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

Electron-Phonon Coupling and Phonon Dynamics in Single-Layer NbSe2 on Graphene: The Role of Moiré Phonons

The interplay between substrate interactions and electron-phonon coupling in two-dimensional (2D) materials presents a significant challenge in understanding and controlling their electronic properties. Here, we present a comparative study of the structural characteristics, phonon dynamics, and electron-phonon interactions in bulk and monolayer NbSe2 on epitaxial bilayer graphene (BLG) using helium atom scattering (HAS). High-resolution helium diffraction reveals a (9 × 9)0° superstructure within the NbSe2 monolayer, commensurate with the BLG lattice, while out-of-plane HAS diffraction spectra indicate a low-corrugated (3√3 × 3√3)30° substructure. By monitoring the thermal attenuation of the specular peak across a temperature range of 100 to 300 K, we determined the electron-phonon coupling constant (λHAS) as 0.76 for bulk 2H-NbSe2. In contrast, the NbSe2 monolayer on graphene exhibits a reduced λHAS of 0.55, corresponding to a superconducting critical temperature (TC) of 1.56 K according to the MacMillan formula, consistent with transport measurement findings. Inelastic HAS data provide, besides a set of dispersion curves of acoustic and lower optical phonons, a soft, dispersionless branch of phonons at 1.7 meV, attributed to the interface localized defects distributed with the superstructure period, thus termed Moiré phonons. Our data show that Moiré phonons contribute significantly to the electron-phonon coupling in monolayer NbSe2. These results highlight the crucial role of the BLG in the electron-phonon coupling in monolayer NbSe2, attributed to enhanced charge transfer effects, providing valuable insights into substrate-dependent electronic interactions in 2D superconductors.

Distinguishing Quasiparticle-Phonon Interactions by Ultrahigh-Resolution Lifetime Measurements

We present a determination of quasiparticle-phonon interaction strengths at surfaces through measurements of phonon spectra with ultrahigh energy resolution. The lifetimes of low energy surface phonons on a pristine Ru(0001) surface were determined over a wide range of temperatures and an analysis of the temperature dependence enables us to attribute separate contributions from electron-phonon interactions, phonon-phonon interactions, and defect-phonon interactions. Strong electron-phonon interactions are evident at all temperatures and we show they dominate over phonon-phonon interactions below 400 K.

Anharmonic theory of superconductivity and its applications to emerging quantum materials

The role of anharmonicity on superconductivity has often been disregarded in the past. Recently, it has been recognized that anharmonic decoherence could play a fundamental role in determining the superconducting properties (electron-phonon coupling, critical temperature, etc) of a large class of materials, including systems close to structural soft-mode instabilities, amorphous solids and metals under extreme high-pressure conditions. Here, we review recent theoretical progress on the role of anharmonic effects, and in particular certain universal properties of anharmonic damping, on superconductivity. Our focus regards the combination of microscopic-agnostic effective theories for bosonic mediators with the well-established BCS theory and Migdal-Eliashberg theory for superconductivity. We discuss in detail the theoretical frameworks, their possible implementation within first-principles methods, and the experimental probes for anharmonic decoherence. Finally, we present several concrete applications to emerging quantum materials, including hydrides, ferroelectrics and systems with charge density wave instabilities.

Surface properties of 1T-TaS2 and contrasting its electron-phonon coupling with TlBiTe2 from helium atom scattering

We present a detailed helium atom scattering study of the charge-density wave (CDW) system and transition metal dichalcogenide 1T-TaS2. In terms of energy dissipation, we determine the electron-phonon (e-ph) coupling, a quantity that is at the heart of conventional superconductivity and may even "drive" phase transitions such as CDWs. The e-ph coupling of TaS2 in the commensurate CDW phase (λ = 0.59 ± 0.12) is compared with measurements of the topo-logical insulator TlBiTe2 (λ = 0.09 ± 0.01). Furthermore, by means of elastic He diffraction and resonance/interference effects in He scattering, the thermal expansion of the surface lattice, the surface step height, and the three-dimensional atom-surface interaction potential are determined including the electronic corrugation of 1T-TaS2. The linear thermal expansion coefficient is similar to that of other transition-metal dichalcogenides. The He-TaS2 interaction is best described by a corrugated Morse potential with a relatively large well depth and supports a large number of bound states, comparable to the surface of Bi2Se3, and the surface electronic corrugation of 1T-TaS2 is similar to the ones found for semimetal surfaces.

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.

The role of high-energy phonons in electron-phonon interaction at conducting surfaces with helium-atom scattering

In previous works it has been shown that the Debye-Waller (DW) exponent for Helium atom specular reflection from a conducting surface, when measured as a function of temperature in the linear high-temperature regime, allows for the determination of the surface electron-phonon coupling. However, there exist a number of experimental measurements that exhibit non-linearities in the DW exponent as a function of the surface temperature. Such non-linearities have been suggested as due to vibrational anharmonicity or a temperature dependence of the surface carrier concentration. In this work, it is suggested, on the basis of a few recent experimental data, that the deviations from linearity of the DW exponent temperature-dependence, as observed for conducting surfaces or supported metal overlayers with the present high-resolution He-atom scattering, permit to single out the specific role of high-energy phonons in the surface electron-phonon mass-enhancement factor.

Surface electronic corrugation of a one-dimensional topological metal: Bi(114)

The surface of Bi(114) is a striking example where the reduced dimensionality gives rise to structural rearrangement and new states at the surface. Here, we present a study of the surface structure and electronic corrugation of this quasi one-dimensional topological metal based on helium atom scattering (HAS) measurements. In contrast to low-index metal surfaces, upon scattering from the stepped (114) truncation of Bi, a large proportion of the incident beam is scattered into higher order diffraction channels which in combination with the large surface unit cell makes an analysis challenging. The surface electronic corrugation of Bi(114) is determined, using measurements upon scattering normal to the steps, together with quantum mechanical scattering calculations. Therefore, minimisation routines that vary the shape of the corrugation are employed, in order to minimise the deviation between the calculations and experimental scans. Furthermore, we illustrate that quantum mechanical scattering calculations can be used to determine the orientation of the in- and outgoing beam with respect to the stepped surface structure.

Correction: Benedek et al. Measuring the Electron–Phonon Interaction in Two-Dimensional Superconductors with He-Atom Scattering. Condens. Matter 2020, 5, 79

In the original publication [...]

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.