Metals at room temperature are traditionally described by the one-electron approximation in which the electrons act independently and have a spectrum of energies and momenta that form energy bands. Among metals, tungsten has a particularly long history as a subject for surface science and therefore provides a well-characterized starting point for the investigation of many-body effects at surfaces by the technique of angle-resolved photoemission (ARPES). With ARPES, researchers can create energy-momentum "maps" of the energy bands for both "bulk" electrons with momenta in three dimensions and surface electrons with momenta in two dimensions parallel to the surface.

(a) For hydrogen on tungsten(110), the splitting of the S₁ surface band near the energy of the symmetric hydrogen stretching mode (dashed line) is clearly visible in ARPES spectra. (b) On substituting deuterium for hydrogen, the vibrational energy decreases because of the H-D isotope effect, and the splitting becomes smaller. (c) In less surface-localized bands (S₂ and B) having poorer overlap to the surface phonon modes, the effects for H disappear altogether.

 

Vibrating Atoms Shape Electrons on Surfaces

Almost any object one can imagine has a surface that separates what's inside from what's outside, the city limits, as it were. In addition to this boundary function, surfaces often have unique features that set them apart from the "bulk" or interior. The electrons at the surface of a material are a case in point. While in the past it has been both computationally convenient and scientifically fruitful to treat electrons as independent particles (one-electron model), this is not the situation at the frontiers of solid-state physics where exotic effects resulting from the collective action of electrons interacting with each other and with other excitations, such as vibrating atoms, predominate.

Since these "many-body" effects are often more prominent in physical systems with less than three dimensions, carefully prepared surfaces furnish good two-dimensional test beds for examining these effects in detail. In the experiments reported here, scientists from the ALS and the University of Oregon showed that the energy spectrum of electrons at the surface of tungsten is modified as the result of a strong interaction (coupling) between the electrons and vibrating hydrogen atoms deposited on the surface. This work demonstrates directly how vibrational energy of surface atoms (and molecules) is dissipated into electronic excitations on a metal, a finding that may benefit those studying catalysis of chemical reactions on surfaces, reactions of considerable industrial import.

In earlier ARPES studies, the ALS/Oregon team discovered that the momenta of electrons at the Fermi energy for two-dimensional energy bands on the (110) surface of tungsten were highly sensitive to the amount of hydrogen on the surfaces. It is one of these surface bands that the new ARPES measurements show is altered by the hydrogen atomic vibrations. In the one-electron model, the creation and destruction of lattice-vibrational quanta (phonons) is a principal mechanism for driving transitions between quantum states as electrons relax or are thermally excited. But in the new experiments, the connection between lattice vibrations and electrons is much more intimate, and it is necessary to think of the two entities forming a composite, many-body system with its own spectrum of energies.

The tell-tale sign of the electron-phonon interactions involving hydrogen is that the energy for the onset of the band splitting matches the energy of the symmetric hydrogen stretching vibration mode. The electron vacancy (hole) left as a result of photoemission has two possible characters depending on its energy. If the hole energy is sufficiently large, its lifetime is short because it can decay into phonons, whereas holes with energies closer to the Fermi energy cannot decay into real phonons. Instead, these holes are longer-lived and carry a cloud of "virtual" phonons that effectively raise the mass of the hole. The hydrogen vibration frequency sets the energy scale that divides these two characteristic behaviors.

The critical test of this explanation is that substituting deuterium (which is heavier than hydrogen and consequently has a smaller vibrational frequency) for hydrogen decreased the onset energy for band splitting. Moreover, among the various surface and bulk bands present, only the particular surface band that is most strongly confined to the surface shows a strong electron-phonon coupling effect, evidence that the interaction is confined to the hydrogen surface layer.

ARPES intensity maps of surface band S₁ in the presence of (a) hydrogen and (b) deuterium with the fitted positions (circles) of the two peaks, the best-fit lines through these data, and the known hydrogen and deuterium symmetric stretch vibrational energies (horizontal dashed lines). From the slopes of these lines, once can derive the electron-phonon coupling parameters.

The results have potential practical implications. That electrons and holes can decay to phonons also implies the reverse: that phonons can decay by excitation of electron-hole pairs. This is an important dissipation channel for energy and will affect chemical reactions at surfaces, such as reactions on catalysts. Another interesting implication is the possibility of an electron-phonon-mediated superconductivity that is confined to the surfaces of metals and has a greatly enhanced critical temperature as compared to ordinary superconductors.

Research conducted by E. Rotenberg (ALS) and J. Schaefer and S.D. Kevan (University of Oregon).

Research Funding: Office of Basic Energy Sciences (BES), U. S. Department of Energy. Operation of the ALS is supported by BES.

Publication about this research: E. Rotenberg, J. Schaefer, and S.D. Kevan "Coupling between adsorbate vibrations and an electronic surface state," Phys. Rev. Lett. 84, 2925 (2000).