Determination of the photoelectron reference plane in nanostructured surfaces

Abstract

View the article online for updates and enhancements. and Enrique G Michel Abstract. In angle-resolved photoemission (ARPES) from crystalline solids, wave-vector conservation applies to the two-dimensional (2D) surface, which may thus be defined as the reference plane in ARPES. We investigate whether such reference varies for photoemitted electrons in nanometer-sized systems that expose different crystal planes. To this aim, we exploit the structural tunability of the Ag/Cu(223) system which is capable of offering surfaces with periodic arrays of nanofacets of varying size and orientation. A thorough, photonenergy-dependent analysis of the surface states confined to such nanostructures is performed comparing different reference planes for photoemitted electrons. Assuming the premise that k || must be a good quantum number for 2D states, we conclude that the (final state) photoelectron reference direction is not the average optical direction but the local facet that confines the (initial state) surface 7 Author to whom any correspondence should be addressed. electrons. Moreover, in the general case of nanostructured systems with uneven surfaces, we show how the photoelectron reference plane can be empirically determined through such a photon-energy-dependent ARPES analysis. Contents

Lateral confinement effects of M¯-point Tamm state in vicinal Cu(100) surfaces

“…Note that the experimental points line up perpendicular to the surface optical plane for the three surfaces, indicating that k ∥ measured with respect to the optical surface does not depend on k ⊥ , and thus it is a conserved quantity [20]. This behavior indicates also that the surface state wave function is referred to the optical surface, and not to the individual terraces [14,20]. In the case of Cu(410), there are two Umklapps, separated by 2π/d 420 and aligned along the optical surface normal direction.…”

“…A remarkable aspect found in vicinal (111) noble metal surfaces is that increasing d this regime changes into confinement of the surface state wave function within the terrace width, resulting in a 2D to 1D crossover at a critical d length value around~20 Å [18]. The transition from one regime into the other is reflected not only in the appearance of confined electronic states [15], but also in a modification of the reference plane of the electron wave function, from the average optical surface into the terraces [14,20]. Fig.…”

“…Steps act as a potential barrier for the surface electrons and depending on the superperiodicity, the wave function of the surface state switches at a critical miscut angle from being localized at the terraces to being delocalized along the optical surface. This means that the 2D surface states displaying superlattice band folding split into 1D quantum well levels with increasing terrace size (d) [12,[14][15][16][17][18][19][20]. The switching has been attributed to a decrease in the effective step barrier, due to the closing of the band gap after a critical miscut angle [12,14,21,22], or to localization induced by disorder [17].…”

Reference plane for the electronic states in thin films on stepped surfaces

“…Recent investigations suggest that the effects of 1D confinement derive from the reduced structural order of the step lattice for large interstep distances [17]. The ARPES analysis of faceted crystals [18] and Ag stripes on Cu vicinal surfaces [1,19,20] shows in a direct way how the local surface atomic structure, rather than the optical surface, defines the photoelectron reference plane in nanostructured systems.…”

“…A consequence is seen in the photoelectric effect, in which an electron is emitted from the surface into the vacuum. The discrete translational symmetry of crystalline surfaces imposes that, during the photoemission process, the parallel component of the photoelectron momentum k || is conserved across the modulation plane of the wave function, i.e., the so-called reference plane [1]. The identification of this plane is straightforward for low Miller index surfaces, where the average (optical) surface and the terrace plane coincide.…”