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 the first example of a transient collective instability in driven Dirac materials.

The quantum anomalous Hall effect (QAHE) has recently been reported to emerge in magnetically doped topological insulators. Although its general phenomenology is well established, the microscopic origin is far from being properly understood and controlled. Here, we report on a detailed and systematic investigation of transition metal (TM) doped Sb 2 Te 3. By combining density functional theory calculations with complementary experimental techniques, i.e., scanning tunneling microscopy, resonant photoemission, and x-ray magnetic circular dichroism, we provide a complete spectroscopic characterization of both electronic and magnetic properties. Our results reveal that the TM dopants not only affect the magnetic state of the host material, but also significantly alter the electronic structure by generating impurity-derived energy bands. Our findings demonstrate the existence of a delicate interplay between electronic and magnetic properties in TM doped topological insulators. In particular, we find that the fate of the topological surface states critically depends on the specific character of the TM impurity: while V-and Fe-doped Sb 2 Te 3 display resonant impurity states in the vicinity of the Dirac point, Cr and Mn impurities leave the energy gap unaffected. The single-ion magnetic anisotropy energy and easy axis, which control the magnetic gap opening and its stability, are also found to be strongly TM impurity dependent and can vary from in plane to out of plane depending on the impurity and its distance from the surface. Overall, our results provide general guidelines for the realization of a robust QAHE in TM doped Sb 2 Te 3 in the ferromagnetic state.

We present results of a microscopic tight-binding modeling of Bi 2 Se 3 three-dimensional topological insulator using a sp 3 Slater-Koster Hamiltonian, with parameters calculated from density functional theory. Based on the calculated atomic-and orbital-projections of the wavefunctions associated with valence-and conduction-band states at the center of the Brillouin zone, we propose a real-space description of band inversion for both bulk and a slab of finite thickness. A systematic analysis of the key features of the surface states, in particular the spatial distribution and the spin-character of the surface states wavefunction, is carried out for slabs of different thickness, ranging from one to tens of quintuple layers. We obtain an estimate of the slab thickness at which the energy gap induced by interaction between the top and bottom surface states becomes negligible, based on the present available numerical precision. We anticipate that this finding will be relevant for all microscopic calculations addressing the effect of external perturbations on the surface states near the Dirac point. The modifications in the helical spin-texture of the Dirac-cone surface states, in the form of in-plane and out-of-plane spin projections, are calculated as a function of the slab thickness. These calculations are important for the interpretation of ongoing experiments, which probe the spin-polarization of the surface states in topological insulator thin films.

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)2Te3 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)2Te3. The Dirac electronic recovery of ∼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)2Te3.