Magnetic susceptibility of Dirac fermions, Bi-Sb alloys, interacting Bloch fermions, dilute nonmagnetic alloys, and Kondo alloys

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• 作者：Felix A. Buot^a ; ^b ; ^c ; ^{fbuot@gmu.edu} ; Roland E.S. Otadoy^b ; Karla B. Rivero^b
• 关键词：72.10Bg ; M72-25-b ; 85.75-d
• 刊名：Physica B: Condensed Matter
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：508
• 期：Complete
• 页码：69-97
• 全文大小：1589 K
• 卷排序：508

文摘

Wide ranging interest in Dirac Hamiltonian is due to the emergence of novel materials, namely, graphene, topological insulators and superconductors, the newly-discovered Weyl semimetals, and still actively-sought after Majorana fermions in real materials. We give a brief review of the relativistic Dirac quantum mechanics and its impact in the developments of modern physics. The quantum band dynamics of Dirac Hamiltonian is crucial in resolving the giant diamagnetism of bismuth and Bi-Sb alloys. Quantitative agreement of the theory with the experiments on Bi-Sb alloys has been achieved, and physically meaningful contributions to the diamagnetism has been identified. We also treat relativistic Dirac fermion as an interband dynamics in uniform magnetic fields. For the interacting Bloch electrons, the role of translation symmetry for calculating the magnetic susceptibility avoids any approximation to second order in the field. The expressions for magnetic susceptibility of dilute nonmagnetic alloys give a firm theoretical foundation of the empirical formulas used in fitting experimental results. The unified treatment of all the above calculations is based on the lattice Weyl-Wigner formulation of discrete phase-space quantum mechanics. For completeness, the magnetic susceptibility of Kondo alloys is also given since Dirac fermions in conduction band and magnetic impurities exhibit Kondo effect.