The Theoretical Study On Topological And Tunneling Properties Of Nodal Loop Semimetals

After recent more than ten years of research progress,topology has already achieved fruitful results in condensed matter physics.Among those,topological semimetals have attracted people’s attentions after topological insulator.Up to now,the big family of topological semimetals include Dirac(Weyl)semimetals and topological nodal line semimetals.Then it is eager to explore the properties of their corresponding surface states.For example,there will be fermi arc surface states between the two Weyl points of opposite charity and it has been observed in ARPES experiments.Recently,due to the protection of combined PT symmetry,it has the drumhead-like surface s-tates in the topological nodal line semimetals.Thus,it’s of high importance to study the construction of the system of topological nodal line semimetals and explore the possibility of material’s realization in the first principle calculations.In Chapter 1,we briefly review the big family of topology in condensed matter physics with Weyl(Dirac)semimetals the highlight and later it leads to the new progress in topological nodal line semimetals.In Chapter 2,we utilize the transfer matrix to develop an analytical method to calculate the surface states of an half-infinite tight binding lattice system.By discussing the equivalent equations of coefficients in detail,we’ve found there exit two kinds of decaying wave functions,one is paralleling decaying and the other is non-paralleling.Besides,this method has applied well in systems like 2D(3D)graphene with various boundaries,Weyl semimetals and so on.In Chapter 3,we’ve constructed a generic two-band model which can describe topological semimetals with multiple closed nodal loops.Any two loops can be con-structed to be Hopf linked,or to be connected to become a nodal-net,or nodal-chain state in the same framework.For the two-loop model,the corresponding drumhead surface states for these topological different bulk states are studied.It is found that the Landau spectrum for the Hopf linked state is characterized by the existence of quadru-ply degenerate zero-energy Landau band,regardless of the direction of the magnetic field.In Chapter 4,we’ve explored the tunneling properties of loop-nodal semimetals when taking the two main factors into consideration.One is the relative geometrical position between nodal loop and the interface of the junction,the other is the different spin texture in nodal line Hamiltonian models.The conclusions are summarized in Chapter 5,and we ask some open questions about topological loop-nodal semimetals for future study.