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Magnetoresistance in many samples of Dirac semimetal and topological insulator displays non-monotonic behaviors over a wide range of magnetic field. Here a formula of magnetoconductivity is presented for massless and massive Dirac fermions in Dirac materials due to quantum interference in scalar impurity scattering potentials. It reveals a striking crossover from positive to negative magnetoresistivity, uncovering strong competition between weak localization and weak antilocalization in multiple Cooperon modes at different chemical potentials, effective masses and finite temperatures. The work sheds light on the important role of strong coupling of the conduction and valence bands in the quantum interference transport in topological nontrivial and trivial Dirac materials.
Exotic electronic states are realized in novel quantum materials. This field is revolutionized by the topological classification of materials. Such compounds necessarily host unique states on their boundaries. Scanning tunneling microscopy studies of
Massive Dirac fermions break the chiral symmetry explicitly and also make the Berry curvature of the band structure non-Abelian. By utilizing the Greens function technique, we develop a microscopic theory to establish a set of quantum diffusive equat
Quantum anomalous Hall (QAH) effect appears in ferromagnetic topological insulators (FMTI) when a Dirac mass gap opens in the spectrum of the topological surface states (SS). Unaccountably, although the mean mass gap can exceed 28 meV (or ~320 K), th
Electrons in low-temperature solids are governed by the non-relativistic Schr$ddot{o}$dinger equation, since the electron velocities are much slower than the speed of light. Remarkably, the low-energy quasi-particles given by electrons in various mat
Exciton problem is solved in the two-dimensional Dirac model with allowance for strong electron-hole attraction. The exciton binding energy is assumed smaller than but comparable to the band gap. The exciton wavefunction is found in the momentum spac