Build-up and dephasing of Floquet-Bloch bands on subcycle timescales.

Strong light fields have created opportunities to tailor novel functionalities of solids1-5. Floquet-Bloch states can form under periodic driving of electrons and enable exotic quantum phases6-15. On subcycle timescales, lightwaves can simultaneously drive intraband currents16-29 and interband transitions18,19,30,31, which enable high-harmonic generation16,18,19,21,22,25,28-30 and pave the way towards ultrafast electronics. Yet, the interplay of intraband and interband excitations and their relation to Floquet physics have been key open questions as dynamical aspects of Floquet states have remained elusive. Here we provide this link by visualizing the ultrafast build-up of Floquet-Bloch bands with time-resolved and angle-resolved photoemission spectroscopy. We drive surface states on a topological insulator32,33 with mid-infrared fields-strong enough for high-harmonic generation-and directly monitor the transient band structure with subcycle time resolution. Starting with strong intraband currents, we observe how Floquet sidebands emerge within a single optical cycle; intraband acceleration simultaneously proceeds in multiple sidebands until high-energy electrons scatter into bulk states and dissipation destroys the Floquet bands. Quantum non-equilibrium calculations explain the simultaneous occurrence of Floquet states with intraband and interband dynamics. Our joint experiment and theory study provides a direct time-domain view of Floquet physics and explores the fundamental frontiers of ultrafast band-structure engineering.

Ultrafast electron dynamics in a topological surface state observed in two-dimensional momentum space.

We study ultrafast population dynamics in the topological surface state of Sb[Formula: see text]Te[Formula: see text] in two-dimensional momentum space with time- and angle-resolved two-photon photoemission spectroscopy. Linearly polarized mid-infrared pump pulses are used to permit a direct optical excitation across the Dirac point. We show that this resonant excitation is strongly enhanced within the Dirac cone along three of the six [Formula: see text]-[Formula: see text] directions and results in a macroscopic photocurrent when the plane of incidence is aligned along a [Formula: see text]-[Formula: see text] direction. Our experimental approach makes it possible to disentangle the decay of transiently excited population and photocurent by elastic and inelastic electron scattering within the full Dirac cone in unprecedented detail. This is utilized to show that doping of Sb[Formula: see text]Te[Formula: see text] by vanadium atoms strongly enhances inelastic electron scattering to lower energies, but only scarcely affects elastic scattering around the Dirac cone.

Non-monotonic variation of the Kramers point band gap with increasing magnetic doping in BiTeI.

Polar Rashba-type semiconductor BiTeI doped with magnetic elements constitutes one of the most promising platforms for the future development of spintronics and quantum computing thanks to the combination of strong spin-orbit coupling and internal ferromagnetic ordering. The latter originates from magnetic impurities and is able to open an energy gap at the Kramers point (KP gap) of the Rashba bands. In the current work using angle-resolved photoemission spectroscopy (ARPES) we show that the KP gap depends non-monotonically on the doping level in case of V-doped BiTeI. We observe that the gap increases with V concentration until it reaches 3% and then starts to mitigate. Moreover, we find that the saturation magnetisation of samples under applied magnetic field studied by superconducting quantum interference device (SQUID) magnetometer has a similar behaviour with the doping level. Theoretical analysis shows that the non-monotonic behavior can be explained by the increase of antiferromagnetic coupled atoms of magnetic impurity above a certain doping level. This leads to the reduction of the total magnetic moment in the domains and thus to the mitigation of the KP gap as observed in the experiment. These findings provide further insight in the creation of internal magnetic ordering and consequent KP gap opening in magnetically-doped Rashba-type semiconductors.

Tunable non-integer high-harmonic generation in a topological insulator.

When intense lightwaves accelerate electrons through a solid, the emerging high-order harmonic (HH) radiation offers key insights into the material1-11. Sub-optical-cycle dynamics-such as dynamical Bloch oscillations2-5, quasiparticle collisions6,12, valley pseudospin switching13 and heating of Dirac gases10-leave fingerprints in the HH spectra of conventional solids. Topologically non-trivial matter14,15 with invariants that are robust against imperfections has been predicted to support unconventional HH generation16-20. Here we experimentally demonstrate HH generation in a three-dimensional topological insulator-bismuth telluride. The frequency of the terahertz driving field sharply discriminates between HH generation from the bulk and from the topological surface, where the unique combination of long scattering times owing to spin-momentum locking17 and the quasi-relativistic dispersion enables unusually efficient HH generation. Intriguingly, all observed orders can be continuously shifted to arbitrary non-integer multiples of the driving frequency by varying the carrier-envelope phase of the driving field-in line with quantum theory. The anomalous Berry curvature warranted by the non-trivial topology enforces meandering ballistic trajectories of the Dirac fermions, causing a hallmark polarization pattern of the HH emission. Our study provides a platform to explore topology and relativistic quantum physics in strong-field control, and could lead to non-dissipative topological electronics at infrared frequencies.

