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.

Combining density-functional theory calculations and microscopic tight-binding models, we investigate theoretically the electronic and magnetic properties of individual substitutional transitionmetal impurities (Mn and Fe) positioned in the vicinity of the (110)

We report on low-temperature magnetotransport and SQUID measurements on heavily doped Mn-implanted GaAs nanowires. SQUID data recorded at low magnetic fields exhibit clear signs of the onset of a spin-glass phase with a transition temperature of about 16 K. Magnetotransport experiments reveal a corresponding peak in resistance at 16 K and a large negative magnetoresistance, reaching 40% at 1.6 K and 8 T. The negative magnetoresistance decreases at elevated temperatures and vanishes at about 100 K. We interpret our transport data in terms of spin-dependent hopping in a complex magnetic nanowire landscape of magnetic polarons, separated by intermediate regions of Mn impurity spins, forming a paramagnetic/spin-glass phase.

At an interface between a topological insulator (TI) and a conventional superconductor (SC), superconductivity has been predicted to change dramatically and exhibit novel correlations. In particular, the induced superconductivity by an s-wave SC in a TI can develop an order parameter with a p-wave component. Here we present experimental evidence for an unexpected proximity-induced novel superconducting state in a thin layer of the prototypical TI, Bi 2 Se 3 proximity coupled to Nb. From depthresolved magnetic field measurements below the superconducting transition temperature of Nb, we observe a local enhancement of the magnetic field in Bi 2 Se 3 that exceeds the externally applied field, thus supporting the existence of an intrinsic paramagnetic Meissner effect arising from an odd-frequency superconducting state. Our experimental results are complemented by theoretical calculations supporting the appearance of such a component at the interface which extends into the TI. This state is topologically distinct from the conventional Bardeen-Cooper-Schrieffer state it originates from. To the best of our knowledge, these findings present a first observation of bulk odd-frequency superconductivity in a TI. We thus reaffirm the potential of the TI-SC interface as a versatile platform to produce novel superconducting states.

Recently it was suggested that transient excitonic instability can be realized in optically-pumped two-dimensional (2D) Dirac materials (DMs), such as graphene and topological insulator surface states. Here we discuss the possibility of achieving a transient excitonic condensate in opticallypumped three-dimensional (3D) DMs, such as Dirac and Weyl semimetals, described by nonequilibrium chemical potentials for photoexcited electrons and holes. Similar to the equilibrium case with long-range interactions, we find that for pumped 3D DMs with screened Coulomb potential two possible excitonic phases exist, an excitonic insulator phase and the charge density wave phase originating from intranodal and internodal interactions, respectively. In the pumped case, the critical coupling for excitonic instability vanishes; therefore, the two phases coexist for arbitrarily weak coupling strengths. The excitonic gap in the charge density wave phase is always the largest one. The competition between screening effects and the increase of the density of states with optical pumping results in a reach phase diagram for the transient excitonic condensate. Based on the static theory of screening, we find that under certain conditions for the value of the dimensionless coupling constant screening in 3D DMs can be weaker than in 2D DMs. Furthermore, we identify the signatures of the transient excitonic condensate that could be probed by scanning tunneling spectroscopy, photoemission and optical conductivity measurements. Finally, we provide estimates of critical temperatures and excitonic gaps for existing and hypothetical 3D DMs.