Theory of surface phonons at metal surfaces: recent advances

A theory of phonon-induced friction on molecular adsorbates

In this manuscript, we provide a general theory for how surface phonons couple to molecular adsorbates. Our theory maps the extended dynamics of a surface's atomic vibrational motions to a generalized Langevin equation, and by doing so captures these dynamics in a single quantity: the non-Markovian friction. The different frequency components of this friction are the phonon modes of the surface slab weighted by their coupling to the adsorbate degrees of freedom. Using this formalism, we demonstrate that physisorbed species couple primarily to acoustic phonons while chemisorbed species couple to dispersionless local vibrations. We subsequently derive equations for phonon-adjusted reaction rates using transition state theory and demonstrate that these corrections improve agreement with experimental results for CO desorption rates from Pt(111).

Fully Ab Initio Approach to Inelastic Atom-Surface Scattering

We introduce a fully ab initio theory for inelastic scattering of any atom from any surface exciting single phonons, and apply the theory to helium scattering from Nb(100). The key aspect making our approach general is a direct first-principles evaluation of the scattering atom-electron vertex. By correcting misleading results from current state-of-the-art theories, this fully ab initio approach will be critical in guiding and interpreting experiments that adopt next-generation, nondestructive atomic beam scattering.

Finite-Size Effect in Phonon-Induced Elliott-Yafet Spin Relaxation in Al

The Elliott-Yafet theory of spin relaxation in nonmagnetic metals predicts proportionality between spin and momentum relaxation times for scattering centers such as phonons. Here, we test this theory in Al nanowires over a very large thickness range (8.5-300 nm), finding that the Elliott-Yafet proportionality "constant" for phonon scattering in fact exhibits a large, unanticipated finite-size effect. Supported by analytical and numerical modeling, we explain this via strong phonon-induced spin relaxation at surfaces and interfaces, driven in particular by enhanced spin-orbit coupling.

A combined helium atom scattering and density-functional theory study of the Nb(100) surface oxide reconstruction: Phonon band structures and vibrational dynamics

Helium atom scattering and density-functional theory (DFT) are used to characterize the phonon band structure of the (3 × 1)-O surface reconstruction of Nb(100). Innovative DFT calculations comparing surface phonons of bare Nb(100) to those of the oxide surface show increased resonances for the oxide, especially at higher energies. Calculated dispersion curves align well with experimental results and yield atomic displacements to characterize polarizations. Inelastic helium time-of-flight measurements show phonons with mixed longitudinal and shear-vertical displacements along both the ⟨[Formula: see text]⟩, [Formula: see text] and ⟨[Formula: see text]⟩, [Formula: see text] symmetry axes over the entire first surface Brillouin zone. Force constants calculated for bulk Nb, Nb(100), and the (3 × 1)-O Nb(100) reconstruction indicate much stronger responses from the oxide surface, particularly for the top few layers of niobium and oxygen atoms. Many of the strengthened bonds at the surface create the characteristic ladder structure, which passivates and stabilizes the surface. These results represent, to our knowledge, the first phonon dispersion data for the oxide surface and the first ab initio calculation of the oxide’s surface phonons. This study supplies critical information for the further development of advanced materials for superconducting radiofrequency cavities.

Measuring phonon dispersion at an interface

The breakdown of translational symmetry at heterointerfaces leads to the emergence of new phonon modes localized at the interface¹. These modes have an essential role in thermal and electrical transport properties in devices, especially in miniature ones wherein the interface may dominate the entire response of the device². Although related theoretical work began decades ago^1,3-5, experimental research is totally absent owing to challenges in achieving the combined spatial, momentum and spectral resolutions required to probe localized modes. Here, using the four-dimensional electron energy-loss spectroscopy technique, we directly measure both the local vibrational spectra and the interface phonon dispersion relation for an epitaxial cubic boron nitride/diamond heterointerface. In addition to bulk phonon modes, we observe modes localized at the interface and modes isolated from the interface. These features appear only within approximately one nanometre around the interface. The localized modes observed here are predicted to substantially affect the interface thermal conductance and electron mobility. Our findings provide insights into lattice dynamics at heterointerfaces, and the demonstrated experimental technique should be useful in thermal management, electrical engineering and topological phononics.

Evidence for a spin acoustic surface plasmon from inelastic atom scattering

Closed-shell atoms scattered from a metal surface exchange energy and momentum with surface phonons mostly via the interposed surface valence electrons, i.e., via the creation of virtual electron-hole pairs. The latter can then decay into surface phonons via electron-phonon interaction, as well as into acoustic surface plasmons (ASPs). While the first channel is the basis of the current inelastic atom scattering (IAS) surface-phonon spectroscopy, no attempt to observe ASPs with IAS has been made so far. In this study we provide evidence of ASP in Ni(111) with both Ne atom scattering and He atom scattering. While the former measurements confirm and extend so far unexplained data, the latter illustrate the coupling of ASP with phonons inside the surface-projected phonon continuum, leading to a substantial reduction of the ASP velocity and possibly to avoided crossing with the optical surface phonon branches. The analysis is substantiated by a self-consistent calculation of the surface response function to atom collisions and of the first-principle surface-phonon dynamics of Ni(111). It is shown that in Ni(111) ASP originate from the majority-spin Shockley surface state and are therefore collective oscillation of surface electrons with the same spin, i.e. it represents a new kind of collective quasiparticle: a Spin Acoustic Surface Plasmon (SASP).

