Quantum Impurity State And Electronic Transport Property In Topological Semimetals

In the past few years,topological semimetals have attracted intensive attention which widens the range of exploring topological phases beyond the topological insulators and superconductors.Semimetals are systems with zero density of state at the touching between conduction band and valence band and topological semimetals are systems of which the conduction and the valence bands have robust crossing points in k-space.In case of Dirac semimetals and Weyl semimetals,the crossising consisits of discrete set of points,while in the case of nodal loop semimetals,the crossing takes the form of a closed loop.In addition,there are two-dimensional semimetal systems,which exist on the boundary of three-dimensional materials and in some thin film materials.Most of these systems are found experimentally or by first principles calculations.In this article,the Anderson impurity state properties and electric transport properties of multi-Weyl semimetals,nodal loop Semimetals and bilayer two dimentional semimetal are studied.In the second section,we investigate the Kondo effect of a spin-1/2 magnetic impurity in a multi-Weyl semimetal of different J by using the variational wave function method.For different J,the binding energy is always positive in the presence of broken inversion symmetry,and a bound state is favored to form between the impurity and the host electrons.It is found that the formed bound state is more stable for larger J.Due to the spin-orbit coupling,the components of spin-spin correlation functions Juv(r)(u,v=x,y,z)show strong anisotropy in the coordinate space.The spin-spin correlation indicates distinct decay behaviors along different directions due to the anisotropic dispersion in the energy band.In the case of J=2 and J=3,the rotational symmetries of the spatial spin-spin correlations are displayed.Especially,the components Jxx and Jyy and Jxy and-Jyx can be related through a ?/(2J)rotation.In the third section we investigate the single-particle ballistic scattering on a rectangular barrier in multi-Weyl semimetals.Because this system has a crystallographic anisotropy,the scattering properties depend on the mutual orientation of the crystalline axis and the barrier.For different J,the vertical component of the wave vector andthe corresponding probability current density j? satisfies)j? ? k?2J-1.In the case of a barrier perpendicular to the z-axis,it is found that the reflectionless incident angles are determined by geometrical resonances between the barrier width and the de Broglie length of the scattered electrons in the barrier region.In the z-axis direction,the local minimum conductance Gmin occurs when the chemical potential equals the barrier height and Gmin ?1/L1/J,where L is the width of the barrier.Differently,in the case of a barrier perpendicular to the x-axis,the angular distribution of the transmission probability is no longer rotation invariant.For the double-Weyl semimetals(J=2),the transmission probability decreases rapidly to 0 as the barrier width L increases for a normal incidence,which is similar to conventional nonrelativistic electrons.It is interesting that perfect transmission is again found for normally incident Weyl fermions for the triple-Weyl semimetals(J=3).In this case,the tunneling indicates a property similar to that in the case of J=1.In the fourth section,we investigate the Kondo effect of a spin-1/2 magnetic impurity in a topological nodal loop semimetal,in which band touchings form a nodal loop.The Fermi surface of a nodal loop semimetal is a torus or a drum-like structure,which is determined by chemical potential.When the chemical potential ? lies at the nodal loop(?=0),the magnetic impurity and the conduction electrons form bound states only if their coupling exceeds a critical value.As the chemical potential is tuned away from the nodal loop,the Fermi surface becomes a torus or drum-like structure and the impurity and the host material always favor a bound state due to the finite density of state.Due to the anisotropic dispersion relationship in the energy band,the spatial spin-spin correlations Juv(r)(u,v=x,y,z)are of power-law decay with the decay rates proportional to l/|r |2 and l/|r|3 in different directions,respectively.The product x3Juu(x)and z2Juu(z)oscillates in coordinate space and the period is enhanced gradually as the Fermi surface evolves from a torus surface into a drum-like structure.In the fifth section,we also use a trial wave function to study the spin-1/2 Kondo effect of two-dimensional hetero semimetal bilayer system.This system can appear on the interface between two kind of topological insulators with different surface state or in some thin film material bilayer system.The energy gap is produced due to the interaction between two layers.When the chemical potential lies at the energy with zero density of the state,the impurity spin is screened only if the coupling between the impurity and the bulk electron exceeds a critical value.In other cases,the impurity spin is always weakly bound for small coupling.The spin-spin correlation function Juv(r)(u,v=x,y,z)between the spin v component of the magnetic impurity at the origin and the spin u component of a bulk electron at spatial point r is found to be strongly anisotropic and quite different from the single layer case.Compare to single layer,the spin-spin correlation function of each layer is slightly distorted by other layer.The total the spin-spin correlation function is mainly determined by the layer which has small Fermi velocity or lager hybridization with impurity.When the impurity only couple to one layer,the spin-spin correlation to other layer is still not zero and some component are ferromagnetic.In the calculation of the spin-spin correlation function of Anderson impurity,by using the fact that Hamiltonian are Hermite matrix,whose diagonalization matrix is unitary matrix,the treatment of calculation is standardized,which makes the whole calculation and derivation process conciser and more clear than the previous similar research.