One-dimensional potential for image-potential states on graphene

In the framework of dielectric theory the static non-local self-energy of an electron near an ultra-thin polarizable layer has been calculated and applied to study binding energies of image-states near free-standing graphene. The corresponding series of eigenvalues and eigenfunctions have been obtained by solving numerically the one-dimensional Schr{\"o}dinger equation. Image-potential-state wave functions accumulate most of their probability outside the slab. We find that a Random Phase Approximation (RPA) for the non-local dielectric function yields a superior description for the potential inside the slab, but a simple Fermi-Thomas theory can be used to get a reasonable quasi-analytical approximation to the full RPA result that can be computed very economically. Binding energies of the image-potential states follow a pattern close to the Rydberg series for a perfect metal with the addition of intermediate states due to the added symmetry of the potential. The formalism only requires a minimal set of free parameters; the slab width and the electronic density. The theoretical calculations are compared to experimental results for work function and image-potential states obtained by two-photon photoemission.Comment: 24 pages; 10 figures. arXiv admin note: text overlap with arXiv:1301.448

Direct resolution of unoccupied states in solids via two photon photoemission

Non-linear effects in photoemission are shown to open a new access to the band structure of unoccupied states in solids, totally different from hitherto used photoemission spectroscopy. Despite its second-order nature, strong resonant transitions occur, obeying exact selection rules of energy, crystal symmetry, and momentum. Ab-initio calculations are used to demonstrate that such structures are present in low-energy laser spectroscopy experimental measurements on Si previously published. Similar resonances are expected in ultraviolet angle-resolved photoemission spectra, as shown in a model calculation on Al.Comment: 12 pages, including 4 figure

Quantum Coherence of Image-Potential States

The quantum dynamics of the two-dimensional image-potential states in front of the Cu(100) surface is measured by scanning tunneling microscopy (STM) and spectroscopy (STS). The dispersion relation and the momentum resolved phase-relaxation time of the first image-potential state are determined from the quantum interference patterns in the local density of states (LDOS) at step edges. It is demonstrated that the tip-induced Stark shift does not affect the motion of the electrons parallel to the surface.Comment: Submitted to Phys. Rev. Lett., 4 pages, 4 figures; corrected typos, minor change

Scanning tunneling microscopy and kinetic Monte Carlo investigation of Cesium superlattices on Ag(111)

Cesium adsorption structures on Ag(111) were characterized in a low-temperature scanning tunneling microscopy experiment. At low coverages, atomic resolution of individual Cs atoms is occasionally suppressed in regions of an otherwise hexagonally ordered adsorbate film on terraces. Close to step edges Cs atoms appear as elongated protrusions along the step edge direction. At higher coverages, Cs superstructures with atomically resolved hexagonal lattices are observed. Kinetic Monte Carlo simulations model the observed adsorbate structures on a qualitative level.Comment: 8 pages, 7 figure

Self-energy and lifetime of Shockley and image states on Cu(100) and Cu(111): Beyond the GW approximation of many-body theory

We report many-body calculations of the self-energy and lifetime of Shockley and image states on the (100) and (111) surfaces of Cu that go beyond the $GW$ approximation of many-body theory. The self-energy is computed in the framework of the GW\Gamma approximation by including short-range exchange-correlation (XC) effects both in the screened interaction W (beyond the random-phase approximation) and in the expansion of the self-energy in terms of W (beyond the GW approximation). Exchange-correlation effects are described within time-dependent density-functional theory from the knowledge of an adiabatic nonlocal XC kernel that goes beyond the local-density approximation.Comment: 8 pages, 5 figures, to appear in Phys. Rev.

Bulk and surface electron dynamics in a p-type topological insulator SnSb2Te4

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY).-- et al.Time-resolved two-photon photoemission was used to study the electronic structure and dynamics at the surface of SnSb2Te4, a p-type topological insulator. The Dirac point is found 0.32±0.03 eV above the Fermi level. Electrons from the conduction band minimum are scattered on a time scale of 43±4 fs to the Dirac cone. From there they decay to the partly depleted valence band with a time constant of 78±5 fs. The significant interaction of the Dirac states with bulk bands is attributed to their bulk penetration depth of ∼3 nm as found from density functional theory calculations.We acknowledge partial support from the Basque Country Government, Departamento de Educacion, Universidades e Investigacion (Grant No. IT-366-07), the Spanish Ministerio de Ciencia e Innovacion (Grant No. FIS2010-19609-C02-00), the Ministry of Education and Science of Russian Federation (Grant No. 2.8575.2013), the Russian Foundation for Basic Research (Grant No. 13-02-12110_ofi_m), and Science Development Foundation under the President of the Republic of Azerbaijan [Grant No. EIF-2011-1(3)-82/69/4-M-50].Peer Reviewe

Unoccupied Topological States on Bismuth Chalcogenides

The unoccupied part of the band structure of topological insulators Bi$_2$Te$_{x}$Se$_{3-x}$ ($x=0,2,3$) is studied by angle-resolved two-photon photoemission and density functional theory. For all surfaces linearly-dispersing surface states are found at the center of the surface Brillouin zone at energies around 1.3 eV above the Fermi level. Theoretical analysis shows that this feature appears in a spin-orbit-interaction induced and inverted local energy gap. This inversion is insensitive to variation of electronic and structural parameters in Bi$_2$Se$_3$ and Bi$_2$Te$_2$Se. In Bi$_2$Te$_3$ small structural variations can change the character of the local energy gap depending on which an unoccupied Dirac state does or does not exist. Circular dichroism measurements confirm the expected spin texture. From these findings we assign the observed state to an unoccupied topological surface state