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.

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).

Amplitude of jump motion signatures in classical vibration-jump dynamics

The classical Langevin dynamics of a particle in a periodic potential energy landscape are studied via the intermediate scattering function (ISF). By construction, the particle performs coupled vibrational and activated jump motion with a wide separation of the vibrational period and the mean residence time between jumps. The long time limit of the ISF is a decaying tail proportional to the function that describes ideal jump motion in the absence of vibrations. The amplitude of the tail is unity in idealized jump dynamics models but is reduced from unity by the intra-well motion. Analytical estimates of the amplitude of the jump motion signature are provided by assuming a factorization of the conditional probability density of the particle position at long times, motivated by the separation of time scales associated with inter-cell and intra-cell motion. The assumption leads to a factorization of the ISF at long correlation times, where one factor is an ideal jump motion signature and the other component is the amplitude of the signature. The amplitude takes the form of a single-particle anharmonic Debye-Waller factor. The factorization approximation is exact at the diffraction conditions associated with the periodic potential. Numerical simulations of the Langevin equation in one and two spatial dimensions confirm that for a strongly corrugated potential the analytical approximation provides a good qualitative description of the trend in the jump signature amplitude, between the points where the factorization is exact.

The electron-phonon interaction at deep Bi 2 Te3-semiconductor interfaces from Brillouin light scattering

It is shown that the electron-phonon interaction at a conducting interface between a topological insulator thin film and a semiconductor substrate can be directly probed by means of high-resolution Brillouin light scattering (BLS). The observation of Kohn anomalies in the surface phonon dispersion curves of a 50 nm thick Bi₂Te₃ film on GaAs, besides demonstrating important electron-phonon coupling effects in the GHz frequency domain, shows that information on deep interface electrons can be obtained by tuning the penetration depth of optically-generated surface phonons so as to selectively probe the interface region, as in a sort of quantum sonar.

Two-Dimensional Excitonic Photoluminescence in Graphene on a Cu Surface

Despite having outstanding electrical properties, graphene is unsuitable for optical devices because of its zero band gap. Here, we report two-dimensional excitonic photoluminescence (PL) from graphene grown on a Cu(111) surface, which shows an unexpected and remarkably sharp strong emission near 3.16 eV (full width at half-maximum ≤3 meV) and multiple emissions around 3.18 eV. As temperature increases, these emissions blue shift, displaying the characteristic negative thermal coefficient of graphene. The observed PL originates from the significantly suppressed dispersion of excited electrons in graphene caused by hybridization of graphene π and Cu d orbitals of the first and second Cu layers at a shifted saddle point 0.525(M+K) of the Brillouin zone. This finding provides a pathway to engineering optoelectronic graphene devices, while maintaining the outstanding electrical properties of graphene.

Unlocking new contrast in a scanning helium microscope

Delicate structures (such as biological samples, organic films for polymer electronics and adsorbate layers) suffer degradation under the energetic probes of traditional microscopies. Furthermore, the charged nature of these probes presents difficulties when imaging with electric or magnetic fields, or for insulating materials where the addition of a conductive coating is not desirable. Scanning helium microscopy is able to image such structures completely non-destructively by taking advantage of a neutral helium beam as a chemically, electrically and magnetically inert probe of the sample surface. Here we present scanning helium micrographs demonstrating image contrast arising from a range of mechanisms including, for the first time, chemical contrast observed from a series of metal–semiconductor interfaces. The ability of scanning helium microscopy to distinguish between materials without the risk of damage makes it ideal for investigating a wide range of systems.

Scanning helium microscopy uses neutral atoms to image traditionally challenging materials (e.g. delicate, insulating and magnetic samples) non-destructively with absolute surface sensitivity. This work reports the first observation of chemical contrast in helium microscopy via inelastic scattering.

