Magnetic Susceptibility of Dirac Fermions, Bi-Sb Alloys, Interacting Bloch Fermions, Dilute Nonmagnetic Alloys, and Kondo Alloys

摘要

Wide ranging interest in Dirac Hamiltomian is due to the emergence of novelmaterials, namely, graphene, topological insulators and superconductors, thenewly-discovered Weyl semimetals, and still actively-sought after Majoranafermions in real materials. We give a brief review of the relativistic Diracquantum mechanics and its impact in the developments of modern physics. Thequantum band dynamics of Dirac Hamiltonian is crucial in resolving the giantdiamagnetism of bismuth and Bi-Sb alloys. Quantitative agreement of the theorywith the experiments on Bi-Sb alloys has been achieved, and physicallymeaningful contributions to the diamagnetism has been identified. We also treatrelativistic Dirac fermion as an interband dynamics in uniform magnetic fields.For the interacting Bloch electrons, the role of translation symmetry forcalculating the magnetic susceptibility avoids any approximation to secondorder in the field. The magnetic susceptibility of Hubbard model and those ofFermi liquids are readily obtained as limiting cases. The expressions formagnetic susceptibility of dilute nonmagnetic alloys give a firm theoreticalfoundation of the empirical formulas used in fitting experimental results. Forcompleteness, the magnetic susceptibility of dilute magnetic or Kondo alloys isalso given for high and low temperature regimes.