some variety of strange physical properties,and naturally they have also received extensive attention.There is a overlap between the conduction band and the valence band of the topological semimetal,forming a finite number of points or nodal coils.We generally classify topological semimetals into Dirac semimetal,Weyl semimetal,and Nodal-line semimetal according to their band structure and energy level degeneracy characteristics.The energy band structure of these topological semimetal materials is protected by time reversal symmetry and space reversal symmetry,and therefore it shows a strong stability.In Chapter 1,we systematically introduce some basic concepts and properties of the topological semimetals from theoretical prediction to experimental verification.We analyzed the research status of topological semimetals in the field of condensed matter physics.We have found that topological semimetals have some special properties from some experiments,which have a very important impact on the future material field.This is also the significance of our research on topological semimetals in the field of condensed matter.Nextly,we mainly introduce the related knowledge about anisotropic magnetoresistance effect and planar Hall effect,which will lay the foundation for our future work.The main work of this paper is to understand the transport properties in Weyl semimetal materials with a Zeeman field through studying the anisotropic magnetoresistance effect and planar Hall effect in Weyl semimetal materials.In Chapter 2,we introduce Green's function theory and linear response theory,which are also the main theoretical basis of this paper.Firstly,we introduce the free fermion Green's function and free boson Green's function in detail from the concrete expression to the representation of Feynman diagram to the physical meaning.Then we discuss the self-energy correction of the disordered Green's function,which is also related to the Dyson equation.Finally,we introduce the linear response theory of conductivity.We extend the linear response theory of conductivity from the general applied potential to the specific linear response theory of conductivity.We successfully derive the Kubo formula of linear response.In Chapter 3,we systematically investigate the anisotropic magneto-conductivity and planar Hall effect in tilted magnetic topological semimetals in the frame of Kubo formula by considering the vertex correction of velocity.The nonzero magneto-conductivity is due to the intrinsic magnetization by magnetic doping rather than the external magnetic field previously studied in literatures.In the scenario,tilt,which is common in band structure,plays a key role in this anisotropic magneto-conductivity.This anisotropic magneto-conductivity completely originates from the band anisotropy.The vertex correction only amends the magnitude,but does not change the qualitative behavior of the longitudinal conductivity.However,the planar Hall conductivity is always zero for tilt along both x and y directions.In the case of external magnetic field,we find that there is still planar Hall effect in the system,and the conductivity is independent of Fermi energy or electron density.Our work offers a route to understand the anisotropic magneto-conductivity effect in tilted Weyl semimetals with Zeeman field.It will be helpful to get a deeper understanding of the transport characteristic in tilted topological semimetals.