Recent progress of transport theory in Dirac quantum materials

Dirac quantum materials comprise a broad category of condensed matter systems characterized by low-energy excitations described by the Dirac equation. These excitations, which can manifest as either collective states or band structure effects, have been identified in a wide range of systems, from exotic quantum fluids to crystalline materials. Over the past several decades, they have sparked extensive experimental and theoretical investigations in various materials, such as topological insulators and topological semimetals. The study of Dirac quantum materials has also opened up new possibilities for topological quantum computing, giving rise to a burgeoning field of physics and offering a novel platform for realizing rich topological phases, including various quantum Hall effects and topological superconducting phases. Furthermore, the topologically non-trivial band structures of Dirac quantum materials give rise to plentiful intriguing transport phenomena, including longitudinal negative magnetoresistance, quantum interference effects, and helical magnetic effects, among others. Currently, numerous transport phenomena in Dirac quantum materials remain poorly understood from a theoretical standpoint, such as linear magnetoresistance in weak fields, anomalous Hall effects in nonmagnetic materials, and three-dimensional quantum Hall effects. Investigating these transport properties will not only deepen our understanding of Dirac quantum materials but also provide crucial insights for their potential applications in spintronics and quantum computing. This review provides a comprehensive overview of the quantum transport theory and quantum anomaly effects related to the Dirac equation, with a focus on massive Dirac fermions and quantum anomalous semimetals. Additionally, it offers insights into the realization of parity anomaly and half-quantized quantum Hall effects in semi-magnetic topological insulators. Lastly, the review discusses the key scientific questions of interest in the field of quantum transport theory.