Magnetotransport properties of Dirac materials

Abstract

Dirac materials are a large class of condensed matter systems with low-energy excitations described by the Dirac equation. Usually, Dirac-like excitations can be either collective states or band structure effects and have been discovered in systems ranging from exotic quantum fluids to crystalline materials. In the past decades, they have inspired intensive experimental and theoretical study in various realistic materials, like topological insulators and topological semimetals. On one hand, the discovery of Dirac materials stimulates the development of topological band theory. On the other hand, due to the nontrivial band structure, Dirac materials can exhibit plentiful intriguing transport phenomena, like the weak anti-localization, quantum oscillations, and negative longitudinal magnetoresistance.

The present thesis mainly focuses on the magnetotransport properties of Dirac materials, including topological insulators and Dirac semimetals. Brief introduction about several typical quantum states of matter, transport properties of Dirac material, and linear response theory are given. The results can be summarized in three parts. The first part is about the intrinsic relative magnetoresistivity, the quantum oscillations, and the high-field conductivity of three-dimensional massive Dirac fermions. In the weak magnetic field, it is shown that there is a negative longitudinal magnetoresistivity and a positive transverse magnetoresistivity. In the weak scattering limit, the magnitude of the relative magnetoresistivity is controlled by the carrier density and the magnetic length, and irrelevant to the external scatterings. Such an intrinsic magnetoresistivity is expected to be detected in Dirac materials with low carrier density and high mobility. In the quantum oscillation regime, the longitudinal and transverse magnetoresistivity share the same phase shift in the Shubnikov–de Haas oscillations, and the phase shift is determined by both the mobility and the magnetic field. In the quantum limit regime, the product of transverse and longitudinal conductivity is independent of the disorder strength and proportional to the magnetic field strength. The second part is about the anomalous temperature dependence of conductivity in magnetic topological insulators. A magnetoconductivity formula from the quantum interference effect is derived for two-dimensional massive Dirac fermions. For magnetic topological insulators, it is shown that the tiny band gap in the energy spectrum of surface states leads to a temperature-dependent Berry phase, which introduces an additional phase breaking rate for surface electrons. As a result, the quantum correction to the conductivity can display a nonmonotonic temperature dependence. A quantitative comparison with the experimental data in magnetic topological insulators confirms our theory. In the last part, a magnetoconductivity formula based on the three-dimensional quantum interference theory is presented for three-dimensional massive Dirac fermions. It is shown that the strong competition of the multiple Cooperon channels results in an unusual crossover from positive to negative magnetoresistivity, which is coincident with the experimental measurements in the Dirac semimetal Cd3As2. This thesis sheds light on the importance of the multi-band effect in Dirac materials.