Research On Quantum Transport Characteristics In ?-T₃ Model

Graphene was first experimentally isolated in 2004^[1]by Novoselov and Geim,the upsurge of studying the electronic properties of graphene has been raised.The unique electronic behavior of graphene shows many unusual quantum effects,such as Klein paradox^[2],anomalous quantum Hall effect^[3-5],minimum conductivity^[4],and so on.When people discover Klein tunneling in graphene with massless Dirac Weyl fermion passing through potential,the tunneling of particles through potential barrier has been attracting more and more attention.Due to the existence of various barriers in electronic devices,it is of great significance to study the tunneling of carriers through barriers.In recent years,a two-dimensional planar material?-T₃ model has appeared,which is different from graphene.The?-T₃ lattice interpolates between graphene??=0?and T₃lattice??=1?via a parameter?to describe the coupling strength between the lattice points of the hexagonal lattice and lattice points of the honeycomb lattice.Other properties of the?-T₃ model which have been investigated include the magneto-optical conductivity and the Hofstadter butterflfly^[6],Floquet topological phase transition^[7],the role of pseudospin polarization and transverse magnetic field on zitterbewegung^[8],its frequency-dependent magneto-optical conductivity^[9,10],its magnetotran-sport properties^[11]as well as the Hall quantization and optical conductivity^[12].In this paper,the barrier dependent transport properties of Dirac Weyl fermions without mass in?-T₃ lattice are studied by using the tight binding model.We theoretically investigate the transport properties for the?-T₃ lattice across magnetic barrier.We provide exact analytical expression of the transmission probability for the?-T₃ lattice.Moreover,we find the complete transmission at the angles?=n?with an integer n for the full range of the parameter?.This implies perfect transmission for incoming electrons at any angle??-?/2????/2?incident to the magnetic barrier,regardless of the incoming energy of the electron.Using the Landauer formula we can calculate the conductance as a function of the relative angle between the magnetization and the electric current.For the two limiting cases of graphene??=0?and the dice lattice??=1?,the conductance has a property,G??+??=G???,i.e.,G???has a periodicity of?.For an intermediate value of the parameter?i.e.for 0<?<1,the periodicity of conductance is absent.In addition,the?-T₃ lattice exhibits extraordinarily large anisotropic magnetoresistance?AMR?which relies significantly on the electron's incident energy.We theoretically studied the transport properties of the?-T₃ lattice through the electric potential barrier.We obtained the transmission coefficient using the transmission matrix method,as well as calculated the conductivity by the Landauer formula.We studied the transport characteristics of the?-T₃ lattice through two barriers and compared it through one barrier.We found that the angle of incidence,barrier height,barrier width,and well width all have an effect on transmission probability and conductivity.In the double-barrier structure,the increase in the number of potential barriers intensifies the oscillation of the particles.Meanwhile,the number of resonances increases and the resonance peaks are also sharper.