Nanoscale surface dynamics of Bi2Te3(111): observation of a prominent surface acoustic wave and the role of van der Waals interactions

Observation of Dirac Charge-Density Waves in Bi2Te2Se

While parallel segments in the Fermi level contours, often found at the surfaces of topological insulators (TIs), would imply "strong" nesting conditions, the existence of charge-density waves (CDWs)-periodic modulations of the electron density-has not been verified up to now. Here, we report the observation of a CDW at the surface of the TI Bi2Te2Se(111), below ≈350K, by helium-atom scattering and, thus, experimental evidence for a CDW involving Dirac topological electrons. Deviations of the order parameter observed below 180K, and a low-temperature break of time reversal symmetry, suggest the onset of a spin-density wave with the same period as the CDW in the presence of a prominent electron-phonon interaction, originating from Rashba spin-orbit coupling.

Water adsorption and dynamics on graphene and other 2D materials: Computational and experimental advances

The interaction of water and surfaces, at molecular level, is of critical importance for understanding processes such as corrosion, friction, catalysis and mass transport. The significant literature on interactions with single crystal metal surfaces should not obscure unknowns in the unique behaviour of ice and the complex relationships between adsorption, diffusion and long-range inter-molecular interactions. Even less is known about the atomic-scale behaviour of water on novel, non-metallic interfaces, in particular on graphene and other 2D materials. In this manuscript, we review recent progress in the characterisation of water adsorption on 2D materials, with a focus on the nano-material graphene and graphitic nanostructures; materials which are of paramount importance for separation technologies, electrochemistry and catalysis, to name a few. The adsorption of water on graphene has also become one of the benchmark systems for modern computational methods, in particular dispersion-corrected density functional theory (DFT). We then review recent experimental and theoretical advances in studying the single-molecular motion of water at surfaces, with a special emphasis on scattering approaches as they allow an unparalleled window of observation to water surface motion, including diffusion, vibration and self-assembly.

Multiple echoes in beam spin-echo spectroscopy and their effect on measurements of ultra-fast dynamics

Helium (³He) spin-echo is a powerful experimental technique used to probe ultra-fast atomic scale surface dynamics. The analysis of these measurements is typically performed assuming there is only a single spin-echo condition, expected to produce a constant signal for pure elastic scattering, a monotonically decaying signal for quasi-elastic scattering and oscillations from inelastic scattering events. In the present work, we show that there are in fact four spin-echoes which must be correctly accounted for, and that even in the case of elastic scattering these additional echoes lead to oscillations which could mistakenly be interpreted as being due to inelastic scattering. We demonstrate that it is possible to accurately simulate the experimental data by propagating the³He through the measured magnetic field profile of the apparatus and considering the geometry of the machine, allowing the effect of these additional echoes to be disentangled from inelastic scattering events in future³He spin-echo measurements.

Kohn anomalies in topological insulator thin films: first-principles study

Kohn anomaly is a non-smooth phonon softening induced by electron-phonon coupling in low-dimensional metals. Some measurements claimed that Kohn anomalies are present in topological materials due to the Dirac fermions in the bulk or in the surface. However, first-principles calculations have not reproduced the Kohn anomalies, especially, on the surface of topological insulators. It is still unclear about the origin of the controversy for the existence of the Kohn anomaly whether it is a numerical shortcoming or misinterpretation in measurement. In this study, we investigate the surface Kohn anomaly in two topological insulators Bi₂Se₃and SnSe using the state-of-the-art Wannier interpolation schemes. We find that Bi₂Se₃exhibits the Kohn anomaly but only in the bulk-like phonon modes by structural confinement along thec-axis. Interestingly, SnSe exhibits the surface Kohn anomaly in support of the experimental report on Pb_0.7Sn_0.3Se. We show that double Dirac cones in SnSe surface states are responsible for the Kohn anomaly, which is even enhanced if the subsurface states are partially occupied.

Temperature-Dependent Bending Rigidity of AB-Stacked Bilayer Graphene

The change in bending rigidity with temperature κ(T) for 2D materials is highly debated: theoretical works predict both increase and decrease. Here we present measurements of κ(T), for a 2D material: AB-stacked bilayer graphene. We obtain κ(T) from phonon dispersion curves measured with helium atom scattering in the temperature range 320-400 K. We find that the bending rigidity increases with temperature. Assuming a linear dependence over the measured temperature region we obtain κ(T)=[(1.3±0.1)+(0.006±0.001)T/K]  eV by fitting the data. We discuss this result in the context of existing predictions and room temperature measurements.

