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Anderson Impurity Model in Dirac Matter

Mashkoori, Mahdi | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47657 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Jafari, Akbar
  7. Abstract:
  8. In this thesis we have been mainly interested in studying Single Impurity Anderson model (SIAM) in Dirac fermions. Although this model seems to be simple, the rich physics of SIAM can not be underestimated. In this thesis we were interested in Dirac materials, systems which their low energy excitations are described by Dirac equation.Therefore, considering Dirac material in two dimensions(2D), we briefly review the distinct features of one atom thick layer of carbon. In addition, we will explain the effective Hamiltonian of Bismuth near L point which is considered a three dimensional(3D) Dirac material. Because of very strong spin-orbit interaction, bismuth is a key element in topological insulator materials. Next, we will review the SIAM in normal metals and base on that, we consider point defect and ad-atom in graphehe. Our calculation shows that two-sublattice nature of graphene lattice in conjunction with the three-fold rotational symmetry, allows for the p-wave hybridization of impurity state with the Bloch states of carbon atoms. Such an opportunity is not available in normal metals where the wave function is scalar. The p-wave hybridization function (⃗) appears when dealing with vacancies, substitutional adatoms and the hollow site impurities. Heavy transition metals like cobalt prefer p-wave hybridization. In contrast, the s-wave mixing on graphene lattice pertains only to the top site impurities; for example hydrogen and nitrogen atoms demonstrate s-wave hybridization.
    We compare the local moment formation in these two cases and find that the local moments formed by p-wave mixing compared to s-wave one are robust against the changes in the parameters of the model. Furthermore, we investigate the stability of the local moments in the above cases. We find that the quantum fluctuations can destroy the local moments in the case of s-wave hybridization, while the local moments formed by p-wave hybridization survive the quantum fluctuations. Considering 3D Dirac materiel, we have investigated SIAM in bismuth within Hartree approximation. The general picture in a host of a simple one-band metal is that a large Hubbard in the impurity orbital is pre-requisite for the formation of localized magnetic states. Here, we show that such a strong spin-orbit interaction allows to form localized magnetic states even with small values of Hubbard . This opens up the fascinating possibility of forming magnetic states with or orbital impurities – different from traditional paradigms of or orbital based magnetic moments. We also consider topological terms in Hamiltonian (2).We show that for the case of topologically non-trivial band structure the effects which arise from spin-orbit interaction will be weakened. Finally we consider Kondo interaction in Weyl semimetal.We show that Kondo temperature can be tuned by chemical potential in the same way as graphene. In addition, by tuning the chemical potential, the bounding energy between the impurity and Weyl quasi-particles passes through a maximum. Therefore,based on our calculation we suggest an optimal doping which corresponds to most probable doping to observe the Kodno effect in Weyl semimetals
  9. Keywords:
  10. Dirac Fermion ; Topological Insulator ; Graphene ; Anderson Impurity Model ; Spin-Orbit Coupling ; Local Magnetic Moment

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