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

TL;DR

This paper reviews the role of Dirac Hamiltonians in modern materials, analyzing magnetic susceptibility across various systems including alloys, topological insulators, and Kondo systems, with theoretical and experimental insights.

Contribution

It provides a comprehensive theoretical framework for magnetic susceptibility in Dirac and related systems, connecting quantum mechanics with experimental observations.

Findings

Quantitative agreement with experiments on Bi-Sb alloys.

Physically meaningful contributions to diamagnetism identified.

Theoretical foundation for empirical formulas in dilute alloys.

Abstract

Wide ranging interest in Dirac Hamiltomian 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 magnetic susceptibility of Hubbard model and those of Fermi liquids are readily obtained as limiting cases. The expressions for magnetic susceptibility of dilute nonmagnetic alloys give a firm theoretical foundation of the empirical formulas used in fitting experimental results. For completeness, the magnetic susceptibility of dilute magnetic or Kondo alloys is also given for high and low temperature regimes.