The role of surface plasmons in the decay of image-potential states on silver surfaces

The combined effect of single-particle and collective surface excitations in the decay of image-potential states on Ag surfaces is investigated, and the origin of the long-standing discrepancy between experimental measurements and previous theoretical predictions for the lifetime of these states is elucidated. Although surface-plasmon excitation had been expected to reduce the image-state lifetime, we demonstrate that the subtle combination of the spatial variation of s-d polarization in Ag and the characteristic non-locality of many-electron interactions near the surface yields surprisingly long image-state lifetimes, in agreement with experiment.Comment: 4 pages, 2 figures, to appear in Phys. Rev. Let

Adiabatic-Connection-Fluctuation-Dissipation approach to the long-range behavior of the exchange-correlation energy at metal surfaces: A numerical study for jellium slabs

A still open issue in many-body theory is the asymptotic behavior of the exchange-correlation energy and potential in the vacuum region of a metal surface. Here we report a numerical study of the position-dependent exchange-correlation energy for jellium slabs, as obtained by combining the formally exact adiabatic-connection-fluctuation-dissipation theorem with either time-dependent density-functional theory or an inhomogeneous Singwi-Tosi-Land-Sj\"olander approach. We find that the inclusion of correlation allows to obtain well-converged semi-infinite-jellium results (independent of the slab thickness) that exhibit an image-like asymptotic behavior close to the classical image potential $V_{im}(z)=-e^2/4z$.Comment: 6 pages, 4 Figure

Time-Resolved Coherent Photoelectron Spectroscopy of Quantized Electronic States on Metal Surfaces

Time-resolved two-photon photoemission in combination with the coherent excitation of several quantum states was used to study the ultrafast electron dynamics of imagepotential states on metal surfaces. For a (100) surface of copper, the spectroscopy of quantum beats made previously unresolved high-order states (quantum number n Ն 4) experimentally accessible. By exciting electrons close to the vacuum level, electron wave packets could be created and detected that described the quasi-classical periodic motion of weakly bound electrons. They traveled more than 200 Å away from the surface and oscillated back and forth with a period of 800 femtoseconds. Photoelectron spectroscopy has developed into one of the most versatile and successful tools for surface studies. Particularly attractive features of this technique are the high surface sensitivity associated with the low escape depth of the photoelectrons and the capability of angle-resolved photoemission to completely characterize electronic states in energy and momentum space (1). Recently, these features have been combined with ultrafast laser excitation for direct time-domain investigations of electron dynamics at surfaces (2). Here, we demonstrate another facet of this powerful technique, the investigation of coherence phenomena in real time. In contrast to experimental methods that rely merely on intensities, coherent spectroscopies offer the unique capability of accessing not only the amplitudes but also the phases of the wave functions of interest (3). This technique dramatically increases the amount of information that one is able to obtain about the temporal evolution of fast processes. In this report, we discuss the dynamics of image-potential states, that is, the quantized excited states of electrons that exist in front of many metal surfaces (4, 5). Using femtosecond time-resolved two-photon photoemission (2PPE), we observed the interference between the wave functions of neighboring eigenstates and the quasi-classical motion of electron wave packets created by the coherent superposition of several quantum states. Recently, the imaging of the static charge density of related surface electronic (ground) states in real space with the scanning tunneling microscope has attracted considerable interest (6); the present results reveal the dynamical evolution of excited electrons in real time. Image-potential states are conceptually rather simple. An electron at a distance z in front of a conducting metal surface experiences an attractive force F(z) ϭ Ϫe 2 /(2z) 2 identical to that produced by a positive (mirror image) charge at a distance z inside the metal converging toward the vacuum energy, where the influence of the surface potential on the binding energy E B ϭ ϪE n is approximated by a quantum defect 0 Յ a Յ 0.5. Experimentally, image-potential states have been studied with 2PPE on many metal surfaces including surfaces covered with adsorbates and metallic overlayers (5, 7-11). One photon with energy ប a (ប is Planck's constant h divided by 2 and is the photon frequency times 2) excites an electron out of an occupied state below the Fermi energy E F into the image-potential state n. A second photon with energy ប b excites the electron to an energy above E vac The experimental setup consisted of a 80-MHz Ti:sapphire laser system that generated infrared (IR) pulses of 70-fs duration. Frequency-tripled 95-fs ultraviolet (UV) pulses from this laser were used for the excitation step (ប a ϭ 4.7 eV). The photoelectrons were emitted by the fundamental IR pulses (ប b ϭ 1.57 eV) and were detected in a hemispherical analyzer with an energy resolution of 30 meV and an angular acceptance of Ϯ0.6°about the surface normal. The preparation of the Cu(111) and Cu(100) samples and details of the ultrahigh-vacuum chamber have been described elsewhere (5). The samples were kept at room temperature. Typical energy-resolved 2PPE spectra of C