Electrochemically exfoliated thin Bi2Se3 films and van der Waals heterostructures Bi2Se3/graphene.

Thin Bi2Se3 flakes with few nanometer thicknesses and sized up to 350 µm were created by using electrochemical splitting from high-quality Bi2Se3 bulk monocrystals. The dependence of film resistance on the Bi2Se3 flake thickness demonstrates that, at room temperature, the bulk conductivity becomes negligible in comparison with the surface conductivity for films with thicknesses lower than 80 nm. Unexpectedly, all these films demonstrated p-type conductivity. The doping effect with sulfur or sulfur-related radicals during electrochemical exfoliation is suggested for the p-type conductivity of the exfoliated Bi2Se3 films. The formation of 2-8 nm films was predominantly found. Van der Waals (vdW) heterostructures of Bi2Se3/Graphene/SiO2/Si were created and their properties were compared with that of Bi2Se3 on the SiO2/Si substrate. The increase of the conductivity and carrier mobility in Bi2Se3 flakes of 3-5 times was found for vdW heterostructures with graphene. Thin Bi2Se3 films are potentially interesting for applications for spintronics, nano- and optoelectronics.

Dirac gap opening and Dirac-fermion-mediated magnetic coupling in antiferromagnetic Gd-doped topological insulators and their manipulation by synchrotron radiation.

A new kind of magnetically-doped antiferromagnetic (AFM) topological insulators (TIs) with stoichiometry Bi1.09Gd0.06Sb0.85Te3 has been studied by angle-resolved photoemission spectroscopy (ARPES), superconducting magnetometry (SQUID) and X-ray magnetic circular dichroism (XMCD) with analysis of its electronic structure and surface-derived magnetic properties at different temperatures. This TI is characterized by the location of the Dirac gap at the Fermi level (EF) and a bulk AFM coupling below the Neel temperature (4-8 K). At temperatures higher than the bulk AFM/PM transition, a surface magnetic layer is proposed to develop, where the coupling between the magnetic moments located at magnetic impurities (Gd) is mediated by the Topological Surface State (TSS) via surface Dirac-fermion-mediated magnetic coupling. This hypothesis is supported by a gap opening at the Dirac point (DP) indicated by the surface-sensitive ARPES, a weak hysteresis loop measured by SQUID at temperatures between 30 and 100 K, XMCD measurements demonstrating a surface magnetic moment at 70 K and a temperature dependence of the electrical resistance exhibiting a mid-gap semiconducting behavior up to temperatures of 100-130 K, which correlates with the temperature dependence of the surface magnetization and confirms the conclusion that only TSS are located at the EF. The increase of the TSS's spectral weight during resonant ARPES at a photon energy corresponding to the Gd 4d-4f edge support the hypothesis of a magnetic coupling between the Gd ions via the TSS and corresponding magnetic moment transfer at elevated temperatures. Finally, the observed out-of-plane and in-plane magnetization induced by synchrotron radiation (SR) due to non-equal depopulation of the TSS with opposite momentum, as seen through change in the Dirac gap value and the k∥-shift of the Dirac cone (DC) states, can be an indicator of the modification of the surface magnetic coupling mediated by the TSS.

Subcycle observation of lightwave-driven Dirac currents in a topological surface band.

Harnessing the carrier wave of light as an alternating-current bias may enable electronics at optical clock rates1. Lightwave-driven currents have been assumed to be essential for high-harmonic generation in solids2-6, charge transport in nanostructures7,8, attosecond-streaking experiments9-16 and atomic-resolution ultrafast microscopy17,18. However, in conventional semiconductors and dielectrics, the finite effective mass and ultrafast scattering of electrons limit their ballistic excursion and velocity. The Dirac-like, quasi-relativistic band structure of topological insulators19-29 may allow these constraints to be lifted and may thus open a new era of lightwave electronics. To understand the associated, complex motion of electrons, comprehensive experimental access to carrier-wave-driven currents is crucial. Here we report angle-resolved photoemission spectroscopy with subcycle time resolution that enables us to observe directly how the carrier wave of a terahertz light pulse accelerates Dirac fermions in the band structure of the topological surface state of Bi2Te3. While terahertz streaking of photoemitted electrons traces the electromagnetic field at the surface, the acceleration of Dirac states leads to a strong redistribution of electrons in momentum space. The inertia-free surface currents are protected by spin-momentum locking and reach peak densities as large as two amps per centimetre, with ballistic mean free paths of several hundreds of nanometres, opening up a realistic parameter space for all-coherent lightwave-driven electronic devices. Furthermore, our subcycle-resolution analysis of the band structure may greatly improve our understanding of electron dynamics and strong-field interaction in solids.

