## 2019

### Statics and dynamics of multivalley charge density waves in Sb(111)

Anton Tamtögl, **Patrick Kraus**, Michael Mayrhofer-Reinhartshuber, Giorgio Benedek, Marco Bernasconi, Daniele Dragoni, Davide Campi and Wolfgang E. Ernst

in: npj Quantum Materials 4, Article Number: 28 (2019)

#### Abstract

Charge density waves (CDWs), periodic modulations of the charge density, are among the most abundant and non-trivial ordered phases in condensed matter. Here we demonstrate the occurrence of multi-valley charge density waves (MV-CDW) on the semimetal Sb(111), a phenomenon previously observed at semiconductor surface inversion layers. The topological nature of the pocket surface states in Sb(111) ensures perfect nesting conditions giving rise to sharp peaks in helium atom scattering (HAS) diffraction spectra. The peculiar temperature dependence permits to distinctly associate the diffraction peaks with surface electron and hole-pocket states due to the non-trivial surface electronic band structure known from recent experimental data and present ab-initio calculations. Inelastic HAS spectra, besides providing the surface phonon dispersion curves in agreement with density functional perturbation theory calculations, reveal two additional dispersion curves of elementary excitations in the gap well below Rayleigh waves. They are attributed to collective excitations of the quasi-commensurate MV-CDWs associated with the surface electron M-pocket states at the Fermi level. These findings suggest that HAS can be regarded as a choice spectroscopy for the investigation of surface electronic excitations in the THz domain, opening up a new window for the search of collective phases at surfaces.

## 2017

### Electron-phonon coupling and Surface Debye temperature of Bi2Te3(111) from helium atom scattering

Anton Tamtögl, **Patrick Kraus**, Nadav Avidor, Martin Bremholm, Ellen M. Hedegaard, Bo B. Iversen, Marco Bianchi, Philip Hofmann, John Ellis, William Allison, Giorgio Benedek and Wolgang E. Ernst

in: Physical Review / B 95 (2017) 195401

#### Abstract

We have studied the topological insulator Bi2Te3(111) by means of helium atom scattering. The average electron-phonon coupling λ of Bi2Te3(111) is determined by adapting a recently developed quantum-theoretical derivation of the helium scattering probabilities to the case of degenerate semiconductors. Based on the Debye-Waller attenuation of the elastic diffraction peaks of Bi2Te3(111), measured at surface temperatures between 110 and 355K, we find λ to be in the range of 0.04–0.11. This method allows us to extract a correctly averaged λ and to address the discrepancy between previous studies. The relatively modest value of λ is not surprising even though some individual phonons may provide a larger electron-phonon interaction. Furthermore, the surface Debye temperature of Bi2Te3(111) is determined as ΘD=(81±6)K. The electronic surface corrugation was analyzed based on close-coupling calculations. By using a corrugated Morse potential a peak-to-peak corrugation of 9% of the lattice constant is obtained.

## 2016

### Adhesion properties of hydrogen on Sb(111) probed by helium atom scattering

**Kraus, P.**; Gösweiner, C.; Tamtögl, A.; Apolloner, F.; Ernst, W.E.

in: Europhysics Letters, 2016, 114 (5)

#### Abstract

We have carried out a series of helium atom scattering measurements in order to characterise the adsorption properties of hydrogen on antimony(111). Molecular hydrogen does not adsorb at temperatures above 110 K in contrast to pre-dissociated atomic hydrogen. Depending on the substrate temperature, two different adlayer phases of atomic hydrogen on Sb(111) occur. At low substrate temperatures (110 K), the deposited hydrogen layer does not show any ordering while we observe a perfectly ordered 1×1 H/Sb(111) structure for deposition at room temperature. Furthermore, the amorphous hydrogen layer deposited at low temperature forms an ordered overlayer upon heating the crystal to room temperature. Hydrogen starts to desorb at T_m = 430 K which corresponds to a desorption energy of E_des = (1.33 ± 0.06) eV. Using measurements of the helium reflectivity during hydrogen exposure at different surface temperatures, we conclude that the initial sticking coefficient of atomic hydrogen on Sb(111) decreases with increasing surface temperature. Furthermore, the scattering cross-section for the diffuse scattering of helium from hydrogen on Sb(111) is determined as Sigma = (12 ± 1) Å^2$ .