Inelastic helium atom scattering from Sb2Te3(111): phonon dispersion, focusing effects and surfing

We present an experimental study of inelastic scattering processes on the (111) surface of the topological insulator Sb₂Te₃ using helium atom scattering. In contrast to other binary topological insulators such as Bi₂Se₃ and Bi₂Te₃, Sb₂Te₃ is much less studied and the as-grown Sb₂Te₃ sample turns out to be p-doped, with the Fermi-level located below the Dirac-point as confirmed by angle-resolved photoemission spectroscopy. We report the surface phonon dispersion along both high symmetry directions in the energy region below 11 meV, where the Rayleigh mode exhibits the strongest intensity. The experimental data is compared with a study based on density functional perturbation theory calculations, providing good agreement except for a set of additional peculiar inelastic events below the Rayleigh mode. In addition, an analysis of angular scans with respect to a number of additional inelastic events is presented, including resonance enhancement, kinematical focusing, focused inelastic resonance and surfing. In the latter case, phonon-assisted adsorption of the incident helium atom gives rise to a bound state where the helium atom rides the created Rayleigh wave.

Atom-surface van der Waals potentials of topological insulators and semimetals from scattering measurements

The phenomenology of resonant scattering has been known since the earliest experiments upon scattering of atomic beams from surfaces and is a means of obtaining experimental information about the fundamentals of weak adsorption systems in the van der Waals regime. We provide an overview of the experimental approach based on new experimental data for the He-Sb₂Te₃(111) system, followed by a comparative overview and perspective of recent results for topological semimetal and insulator surfaces. Moreover, we shortly discuss the perspectives of calculating helium-surface interaction potentials from ab initio calculations. Our perspective demonstrates that atom-surface scattering provides direct experimental information about the atom-surface interaction in the weak physisorption regime and can also be used to determine the lifetime and mean free path of the trapped atom. We further discuss the effects of elastic and inelastic scattering on the linewidth and lifetime of the trapped He atom with an outlook on future developments and applications.

Inter-adsorbate forces and coherent scattering in helium spin-echo experiments

In studies of dynamical systems, helium atoms scatter coherently from an ensemble of adsorbates as they diffuse on the surface. The results give information on the co-operative behaviour of interacting adsorbates and thus include the effects of both adsorbate-substrate and adsorbate-adsorbate interactions. Here, we discuss a method to disentangle the effects of interactions between adsorbates from those with the substrate. The result gives an approximation to observations that would be obtained if the scattering was incoherent. Information from the experiment can therefore be used to distinguish more clearly between long-range inter-adsorbate forces and the short range effects arising from the local lattice potential and associated thermal excitations. The method is discussed in the context of a system with strong inter-adsorbate interactions, sodium atoms diffusing on a copper (111) surface.

Material properties particularly suited to be measured with helium scattering: selected examples from 2D materials, van der Waals heterostructures, glassy materials, catalytic substrates, topological insulators and superconducting radio frequency materials

Helium Atom Scattering (HAS) and Helium Spin-Echo scattering (HeSE), together helium scattering, are well established, but non-commercial surface science techniques. They are characterised by the beam inertness and very low beam energy (<0.1 eV) which allows essentially all materials and adsorbates, including fragile and/or insulating materials and light adsorbates such as hydrogen to be investigated on the atomic scale. At present there only exist an estimated less than 15 helium and helium spin-echo scattering instruments in total, spread across the world. This means that up till now the techniques have not been readily available for a broad scientific community. Efforts are ongoing to change this by establishing a central helium scattering facility, possibly in connection with a neutron or synchrotron facility. In this context it is important to clarify what information can be obtained from helium scattering that cannot be obtained with other surface science techniques. Here we present a non-exclusive overview of a range of material properties particularly suited to be measured with helium scattering: (i) high precision, direct measurements of bending rigidity and substrate coupling strength of a range of 2D materials and van der Waals heterostructures as a function of temperature, (ii) direct measurements of the electron-phonon coupling constant λ exclusively in the low energy range (<0.1 eV, tuneable) for 2D materials and van der Waals heterostructures (iii) direct measurements of the surface boson peak in glassy materials, (iv) aspects of polymer chain surface dynamics under nano-confinement (v) certain aspects of nanoscale surface topography, (vi) central properties of surface dynamics and surface diffusion of adsorbates (HeSE) and (vii) two specific science case examples - topological insulators and superconducting radio frequency materials, illustrating how combined HAS and HeSE are necessary to understand the properties of quantum materials. The paper finishes with (viii) examples of molecular surface scattering experiments and other atom surface scattering experiments which can be performed using HAS and HeSE instruments.

Measuring the Electron–Phonon Interaction in Two-Dimensional Superconductors with He-Atom Scattering

Helium-atom scattering (HAS) spectroscopy from conducting surfaces has been shown to provide direct information on the electron–phonon interaction, more specifically the mass-enhancement factor λ from the temperature dependence of the Debye–Waller exponent, and the mode-selected electron–phonon coupling constants λQν from the inelastic HAS intensities from individual surface phonons. The recent applications of the method to superconducting ultra-thin films, quasi-1D high-index surfaces, and layered transition-metal and topological pnictogen chalcogenides are briefly reviewed.

