Topological insulator (TI) thin films with surface magnetism are expected to exhibit a quantized anomalous Hall effect (QAHE) when the magnetizations on the top and bottom surfaces are parallel, and a quantized topological magnetoelectric effect (QTME) when the magnetizations have opposing orientations (axion-insulator phase) and the films are sufficiently thick. We present a unified picture of both effects that associates deviations from exact quantization of the QTME caused by finite thickness with nonlocality in the sidewall current response function. Using realistic tight-binding model calculations, we show that in Bi2Se3 TI thin films, deviations from quantization in the axion-insulator phase are reduced in size when the exchange coupling of tight-binding model basis states to the local magnetization near the surface is strengthened. Stronger exchange coupling also reduces the effect of potential disorder, which is unimportant for the QAHE but detrimental for the QTME, which requires that the Fermi energy lie inside the gap at all positions.

Non-magnetic gap at the Dirac point of topological insulators remains an open question in the field. Here, we present angle-resolved photoemission spectroscopy experiments performed on Cr-doped Bi2Se3 and showed that the Dirac point is progressively buried by the bulk bands and a low spectral weight region in the vicinity of the Dirac point appears. These two mechanisms lead to spectral weight suppression region being mistakenly identified as an energy gap in earlier studies. We further calculated the band structure and found that the original Dirac point splits into two nodes due to the impurity resonant states and the energy separation between the nodes is the low density of state region which appears to be like an energy gap in potoemission experiments. We supported our arguments by presenting photoemission experiments carried out with on- and off- resonant photon energies. Our observation resolves the widely debated questions of apparent energy gap opening at the Dirac point without long range ferromagnetic order in topological insulators.

A first-principles investigation of the optical response of the Weyl Semimetals MoTe2 and WTe2 is presented. The approach, based on combining two formulations, allows to both separate the intraband and interband parts of the optical conductivity and to distinguish between the bulk and surface contributions to the optical response. It is found that the response is truly anisotropic, with peaks that can be associated with interband transitions involving either bulk or surface states. The role of the relaxation time, and the relation of the calculated results with available experimental measurements, are also discussed. Furthermore, the approach reported is transferable to any system, topologically trivial or non-trivial, thus addressing the long-standing need for comprehensive characterization of the optical response.

We present the result of an ab initio search for new Dirac materials among inverse perovskites. Our investigation is focused on the less studied class of lanthanide antiperovskites containing heavy f-electron elements in the cation position. Some of the studied compounds have not yet been synthesized experimentally. Our computational approach is based on density functional theory calculations which account for spin-orbit interaction and strong correlations of the f-electron atoms. We find several promising candidates among lanthanide antiperovskites which host bulk Dirac states close to the Fermi level. Specifically, our calculations reveal massive three-dimensional Dirac states in materials of the class A(3)BO, where A=Sm, Eu, Gd, Yb, and B=Sn, Pb. In materials with finite magnetic moment, such as Eu3BO (B=Sn, Pb), the degeneracy of the Dirac nodes is lifted, leading to appearance of Weyl nodes.

Recent pump-probe experiments demonstrate the possibility that Dirac materials may be driven into transient excited states describable by two chemical potentials, one for the electrons and one for the holes. Given the Dirac nature of the spectrum, such an inverted population allows the optical tunability of the density of states of the electrons and holes, effectively offering control of the strength of the Coulomb interaction. Here we discuss the feasibility of realizing transient excitonic instabilities in optically pumped Dirac materials. We demonstrate, theoretically, the reduction of the critical coupling leading to the formation of a transient condensate of electron-hole pairs and identify signatures of this state. Furthermore, we provide guidelines for experiments by both identifying the regimes in which such exotic many-body states are more likely to be observed and estimating the magnitude of the excitonic gap for a few important examples of existing Dirac materials. We find a set of material parameters for which our theory predicts large gaps and high critical temperatures and which could be realized in future Dirac materials. We also comment on transient excitonic instabilities in three-dimensional Dirac and Weyl semimetals. This study provides an example of a transient collective instability in driven Dirac materials.

Topological insulators (TIs) possess spin-polarized Dirac fermions on their surface but their unique properties are often masked by residual carriers in the bulk. Recently, (Sb1-xBix)(2)Te-3 was introduced as a non-metallic TI whose carrier type can be tuned from n to p across the charge neutrality point. By using time-and angle-resolved photoemission spectroscopy, we investigate the ultrafast carrier dynamics in the series of (Sb1-xBix)(2)Te-3. The Dirac electronic recovery of similar to 10 ps at most in the bulk-metallic regime elongated to >400 ps when the charge neutrality point was approached. The prolonged nonequilibration is attributed to the closeness of the Fermi level to the Dirac point and to the high insulation of the bulk. We also discuss the feasibility of observing excitonic instability of (Sb1-xBix)(2)Te-3.

We present a microscopic theory of the chiral one-dimensional electron gas system localized on the sidewalls of magnetically doped Bi2Se3-family topological insulator nanoribbons in the quantum anomalous Hall effect (QAHE) regime. Our theory is based on a simple continuum model of sidewall states whose parameters are extracted from detailed ribbon and film geometry tight-binding model calculations. In contrast to the familiar case of the quantum Hall effect in semiconductor quantum wells, the number of microscopic chiral channels depends simply and systematically on the ribbon thickness and on the position of the Fermi level within the surface state gap. We use our theory to interpret recent transport experiments that exhibit nonzero longitudinal resistance in samples with accurately quantized Hall conductances.