## 2015

### Surface Structure of Bi(111) from Helium Atom Scattering Measurements. Inelastic Close Coupling Formalism

**Kraus, P.;** Tamtögl, A.; Mayrhofer-Reinhartshuber M.; Apolloner, F.; Gösweiner, C.; Miret-Artés, S.; Ernst, W.E.

in: J. Phys. Chem. C, 2015, 119 (30), pp 17235-17242

#### Abstract

Elastic and inelastic close-coupling (CC) calculations have been used to extract information about the corrugation amplitude and the surface vibrational atomic displacement by fitting to several experimental diffraction patterns. To model the three-dimensional interaction between the He atom and the Bi(111) surface under investigation, a corrugated Morse potential has been assumed. Two different types of calculations are used to obtain theoretical diffraction intensities at three surface temperatures along the two symmetry directions. Type one consists of solving the elastic CC (eCC) and attenuating the corresponding diffraction intensities by a global Debye–Waller (DW) factor. The second one, within a unitary theory, is derived from merely solving the inelastic CC (iCC) equations, where no DW factor is necessary to include. While both methods arrive at similar predictions for the peak-to-peak corrugation value, the variance of the value obtained by the iCC method is much better. Furthermore, the more extensive calculation is better suited to model the temperature induced signal asymmetries and renders the inclusion for a second Debye temperature for the diffraction peaks futile.

## 2014

### A Comparative Study of the He-Sb(111) Interaction Potential from Close-Coupling Calculations and Helium Atom Scattering Experiments

**Kraus, P.;** Mayrhofer-Reinhartshuber M.; Gösweiner, C.; Apolloner, F.; Miret-Artés, S.; Ernst, W.E.

in: Surface Science 630 (2014), S 208-215

#### Abstract

The exact elastic close-coupling formalism is used to compare the performance of several interaction potentials suggested in literature for describing the measured elastic diffraction peak intensities in helium scattering experiments. The coupling parameters have been analytically calculated for the corrugated Morse potential on a hexagonal surface structure and adapted for usage with similar interaction potentials. The potentials used have been fitted to previously known bound state energies complemented by two additional levels which are found by improving energy resolution. It is established that the shifted Morse potential reproduces the experimental He–Sb(111) bound state more closely than the other considered potential shapes. The performance of several interaction potentials in describing the elastic scattering intensities is presented and discussed. Morse and Morse-related potentials provide the best compromise for the description of elastic scattering intensities. The different effects of the potential shape were determined by comparing the calculated scattering intensities.

## 2013

### Helium atom scattering investigation of the Sb(111) surface.

Mayrhofer-Reinhartshuber M.; Tamtögl, A.; **Kraus, P.;** Ernst, W.E.

in: Journal of Physics / Condensed matter 25 (2013), S 395002-1 – 395002-9

#### Abstract

The Sb(111) surface was studied with helium atom scattering (HAS). Elastic HAS at different energies of the incident helium beam (15.3, 21.9, 28.4 meV) was applied for structural investigations. The lattice constants derived from the positions of the observed diffraction peaks up to third order were found to be in perfect agreement with previous structure determinations of Sb(111). The observed diffraction patterns with clear peaks up to second order were used to model the electronic surface corrugation with the GR method. As an estimation for the attractive part of the interaction potential a well depth of (4.0 ± 0.5) meV was found. Best fit results were obtained with a corrugation height of 12–13% of the lattice constant, which is rather large compared to other surfaces with metallic character. Intensity measurements of the specular peak as a function of incident energy were analysed to determine the distribution of terraces on the surface. The results show a quite flat Sb(111) surface and a step height of 3.81 Å of the remaining terraces.

