Topological Surface Band Research Articles

Carrier doping of Bi[formula omitted]Se[formula omitted] surface by chemical adsorption—A DFT study

Bi2Se3 is one of the most promising topological insulators, but it suffers from intrinsic n-doping due to Se-vacancies, which shifts the Fermi level into the bulk conduction band, leading to topologically trivial carriers. Recently it was shown that this Fermi-level shift can be compensated by a locally controlled surface p-doping process, through water adsorption and XUV irradiation. Here, the microscopic mechanism of this surface doping is studied by means of density functional theory (DFT) focusing on the adsorption of H2O, OH, O, C and CH on Bi2Se3. We find that water adsorption has a negligible doping effect while hydroxyl groups lead to n-doping. Carbon adsorption on Se vacancies gives rise to p-doping but it also strongly modifies the electronic band structure around the Dirac point. Only if the Se vacancies are filled with atomic oxygen, the experimentally observed p-doping without change of the topological surface bands is reproduced. Based on the DFT results, we propose a reaction path where photon absorption gives rise to water splitting and the produced O atoms fill the Se vacancies. Adsorbed OH groups appear as intermediate states and carbon impurities may have a catalytic effect in agreement with experimental observations.

Topological electronic structure evolution with symmetry-breaking spin reorientation in (Fe1−xCox)Sn

Topological materials hosting kagome lattices have drawn considerable attention due to the interplay between topology, magnetism, and electronic correlations. The (Fe$_{1-x}$Co$_x$)Sn system not only hosts a kagome lattice but has a tunable symmetry breaking magnetic moment with temperature and doping. In this study, angle resolved photoemission spectroscopy and first principles calculations are used to investigate the interplay between the topological electronic structure and varying magnetic moment from the planar to axial antiferromagnetic phases. A theoretically predicted gap at the Dirac point is revealed in the low temperature axial phase but no gap opening is observed across a temperature dependent magnetic phase transition. However, topological surface bands are observed to shift in energy as the surface magnetic moment is reduced or becomes disordered over time during experimental measurements. The shifting surface bands may preclude the determination of a temperature dependent bulk gap but highlights the intricate connections between magnetism and topology with a surface/bulk dichotomy that can affect material properties and their interrogation.

Strong-field physics in three-dimensional topological insulators

We investigate theoretically the strong-field regime of light-matter interactions in the topological-insulator class of quantum materials. In particular, we focus on the process of non-perturbative high-order harmonic generation from the paradigmatic three-dimensional topological insulator bismuth selenide (Bi$_2$Se$_3$) subjected to intense mid-infrared laser fields. We analyze the contributions from the spin-orbit-coupled bulk states and the topological surface bands separately and reveal a major difference in how their harmonic yields depend on the ellipticity of the laser field. Bulk harmonics show a monotonous decrease in their yield as the ellipticity increases, in a manner reminiscent of high harmonic generation in gaseous media. However, the surface contribution exhibits a highly non-trivial dependence, culminating with a maximum for circularly polarized fields. We attribute the observed anomalous behaviour to: (i) the enhanced amplitude and the circular pattern of the interband dipole and the Berry connections in the vicinity of the Dirac point; and (ii) the influence of the higher-order, "hexagonal warping" terms in the Hamiltonian, which are responsible for the hexagonal deformation of the energy surface at higher momenta. The latter are associated directly with spin-orbit-coupling parameters. Our results thus establish the sensitivity of strong-field driven high harmonic emission to the topology of the band structure as well as to the manifestations of spin-orbit interaction.

Observation of optical absorption correlated with surface state of topological insulator

We performed broadband optical transmission measurements of Bi2Se3 and In-doped Bi(1-x)In(x)2Se3 thin films, where in the latter the spin-orbit coupling (SOC) strength can be tuned by introducing In. Drude and interband transitions exhibit In-dependent changes that are consistent with evolution from metallic (x=0) to insulating (x=1) nature of the end compounds. Most notably, an optical absorption peak located at hw=1eV in Bi2Se3 is completely quenched at x=0.06, the critical concentration where the phase transition from TI into non-TI takes place. For this x, the surface state (SS) is vanished from the band structure as well. The correlation between the 1eV optical peak and the SS in the x-dependences suggests that the peak is associated with the SS. We further show that when Bi2Se3 is electrically gated, the 1eV-peak becomes stronger(weaker) when electron is depleted from (accumulated into) the SS. These observations combined together demonstrate that under the hw=1eV illumination electron is excited from a bulk band into the topological surface band of Bi2Se3. The optical population of surface band is of significant importance not only for fundamental study but also for TI-based optoelectronic device application.

Observation of Restored Topological Surface States in Magnetically Doped Topological Insulator

The introduction of ferromagnetic order in topological insulators in general breaks the time-reversal symmetry and a gap is opened in topological surface bands. Various studies have focused on gap-opened magnetic topological insulators, because such modified band structures provide a promising platform for observing exotic quantum physics. However, the role of antiferromagnetic order in topological insulators is still controversial. In this report, we demonstrate that it is possible to restore the topological surface states by effectively reducing the antiferromagnetic ordering in Gd-substituted Bi2Te3. We successfully control the magnetic impurities via thermal treatments in ultra-high vacuum condition and observe apparent restoration of topological surface band dispersions. The microscopic mechanism of atomic rearrangements and the restoration process of topological surface states are unraveled by the combination of scanning tunneling microscopy measurements and density functional theory calculations. This work provides an effective way to control the magnetic impurities which is strongly correlated with topological surface states.

