Image potential and field states at Ag(100) and Fe(110) surfaces

Abstract

By combining the first-principles concept based on the density functional theory with a model vacuum potential, we calculate image potential states and analogous ones in the presence of an electric field applied on a nonmagnetic Ag͑100͒ surface and a magnetic Fe͑110͒ surface. Our investigations are based on the Greenfunction embedding technique, which allows us to treat a truly semi-infinite surface and whence yields a continuum of bulk states. This turns out to be of crucial importance in order to investigate the qualitative difference between localized image or field states located in a band gap of the substrate and states in resonance with bulk states present at the same energies. This difference leads to remarkable changes in the binding energy versus field dispersion of the states. Furthermore, we show that in the case of the Fe͑110͒ surface, the calculated magnetic exchange splitting increases with the electric field and is also modified by the transition from field states to surface resonance states.

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.…”

“…Different strategies have been proposed to restore the correct imagelike behavior outside the surface. [24][25][26] In this work, such DFT limitation has been overcome by applying a matching procedure 23,27,28 to enforce the correct imagelike potential tail within our DFT-based self-consistent approach. The inclusion of the image potential, together with the self-consistent treatment of the finite voltage drop across the system, enables the quantitative analysis of FERs.…”

“…15 Most of previous descriptions of FERs have been based on the use of 1D model potentials that restrict the treatment to planar tip geometry only. 14,16,23,33,34 With our approach, instead, any tip geometry can be used, which opens up the possibility of understanding the influence of different tips on FERs.…”

Quantitative determination of a nano-object's atom density without atomic resolution

“…The determination of the image potential state properties by STS is hampered by the fact that the electric field applied between the sample and the tip deforms the potential at the solid-vacuum interface, leading to both an energy upshift [28,29] and a line broadening [30] of the image potential state. The amount of energy upshift (Stark shift) thereby differs for image potential states of different order [29], such that the natural 1/n 2 energy spacing is not observed in STS [1].…”

“…The amount of energy upshift (Stark shift) thereby differs for image potential states of different order [29], such that the natural 1/n 2 energy spacing is not observed in STS [1]. Stark-shifted image potential states (S-IPS) are often named field emission resonances and are published for the two surfaces of relevance here, Ag(100) [31] and Cu(111) [32].…”