Dirac cone intensity asymmetry and surface magnetic field in V-doped and pristine topological insulators generated by synchrotron and laser radiation.

Effect of magnetization generated by synchrotron or laser radiation in magnetically-doped and pristine topological insulators (TIs) is presented and analyzed using angle-resolved photoemission spectroscopy. It was found that non-equal photoexcitation of the Dirac cone (DC) states with opposite momenta and spin orientation indicated by the asymmetry in photoemission intensity of the DC states is accompanied by the k||-shift of the DC states relative to the non-spin-polarized conduction band states located at k|| = 0. We relate the observed k||-shift to the induced surface in-plane magnetic field and corresponding magnetization due to the spin accumulation. The direction of the DC k||-shift and its value are changed with photon energy in correlation with variation of the sign and magnitude of the DC states intensity asymmetry. The theoretical estimations describe well the effect and predict the DC k||-shift values which corroborate the experimental observations. This finding opens new perspectives for effective local magnetization manipulation.

Prolonged duration of nonequilibrated Dirac fermions in neutral topological insulators.

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-x Bi x )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-x Bi x )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-x Bi x )2Te3.

Giant Magnetic Band Gap in the Rashba-Split Surface State of Vanadium-Doped BiTeI: A Combined Photoemission and Ab Initio Study.

One of the most promising platforms for spintronics and topological quantum computation is the two-dimensional electron gas (2DEG) with strong spin-orbit interaction and out-of-plane ferromagnetism. In proximity to an s-wave superconductor, such 2DEG may be driven into a topologically non-trivial superconducting phase, predicted to support zero-energy Majorana fermion modes. Using angle-resolved photoemission spectroscopy and ab initio calculations, we study the 2DEG at the surface of the vanadium-doped polar semiconductor with a giant Rashba-type splitting, BiTeI. We show that the vanadium-induced magnetization in the 2DEG breaks time-reversal symmetry, lifting Kramers degeneracy of the Rashba-split surface state at the Brillouin zone center via formation of a huge gap of about 90 meV. As a result, the constant energy contour inside the gap consists of only one circle with spin-momentum locking. These findings reveal a great potential of the magnetically-doped semiconductors with a giant Rashba-type splitting for realization of novel states of matter.

Spin-resolved band structure of heterojunction Bi-bilayer/3D topological insulator in the quantum dimension regime in annealed Bi2Te2.4Se0.6.

Two- and three-dimensional topological insulators are the key materials for the future nanoelectronic and spintronic devices and quantum computers. By means of angle- and spin-resolved photoemission spectroscopy we study the electronic and spin structure of the Bi-bilayer/3D topological insulator in quantum tunneling regime formed under the short annealing of Bi2Te2.4Se0.6. Owing to the temperature-induced restructuring of the topological insulator's surface quintuple layers, the hole-like spin-split Bi-bilayer bands and the parabolic electronic-like state are observed instead of the Dirac cone. Scanning Tunneling Microscopy and X-ray Photoemission Spectroscopy measurements reveal the appearance of the Bi2 terraces at the surface under the annealing. The experimental results are supported by density functional theory calculations, predicting the spin-polarized Bi-bilayer bands interacting with the quintuple-layers-derived states. Such an easily formed heterostructure promises exciting applications in spin transport devices and low-energy electronics.

Systematics of molecular self-assembled networks at topological insulators surfaces.

The success of topological insulators (TI) in creating devices with unique functionalities is directly connected to the ability of coupling their helical spin states to well-defined perturbations. However, up to now, TI-based heterostructures always resulted in very disordered interfaces, characterized by strong mesoscopic fluctuations of the chemical potential that make the spin-momentum locking ill-defined over length scales of few nanometers or even completely destroy topological states. These limitations call for the ability to control topological interfaces with atomic precision. Here, we demonstrate that molecular self-assembly processes driven by inherent interactions among the constituents offer the opportunity to create well-defined networks at TIs surfaces. Even more remarkably, we show that the symmetry of the overlayer can be finely controlled by appropriate chemical modifications. By analyzing the influence of the molecules on the TI electronic properties, we rationalize our results in terms of the charge redistribution taking place at the interface. Overall, our approach offers a precise and fast way to produce tailor-made nanoscale surface landscapes. In particular, our findings make organic materials ideal TIs counterparts, because they offer the possibility to chemically tune both electronic and magnetic properties within the same family of molecules, thereby bringing us a significant step closer toward an application of this fascinating class of materials.