### Resonance-enhanced inelastic He-atom scattering from subsurface optical phonons of Bi(111)

**Kraus, P.;** Tamtögl, A.; Mayrhofer-Reinhartshuber M.; Benedek, G.; Ernst, W.E.

in: Physical Review / B 87 (2013) 24 245433, S. 245433-1 – 245433-7

#### Abstract

Helium-atom scattering angular distributions from Bi(111) show a number of selective-adsorption resonance features corresponding to three bound states of the He atom in the surface-averaged Bi(111) potential. They are well represented by a 3-9 potential with a potential depth of 8.3 meV. The bound-state resonance enhancement of inelastic scattering is shown to provide the mechanism for the observation of subsurface optical phonons and for their comparatively large intensity.

### Surface and Sub-surface Phonons of Bi(111) Measured with Helium Atom Scattering.

Tamtögl, A.; **Kraus, P.;** Mayrhofer-Reinhartshuber M.; Campi, D.; Bernasconi, M.; Benedek, G.; Ernst, W.E.

in: Physical Review / B 87 (2013) 3, S. 035410-1 – 035410-10

#### Abstract

The surface phonon dispersion curves of Bi(111) have been measured by inelastic helium atom scattering (HAS) along the two symmetry directions. The complex set of observed dispersion curves, including several branches in the acoustic region, plus a localized and a resonant branch in the optical region, is interpreted by means of calculations based on density functional perturbation theory (DFPT). It is recognized that the upper phonon branches in the acoustic region starting at about 5.3 meV and 4.3 meV at zero wave vector correspond to shear-vertical and longitudinal modes localized on the third surface layer (second bilayer), respectively. The HAS ability of detecting subsurface phonons previously observed for Pb(111) multilayers is attributed to the comparatively strong electron-phonon interaction, and confirmed through a DFPT calculation of the phonon-induced surface charge-density oscillations. A comparison of the integrated HAS intensities with those of Pb(111) multilayers measured under similar kinematic conditions allows for an estimation of the electron-phonon mass-enhancement parameter for the Bi(111) surface. An anomaly at the M point, quite sharp at 123 K but very broad at room temperature, is associated with recombination processes of bulk M-point pocket electrons with bulk pocket holes at either Γ or equivalent M points.

### Surface Debye Temperature and Vibrational Dynamics of Antimony(111)

Tamtögl, A.; Mayrhofer-Reinhartshuber M.; **Kraus, P.;** Ernst, W.E.

in: Surface Science 617 (2013), S. 225-228

#### Abstract

The surface Debye temperature and the vibrational dynamics of Sb(111) were studied using helium atom scattering. The Debye–Waller attenuation of the elastic diffraction peaks was measured at surface temperatures between 98 K and 447 K. A surface Debye temperature of (155 ± 3) K is obtained within the description originally derived for electron diffraction. The attractive well depth for the He–Sb(111) interaction is determined to be (4.5 ± 0.5) meV. The perpendicular mean-square displacement for the surface at room temperature is estimated to be (1.8 ± 0.4) × 10^−2 Å^2.

### The Atom-Surface Interaction Potential of Sb(111) Measured with Helium Atom Scattering

Mayrhofer-Reinhartshuber M.; **Kraus, P.;** Tamtögl, A.; Miret-Artés, S.; Ernst, W.E.

in: Physical Review / B 88 (2013) 20, S. 205425-1 – 205425-11

#### Abstract

Helium atom scattering (HAS) was used to study the antimony Sb(111) surface beyond the hard-wall model. HAS angular distributions and drift spectra show a number of selective adsorption resonance features, which correspond to five bound-state energies for He atoms trapped in the surface-averaged He-Sb(111) potential. As their best representation, a 9-3 potential with a depth of (4.4 ± 0.1) meV was determined. Furthermore, the charge density corrugation of the surface was analyzed using close-coupling calculations. By using a hybrid potential, consisting of a corrugated Morse potential (short range) and a 9-3 potential (long range), a peak-to-peak corrugation of 17% was obtained. The kinematic focusing effects that occurred were in good agreement with surface phonon dispersion curves from already published density functional perturbation theory calculations.