Origin of the Electron-Phonon Interaction of Topological Semimetal Surfaces Measured with Helium Atom Scattering

He atom scattering has been demonstrated to be a sensitive probe of the electron-phonon interaction parameter λ at metal and metal-overlayer surfaces. Here it is shown that the theory linking λ to the thermal attenuation of atom scattering spectra (the Debye-Waller factor) can be applied to topological semimetal surfaces, such as the quasi-one-dimensional charge-density-wave system Bi(114) and the layered pnictogen chalcogenides. The electron-phonon coupling, as determined for several topological insulators belonging to the class of bismuth chalcogenides, suggests a dominant contribution of the surface quantum well states over the Dirac electrons in terms of λ.

Nanoscopic diffusion of water on a topological insulator

The microscopic motion of water is a central question, but gaining experimental information about the interfacial dynamics of water in fields such as catalysis, biophysics and nanotribology is challenging due to its ultrafast motion, and the complex interplay of inter-molecular and molecule-surface interactions. Here we present an experimental and computational study of the nanoscale-nanosecond motion of water at the surface of a topological insulator (TI), Bi[Formula: see text]Te[Formula: see text]. Understanding the chemistry and motion of molecules on TI surfaces, while considered a key to design and manufacturing for future applications, has hitherto been hardly addressed experimentally. By combining helium spin-echo spectroscopy and density functional theory calculations, we are able to obtain a general insight into the diffusion of water on Bi[Formula: see text]Te[Formula: see text]. Instead of Brownian motion, we find an activated jump diffusion mechanism. Signatures of correlated motion suggest unusual repulsive interactions between the water molecules. From the lineshape broadening we determine the diffusion coefficient, the diffusion energy and the pre-exponential factor.

Phononic Helical Nodal Lines with PT Protection in MoB_{2}

While condensed matter systems host both fermionic and bosonic quasiparticles, reliably predicting and empirically verifying topological states is only mature for Fermionic electronic structures, leaving topological Bosonic excitations sporadically explored. This is unfortunate, as Bosonic systems such as phonons offer the opportunity to assess spinless band structures where nodal lines can be realized without invoking special additional symetries to protect against spin-orbit coupling. Here we combine first-principles calculations and meV-resolution inelastic x-ray scattering to demonstrate the first realization of parity-time reversal symmetry protected helical nodal lines in the phonon spectrum of MoB_{2}. This structure is unique to phononic systems as the spin-orbit coupling present in electronic systems tends to lift the degeneracy away from high-symmetry locations. Our study establishes a protocol to accurately identify topological Bosonic excitations, opening a new route to explore exotic topological states in crystalline materials.

Helium-Surface Interaction and Electronic Corrugation of Bi2Se3(111)

We present a study of the atom-surface interaction potential for the He-Bi₂Se₃(111) system. Using selective adsorption resonances, we are able to obtain the complete experimental band structure of atoms in the corrugated surface potential of the topological insulator Bi₂Se₃. He atom scattering spectra show several selective adsorption resonance features that are analyzed, starting with the free-atom approximation and a laterally averaged atom-surface interaction potential. Based on quantum mechanical calculations of the He-surface scattering intensities and resonance processes, we are then considering the three-dimensional atom-surface interaction potential, which is further refined to reproduce the experimental data. Following this analysis, the He-Bi₂Se₃(111) interaction potential is best represented by a corrugated Morse potential with a well depth of D = (6.54 ± 0.05) meV, a stiffness of κ = (0.58 ± 0.02) Å^-1, and a surface electronic corrugation of (5.8 ± 0.2)% of the lattice constant. The experimental data may also be used as a challenging benchmark system to analyze the suitability of several van der Waals approaches: the He-Bi₂Se₃(111) interaction captures the fundamentals of weak adsorption systems where the binding is governed by long-range electronic correlations.

Contrasting the Surface Phonon Dispersion of Pb_{0.7}Sn_{0.3}Se in Its Topologically Trivial and Nontrivial Phases

We report inelastic He atom scattering measurements of the (001) surface phonon dispersion of the topological crystalline insulator Pb_{0.7}Sn_{0.3}Se. This material exhibits a temperature-dependent topological transition, so we measure the surface dispersion curves in both the trivial and nontrivial phases. We identify that, peculiarly, most surface modes are resonances, rather than pure surface states. We find that a shear vertical surface resonance branch around 9.0 meV dramatically changes on going from the trivial to the topological phase. We associate this remarkable change with the emergence of surface Dirac fermions. We use the measured dispersion of this resonance branch to determine the corresponding mode-dependent electron-phonon coupling λ_{ν}(q).

Vibrational spectra of Pb2Bi2Te3, PbBi2Te4, and PbBi4Te7 topological insulators: temperature-dependent Raman and theoretical insights from DFT simulations

Insertion of lead and lead telluride in Bi₂Te₃ leads to a change in the thermal conductivity, frequency shift, and the broadening of phonon modes.