Tuning the Dirac point position in Bi(2)Se(3)(0001) via surface carbon doping.

Angular resolved photoemission spectroscopy in combination with ab initio calculations show that trace amounts of carbon doping of the Bi_{2}Se_{3} surface allows the controlled shift of the Dirac point within the bulk band gap. In contrast to expectation, no Rashba-split two-dimensional electron gas states appear. This unique electronic modification is related to surface structural modification characterized by an expansion of the top Se-Bi spacing of ≈11% as evidenced by surface x-ray diffraction. Our results provide new ways to tune the surface band structure of topological insulators.

Defects in GaSe grown by Bridgman method.

Optical quality GaSe crystals have been grown by vertical Bridgman method. The structural properties and micromorphology of a cleaved GaSe(001) surface have been evaluated by RHEED, SEM and AFM. The cleaved GaSe(001) is atomically flat with as low roughness as ∼0.06 nm excepting local hillock type defects. The hillock-type formations are round-shaped with a bottom diameter of ∼200 nm and a height of ∼20-35 nm. The drastic depletion of the hillock material by gallium has been indicated by EDX measurements.

Probing the electronic properties of individual MnPc molecules coupled to topological states.

Hybrid organic/inorganic interfaces have been widely reported to host emergent properties that go beyond those of their single constituents. Coupling molecules to the recently discovered topological insulators, which possess linearly dispersing and spin-momentum-locked Dirac fermions, may offer a promising platform toward new functionalities. Here, we report a scanning tunneling microscopy and spectroscopy study of the prototypical interface between MnPc molecules and a Bi2Te3 surface. MnPc is found to bind stably to the substrate through its central Mn atom. The adsorption process is only accompanied by a minor charge transfer across the interface, resulting in a moderately n-doped Bi2Te3 surface. More remarkably, topological states remain completely unaffected by the presence of the molecules, as evidenced by the absence of scattering patterns around adsorption sites. Interestingly, we show that, while the HOMO and LUMO orbitals closely resemble those of MnPc in the gas phase, a new hybrid state emerges through interaction with the substrate. Our results pave the way toward hybrid organic-topological insulator heterostructures, which may unveil a broad range of exciting and unknown phenomena.

Snapshots of Dirac fermions near the Dirac point in topological insulators.

The recent focus on topological insulators is due to the scientific interest in the new state of quantum matter as well as the technology potential for a new generation of THz optoelectronics, spintronics and quantum computations. It is important to elucidate the dynamics of the Dirac fermions in the topologically protected surface state. Hence we utilized a novel ultrafast optical pump mid-infrared probe to explore the dynamics of Dirac fermions near the Dirac point. The femtosecond snapshots of the relaxation process were revealed by the ultrafast optics. Specifically, the Dirac fermion-phonon coupling strength in the Dirac cone was found to increase from 0.08 to 0.19 while Dirac fermions were away from the Dirac point into higher energy states. Further, the energy-resolved transient reflectivity spectra disclosed the energy loss rate of Dirac fermions at room temperature was about 1 meV/ps. These results are crucial to the design of Dirac fermion devices.

Circular dichroism and superdiffusive transport at the surface of BiTeI.

We investigate the electronic states of BiTeI after the optical pumping with circularly polarized photons. Our data show that photoexcited electrons reach an internal thermalization within 300 fs of the arrival of the pump pulse. Instead, the dichroic contrast generated by the circularly polarized light relaxes on a time scale shorter than 80 fs. This result implies that orbital and spin polarization created by the circular pump pulse rapidly decays via manybody interaction. The persistent dichroism at longer delay times is due to the helicity dependence of superdiffussive transport. We ascribe it to the lack of inversion symmetry in an electronic system far from equilibrium conditions.

Terahertz time-domain spectroscopy for textile identification.

A range of natural and artificial textiles are examined using terahertz time-domain spectroscopy. Different types of textiles are shown to have different terahertz optical properties, which may be employed for textile identification and to combat textile counterfeiting.

Topological surface states with persistent high spin polarization across the Dirac point in Bi2Te2Se and Bi2Se2Te.

Helical spin textures with marked spin polarizations of topological surface states have been unveiled for the first time by state-of-the-art spin- and angle-resolved photoemission spectroscopy for two promising topological insulators, Bi(2)Te(2)Se and Bi(2)Se(2)Te. Their highly spin-polarized natures are found to be persistent across the Dirac point in both compounds. This novel finding paves a pathway to extending the utilization of topological surface states of these compounds for future spintronic applications.