The Quantum Hall Effect Of Nodal-Line Semimetal

In 1980,Klaus von Klitzing found the quantum Hall effect in a two-dimensional electron gas,this new phase can't be described by Landau's symmetry breaking theory.After that,many scientists were attracted by this novel phenomena.Then in 1982,Thouless and some other physicists proposed a new theory,which needs a topological number to denote the phase,called TKNN invariant.In the meantime,Many experimentalists want to find other topological phases in materials,first the topological insulator,or the quantum spin Hall phase,the system have gapless boundary states and gapped bulk states.And then the topological superconductor,after the topological insulator and superconductor,scientists shifted the focus towards the topological semimetals,this shift was triggered by the theoretical discovery of Weyl and later Dirac semimetals.Within the past couple of years,the experimental realization of Weyl and Dirac semimetal brought this field to a hot point in condensed matter physics,topological semimetal has gapless bulk states and the corresponding surface states,which have many topological properties.Generally speaking,The integer quantum Hall effect should only be observed in a two dimensional system,But recently,scientists proposed that the quantum Hall effect can exist in the semimetal through the Weyl orbit,and there are some experiments that confirmed that Dirac semimetal CdAs have the quantum Hall effect.The theoretical calculation of quantum Hall effect in Dirac and Weyl semimetal all be done.In this research,we researched a new topological semimetal,nodal-line semimetal,which has a line Fermi surface.First,We read the papers recently published in this field,summed up the materials that were proposed or identified to be a nodal-line semimetal,classified different nodal-line semimetals through different symmetries.The topological properties of nodal-line semimetal were deduced,we began from a model Hamiltonian that contains all the topological properties of nodal-line semimetal,calculated the topological invariants of nodal-line semimetals,including the Winding number,which is an one dimensional k_x,k_ydepending topological number,we find the nodal-line semimetal has a nonzero winding number when k_x,k_ymeet some condition.Then the Berry phase,it has a±?values,the sign depends on different integral loops.We testified that the Berry phase is equivalent to the winding number in the topological semimetal.The surface states of nodal-line semimetal were also deduced for three cases,distinguished by with or without trivial terms in Hamiltonian and with or without magnetic field,and we saw the bulk-boundary correspondence of topological semimetal,with means the properties of the boundary is depended by the bulk properties,which have a profound physical significance.Then We calculated the quantum Hall effect of nodal-line semimetal numerically by using the Kubo formula,we found that like the Dirac semimetal and the Weyl semimetal,the topological nodal-line semimetal can also hold the quantum Hall effect,which is the most significant result in this research.Finally,we want to figure out the reason behind the three dimensional quantum Hall effect of topological semimetal,we researched the factors effect of sample thickness and Fermi energy to the quantum Hall effect,explained the results by using the Onsager relation,analyzed the origin of 3D quantum Hall effect simply and inroduced the works we will do next.