Disorder Effect in Spin-1 Dirac Systems

Author:Yang Zhi

Supervisor:shi qin wei


Degree Year:2019





The great development of graphene opens a door for discovering more two-dimensional Dirac materials.Recently,it is reported that the Dirac cones in Dirac materials with spin-1 are possible.The spin-1 Dirac systems have an unusual spectrum consisting of two graphene-like bands and one additional flat band intersecting with them at the Dirac point,which implies the emergence of novel electronic properties.For example,the enlarged spin leads to an enhanced "super" Klein tunneling through rectangular electrostatic barriers:when the energy of the incoming wave equals half the barrier height,the quasiparticles can be transmitted with probability 1 through a classically forbidden region independently of the incident angle.Since the disorder is unavoidable in any material,there has been a great deal of interest in trying to understand how the disorder affects the physics of electrons in graphene and its transport properties.We investigate the weak localization in spin-1 Dirac systems and the effect of disorder on Landau levels in this thesis.In the first chapter,we review the recent theoretical and experimental aspects of spin-1 Dirac Fermions.The massless Dirac-Weyl fennions with a spin 1 have inter-esting properties that are different from 1,such as super Klein tunneling,diverging dc conductivity at Dirac point,and anomalous Anderson localization in a one-dimensional disorder potential.In the second chapter,the tight-binding models of the T3 and Li(?)b lattices are pre-sented.We show that the dynamics nearing the Dirac point(s)in both lattices is governed by the spin-1 Dirac-Weyl equation by means of the k·p perturbation theory.The effec-tive potential of a scalar disorder in a k·p scheme is also derived.When the potential range in the T3 model is smaller than the lattice constant,it has off-diagonal element thus the intervalley scattering is not negligible.With the increase of the range,these off-diagonal elements decrease rapidly,and the potential is either sublattice correlated or sublattice uncorrelated.For the Lieb lattice,since it has only one Dirac point in the first Brillouin zone,the effective potential takes the form of either sublattice correlated or sublattice uncorrelated type.Finally,we analyze the symmetries of both lattices and potential disorders.In the third chapter,using the Feynman diagram techniques,we theoretically ob-tain the quantum conductivity correction for a two-dimensional spin-1 electron system in the presence of long-range diagonal disorder.Theoretical results clearly reveal that the quantum correction depends on the sublattice correlation properties of disorder po-tential.The sublattice correlated disorder gives rise to normal weak localization,while the sublattice uncorrelated impurity potential leads to the absence of a logarithmic term in quantum conductivity correction.Remarkably,those results cannot be understood by conventional symmetry classification.A new type of symmetry operator involving internal sublattice degrees of freedom,analogous with the time reversal symmetry op-erator,enables us to clarify our findings from symmetry consideration.The intervalley scattering in the T3 model leads to the weak localization,while the quantum correction-s to conductivity in the Lieb model are negative under either sublattice correlated or sublattice uncorrelated disorders.In the fourth chapter,Using the Lanczos recursion method,we exactly determine the shape of the zero-energy Landau level in a disordered T3 lattice under a strong mag-netic field.We discover that the shape of the zero-energy Landau level depends on the distribution of disorder,but is independent of magnetic field strength.Our analytical study attributes this intriguing behavior to the macroscopic and magnetic field inde-pendent degeneracy owing to the existence of the flat band.Moreover,our simulations unravel that the density of states obeys an unconventional scaling law,leading to the fact that the relation between the magnetoconductivity and the carrier density is independent of the disorder strengthIn the last chapter,we study the spin-1 Dirac system under the scalar disorder by means of renormalization-group approach.The renormalization-group equations are obtained,which is analog to that of the conventional two-dimensional electron gas in the weak scattering limit.The relation between system scale and the mean free length is derived.The beta function of conductance is shown to take the form consistent with the result in weak localization.In this thesis,we study the effects of disorder of sin-1 Dirac Fermions,including transport properties especially the weak localization,the broadening of Landau levels,the magnetoconductivity,and the scaling behavior.Our work not only deepens the understanding of the physical properties of spin-1 Dirac Fermions but also provides theoretical support for future experimental observations and applications of spin-1 Dirac systems.