A Research On Topological Nodal-line Semimetals And Their Transport Properties

Topological phase was first discovered in the system of quantum Hall effect,which does not conform to the traditional condensed matter research paradigm and can not be described by the Landau theory.For explaining this novel phenomenon,Researchers introduce a concept of mathematics–topology in quantum Hall effect.Recently,according to the study on the band system and spin-orbital coupling effect,topological insulator phase was theoretically predicted and experimentally verified.The bulk energy band of topological insulator phase has a gap,while the boundaries of system have the edge states of topological protection.However,the topological states of bulk gapless energy band also can exist in the realistic materials,which is known as topological semimetals.Due to the dimensionality of the manifolds of crossings between the conduction and valence bands,topological semimetals can be classified into Weyl/Dirac semimetals and nodal-line semimetals.Symmetry plays an important role in this topological system,which guarantees the stability of topological structure.In this dissertation,by introducing a new model construction method,we can obtain various topological configuration of semimetal model.Meanwhile,we also study the transport properties of topological nodal-line semimetals.The following is the structure of this dissertation.In Chapter 1,we introduce the concept of Berry phase,which can be used to describe the topological phase.The physical effect induced by Berry phase has been discussed.In addition,we briefly review the Weyl semimetals and consider the symmetry how to protect the topological structure.Furthermore,the chiral anomaly of the Weyl semimetals and the effect induced by the surface states of semimetals have been presented.In Chapter 2,we introduce several nodal-line semimetals with different symmetry.The surface states of nodal-line semimetals have been discussed.Finally,the realistic materials of nodal and nodal line semimetals are presented.In Chapter 3,we newly construct a generic multi-nodal-loop model which is capable of describing all the existing topological nodal-loop semimetals,including the nodal-net,nodal-chain,and Hopf-link semimetals.The connection between Hopf-link semimetals and Hopf insulator have also been discussed.In addition,the effects of semimetals induced by the electromagnetic field(such as Landau level and Floquet states)have been studied.In Chapter 4,we introduce a wave-function method in lattice form to study transport properties of Weyl nodal-loop semimetals.Compared with the Green-function transport method,it has a simpler calculative structure.when we consider a junction made up of Weyl nodal-loop semimetals and normal metal,we find that the transport properties have a relation with the angle between the nodal loop and interface.Especially,when the nodal loop is parallel with interfaces,the transmitted electrons are nearly fully spinpolarized.This conclusion is model-independent and can be generalized to multi-band Weyl nodal-loop semimetals.In Chapter 5,We introduce the recent research of topological phases in nonHermitian systems,and discuss the condition of continuum bands in non-Hermitian systems.Meanwhile,we study the non-Hermitian band structure and boundary states of Weyl semimetals with different Chern number under the non-Hermitian effect.The realize of Hopf-link semimetal in the non-Hermitian system is discussed.The conclusions are summarized in Chapter 6.together with some discussions and prospects.