Image potential states and electronic structure ofNa∕Cu(111)

Abstract

We report a density functional theory investigation of the electronic structure of a monolayer of Na adsorbed on a Cu͑111͒ substrate. We approach this problem by taking into account a truly semi-infinite substrate within the embedding Green function method, which allows one to clearly distinguish surface states from bulk projected ones and to describe them with high accuracy. The quantum-well state induced by Na adsorption is discussed and compared with the surface state of the clean Cu͑111͒ surface. By suitably modifying the method, we are able to study image potential induced states which are normally not available in standard density functional theory calculations. In our approach these states are fully accounted for by introducing the image tail in the effective potential. The theoretical results are compared with experiments when available, for both the clean metal surface and the adsorbate system.

Theoretical approaches in adsorption: alkali adatom investigations

“…This structure, located outside the surface, is bound by the potential tail towards vacuum. Standard DFT is unable to correctly reproduce the correct image form v eff (z) = V im (z) −1/4z at large distance z, and such deficiency strongly affects this "pseudo-image" state, as recently explained [31]. Na (3×3) on Cu (111) Energy (eV) Figure 6.…”

“…However, in order to keep a lower computational cost, it is convenient to take advantage of the phenomenological approach introduced by Nekovee and Inglesfield [56,57], which exploits the lack of periodicity of embedding in the z direction. In practice in the last step of the calculation, one takes into account the correct image potential behaviour in the construction of the embedding potential at the vacuum side, and let the self-consistent potential v eff merge smoothly into the image one in the outermost part of the embedded region [31]. We have performed the calculation of the image states in the just mentioned framework.…”

“…All these reasons have motivated several theoretical studies of alkali adatoms in the DFT framework [27,28,29,30,31]. Regarding image state calculations, manybody treatments beyond DFT have concentrated so far to lifetimes of electrons at free surfaces [32,33].…”

Image potential states of supported metallic nanoislands

“…Present results compare well with available experimental and theoretical data. 7,20,25,26 Thus, at ⌫ , the 1 ML Na on Cu͑111͒ exhibits a quantum well state ͑QWS͒ at −127 meV below the Fermi level and a series of ISs with energies E n=1 = −992 meV, E n=2 = −215 meV, and E n=3 = −90 meV with respect to the vacuum level. Here, the ISs are labeled by their principal quantum number n. The entire ISs series is in the projected band gap of Cu͑111͒ because of the −1.53 eV shift of the vacuum level as induced by the Na monolayer.…”

Plane-wave based electron tunneling through field emission resonance states

“…[8][9][10][11][12][13][14][15][16][17][18][19] The theoretical interpretation of FERs is commonly done using simple one-dimensional (1D) models for the description of the surface potential. 14,[20][21][22][23] However, there are many drawbacks using model effective mass theory with 1D model potentials that can be overcome with an atomicscale description of the effective potential in which electrons propagate: the description of states near the surface accounting for corrugation and, in particular, the different dispersion of surface states from those located in the bulk and vacuum regions. In this work, we describe a density functional theory (DFT) based calculation method that treats the full system under nonzero bias voltage and solves the potential of the tip-sample system self-consistently.…”