## 2012

### Vibrational dynamics and durface structure of Bi(111) from helium atom scattering measurements

Mayrhofer-Reinhartshuber M.; Tamtögl, A.; **Kraus, P.;** Rieder, K.-H.; Ernst, W.E.

in: Journal of Physics / Condensed matter 24 (2012) 10, S. 104008 – 104013

#### Abstract

The Bi(111) surface was studied by elastic scattering of helium atoms at temperatures between 118 and 423 K. The observed diffraction patterns with clear peaks up to third order were used to model the surface corrugation using the eikonal approximation as well as the GR method. Best fit results were obtained with a rather large corrugation height compared to other surfaces with metallic character. The corrugation shows a slight enhancement of the surface electron density in between the positions of the surface atoms. The vibrational dynamics of Bi(111) were investigated by measurements of the Debye–Waller attenuation of the elastic diffraction peaks and a surface Debye temperature of (84 ± 8) K was determined. A decrease of the surface Debye temperature at higher temperatures that was recently observed on Bi nanofilms could not be confirmed in the case of our single-crystal measurements.

# Präsentationen bei internationalen Konferenzen

## 2016

### Evidence for an extremely low-lying electron-hole excitation mode in the Sb(111)-phonon dispersion measured by HAS

Frühjahrstagung der Deutschen Physikalischen Gesellschaft, Regensburg, Deutschland

## 2015

### Investigation of surface structure and diffusion dynamics of hydrogen absorbed on Sb(111)

15th International Conference on Vibrations at Surfaces, VAS-15, San Sebastián, Spanien

### Determination of the Sb(111)-phonon dispersion relation using inelastic HAS measurements

European Conference on Surface Science, ECOSS-31, Barcelona, Spanien

### Helium atom scattering measurements revealing the full phononic disperion of Sb(111)

Jahrestagung der Österreichischen Physikalischen Gesellschaft ÖPG-65, Wien, Österreich

## 2014

### Unraveling inelastic HAS intensities on Sb(111): Evidence for an extremely low-lying acoustic plasmon mode

European Conference on Surface Science, ECOSS-30, Antalya, Türkei

### Measuring the mode-selective e-ph interaction constant on Sb(111) using Helium Atom Scattering (HAS)

Frühjahrstagung der Deutschen Physikalischen Gesellschaft, Dresden, Deutschland

### Inelastic HAS intensities on Sb(111): Indication of a low-lying acoustic plasmon mode

Jahrestagung der Österreichischen Physikalischen Gesellschaft ÖPG-64, Pöllau, Österreich

## 2013

### Bound-state resonance effects in the mode-selected electron-phonon coupling strenghts measured by He atom scattering

15th International Conference on Solid Surfaces ICSS-15, Paris, Frankreich

## 2012

### Observation of non-adiabatic Kohn anomalies on Bi(111) – inducing spin-flip electronic transitions using Helium Atom Scattering

14th International Conference on Vibrations at Surfaces, Kobe, Japan

# Posterpräsentationen bei internationalen Konferenzen

## 2015

### Measuring the Sb(111) phonon dispersion using HAS: Evidence for an extremely low lying acoustic plasmon mode

15th International Conference on Vibrations at Surfaces Donostia/San Sebastián, Spanien

## 2014

### Phonon-assisted electron-hole relaxations on Sb(111) and Bi(111) in iHAS measurements

XXIInd International Symposium on the Jahn-Teller Effect, Graz, Österreich

## 2013

### Indication of phonon-assisted electron-hole relaxations on Sb(111) and Bi(111) in iHAS Measurements

Jahrestagung der Österreichischen Physikalischen Gesellschaft ÖPG-63, Linz Österreich

## 2012

### Exploiting Resonance Effects on Bi(111)

European Conference on Surface Science, ECOSS-29, Edinburgh, Schottland

## 2011

### Calculation of surface phonon dispersions on Bi(111)

Joint Annual Meeting of the Swiss Physical Society and the Austrian Physical Society ÖPG/SPS, Lausanne, Schweiz