Graphene on Ni(111): Electronic Corrugation and Dynamics from Helium Atom Scattering

Using helium atom scattering, we have studied the structure and dynamics of a graphene layer prepared in situ on a Ni(111) surface. Graphene/Ni(111) exhibits a helium reflectivity of ∼20% for a thermal helium atom beam and a particularly small surface electron density corrugation ((0.06 ± 0.02) Å peak to peak height). The Debye-Waller attenuation of the elastic diffraction peaks of graphene/Ni(111) and Ni(111) was measured at surface temperatures between 150 and 740 K. A surface Debye temperature of θ_D = (784 ± 14) K is determined for the graphene/Ni(111) system and θ_D = (388 ± 7) K for Ni(111), suggesting that the interlayer interaction between graphene and the Ni substrate is intermediary between those for strongly interacting systems like graphene/Ru(0001) and weakly interacting systems like graphene/Pt(111). In addition we present measurements of low frequency surface phonon modes on graphene/Ni(111) where the phonon modes of the Ni(111) substrate can be clearly observed. The similarity of these findings with the graphene/Ru(0001) system indicates that the bonding of graphene to a metal substrate alters the dynamic properties of the graphene surface strongly and is responsible for the high helium reflectivity of these systems.

How Atomic Steps Modify Diffusion and Inter-adsorbate Forces: Empirical Evidence from Hopping Dynamics in Na/Cu(115)

We followed the collective atomic-scale motion of Na atoms on a vicinal Cu(115) surface within a time scale of pico- to nanoseconds using helium spin echo spectroscopy. The well-defined stepped structure of Cu(115) allows us to study the effect that atomic steps have on the adsorption properties, the rate for motion parallel and perpendicular to the step edge, and the interaction between the Na atoms. With the support of a molecular dynamics simulation we show that the Na atoms perform strongly anisotropic 1D hopping motion parallel to the step edges. Furthermore, we observe that the spatial and temporal correlations between the Na atoms that lead to collective motion are also anisotropic, suggesting the steps efficiently screen the lateral interaction between Na atoms residing on different terraces.

Hybridization of surface waves with organic adlayer librations: a helium atom scattering and density functional perturbation theory study of methyl-Si(111)

The interplay of the librations of a covalently bound organic adlayer with the lattice waves of an underlying semiconductor surface was characterized using helium atom scattering in conjunction with analysis by density functional perturbation theory. The Rayleigh wave dispersion relation of CH3- and CD3-terminated Si(111) surfaces was probed across the entire surface Brillouin zone by the use of inelastic helium atom time-of-flight experiments. The experimentally determined Rayleigh wave dispersion relations were in agreement with those predicted by density functional perturbation theory. The Rayleigh wave for the CH3- and CD3-terminated Si(111) surfaces exhibited a nonsinusoidal line shape, which can be attributed to the hybridization of overlayer librations with the vibrations of the underlying substrate. This combined synthetic, experimental, and theoretical effort clearly demonstrates the impact of hybridization between librations of the overlayer and the substrate lattice waves in determining the overall vibrational band structure of this complex interface.

Determination of the surface corrugation amplitude from classical atom scattering

The energy landscape of an atomic or molecular projectile interacting with a surface is often described in terms of a corrugation function that gives the classical turning point as a function of position vector parallel to the surface. It is shown here that the relative height variation of the corrugation function for scattering of atoms under classical conditions can be determined by a measurement of the maximum intensity in energy-resolved scattering spectra as a function of surface temperature. This is demonstrated by developing a semiclassical quantum theory of atomic scattering from corrugated surfaces and then extending the theory to the classical limit of large incident energies and high surface temperatures. Comparisons of calculations with available data for Ar atom scattering determine the corrugation amplitude for a molten In surface to be about 29% of the mean interparticle spacing in the bulk liquid.

Interaction of phonons and dirac fermions on the surface of Bi2Se3: a strong Kohn anomaly

We report the first measurements of phonon dispersion curves on the (001) surface of the strong three-dimensional topological insulator Bi2Se3. The surface phonon measurements were carried out with the aid of coherent helium beam surface scattering techniques. The results reveal a prominent signature of the exotic metallic Dirac fermion quasiparticles, including a strong Kohn anomaly. The signature is manifest in a low energy isotropic convex dispersive surface phonon branch with a frequency maximum of 1.8 THz and having a V-shaped minimum at approximately 2kF that defines the Kohn anomaly. Theoretical analysis attributes this dispersive profile to the renormalization of the surface phonon excitations by the surface Dirac fermions. The contribution of the Dirac fermions to this renormalization is derived in terms of a Coulomb-type perturbation model.

Vibrational properties of the LiNbO3 z-surfaces

The existence of localized vibrational modes both at the positive and at the negative LiNbO3 (0001) surface is demonstrated by means of first-principles calculations and Raman spectroscopy measurements. First, the phonon modes of the crystal bulk and of the (0001) surface are calculated within the density functional theory. In a second step, the Raman spectra of LiNbO(3) bulk and of the two surfaces are measured. The phonon modes localized at the two surfaces are found to be substantially different, and are also found to differ from the bulk modes. The calculated and measured frequencies are in agreement within the error of the method. Raman spectroscopy is shown to be sensitive to differences between bulk and surface and between positive and negative surface. It represents therefore an alternative method to determine the surface polarity, which does not exploit the pyroelectric or piezoelectric properties of the material.