Lightwave-driven Dirac currents in a topological surface band

Lightwave-driven Dirac currents in a topological surface band

Generalization of Bloch's theorem for arbitrary boundary conditions: Interfaces and topological surface band structure

We describe a method for exactly diagonalizing clean $D$-dimensional lattice systems of independent fermions subject to arbitrary boundary conditions in one direction, as well as systems composed of two bulks meeting at a planar interface. Our method builds on the generalized Bloch theorem [A. Alase et al., Phys. Rev. B 96, 195133 (2017)] and the fact that the bulk-boundary separation of the Schrodinger equation is compatible with a partial Fourier transform operation. Bulk equations may display unusual features because they are relative eigenvalue problems for non-Hermitian, bulk-projected Hamiltonians. Nonetheless, they admit a rich symmetry analysis that can simplify considerably the structure of energy eigenstates, often allowing a solution in fully analytical form. We illustrate our extension of the generalized Bloch theorem to multicomponent systems by determining the exact Andreev bound states for a simple SNS junction. We then analyze the Creutz ladder model, by way of a conceptual bridge from one to higher dimensions. Upon introducing a new Gaussian duality transformation that maps the Creutz ladder to a system of two Majorana chains, we show how the model provides a first example of a short-range chiral topological insulator hosting topological zero modes with a power-law profile. Additional applications include the complete analytical diagonalization of graphene ribbons with both zigzag-bearded and armchair boundary conditions, and the analytical determination of the edge modes in a chiral $p+ip$ two-dimensional topological superconductor. Lastly, we revisit the phenomenon of Majorana flat bands and anomalous bulk-boundary correspondence in a two-band gapless $s$-wave topological superconductor. We analyze the equilibrium Josephson response of the system, showing how the presence of Majorana flat bands implies a substantial enhancement in the $4\pi$-periodic supercurrent.

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.

Electronic investigation on topological surface states of Bi0.9Sb0.1

Topological surface states of Bi0.9Sb0.1 single crystal were reinvestigated by using the angle-resolved photoemission measurements. We identify the surface band topology near the point with two separate electron Fermi surfaces. It provides an indisputable picture of two topological surface bands between the and points, excluding the possible existence of a hypothetic trivial surface band proposed previously. We also examine the detailed nature of topological surface bands and estimate the Fermi velocity . The surface band near the point displays a characteristic warping structure originating from the rhombohedral symmetry, and the turns out to be highly anisotropic in both the hexagon-shaped electron and teardrop-shaped hole Fermi surface. Our investigation clarifies the topological surface states on Bi0.9Sb0.1, which is essential for the topological spintronics applications.

Dirac Node Lines in Pure Alkali Earth Metals.

Beryllium is a simple alkali earth metal, but has been the target of intensive studies for decades because of its unusual electron behavior at surfaces. The puzzling aspects include (i)severe deviations from the description of the nearly free-electron picture, (ii)an anomalously large electron-phonon coupling effect, and (iii)giant Friedel oscillations. The underlying origins for such anomalous surface electron behavior have been under active debate, but with no consensus. Here, by means of first-principles calculations, we discover that this pure metal system, surprisingly, harbors the Dirac node line (DNL) that in turn helps to rationalize many of the existing puzzles. The DNL is featured by a closed line consisting of linear band crossings, and its induced topological surface band agrees well with previous photoemission spectroscopy observations on the Be (0001) surface. We further reveal that each of the elemental alkali earth metals of Mg, Ca, and Sr also harbors the DNL and speculate that the fascinating topological property of the DNL might naturally exist in other elemental metals as well.

Effects of surface modification on the properties of topological surface states in Bi2Se3

The effects of surface modification on the topological surface states in Bi2Se3 have been studied using first-principles calculations. Although surface modification cannot change the topological order, however, the spin polarization, dispersion of topological surface bands and the position of Dirac points are altered. All the studied surface modifications can push Dirac cone upwards effectively. Bi-capped surface can attract the quantum well states into bulk band gap, forming new Dirac cone at M¯ point. Both Bi-capped and Se-removed surface can slightly enhance spin polarization of topological surface states, while flatten the energy dispersion of the topological surface bands above Dirac point.

Stability of theBi2Se3(111) topological state: Electron-phonon and electron-defect scattering

The electron dynamics of the topological surface state on Bi2Se3(111) is investigated by temperature-dependent angle-resolved photoemission. The electron-phonon coupling strength is determined in a spectral region for which only intraband scattering involving the topological surface band is possible. The electron-phonon coupling constant is found to be lambda=0.25(5), more than an order of magnitude higher than the corresponding value for intraband scattering in the noble metal surface states. The stability of the topological state with respect to surface irregularities was also tested by introducing a small concentration of surface defects via ion bombardment. It is found that, in contrast to the bulk states, the topological state can no longer be observed in the photoemission spectra and this cannot merely be attributed to surface defect-induced momentum broadening.