Recently, a novel low-energy collective excitation has been predicted to exist at metal surfaces where a quasi two-dimensional (2D) surface-state band coexists with the underlying three-dimensional (3D) continuum. Here we present a model in which the screening of a semiinfinite 3D metal is incorporated into the description of electronic excitations in a 2D electron gas through the introduction of an effective 2D dielectric function. Our self-consistent calculations of the dynamical response of the 3D substrate indicate that an acoustic surface plasmon exists for all possible locations of the 2D sheet relative to the metal surface. This low-energy excitation, which exhibits linear dispersion at low wave vectors, is dictated by the nonlocality of the 3D dynamical response providing incomplete screening of the 2D electron-density oscillations.Comment: 10 pages, 7 figures, to appear in Phys. Rev.

View the article online for updates and enhancements. Related contentToward a novel theoretical approach for determining the nature of electronic excitations in quasi-two-dimensional systems A Politano, G Chiarello and A Cupolillo -Low-energy dielectric screening in Pd and PdHx systems V M Silkin, V U Nazarov, I P Chernov et al.Acoustic plasmons in extrinsic freestanding graphene M Pisarra, A Sindona, P Riccardi et al. AbstractThe ab initio theory of electronic excitations in atomically thin (quasi-two-dimensional (Q2D)) crystals presents extra challenges in comparison to both the bulk and purely 2D cases. We argue that the conventionally used energy-loss function Im(where q , ϵ , and ω are the dielectric function, the momentum, and the energy transfer, respectively) is not, generally speaking, the suitable quantity for the interpretation of the electron-energy loss spectroscopy (EELS) in the Q2D case, and we construct different functions pertinent to the EELS experiments on Q2D crystals. Secondly, we emphasize the importance and develop a convenient procedure of the elimination of the spurious inter-layer interaction inherent to the use of the 3D super-cell method for the calculation of excitations in Q2D crystals. Thirdly, we resolve the existing controversy in the interpretation of the so-called π and π σ + excitations in monolayer graphene by demonstrating that both dispersive collective excitations (plasmons) and non-dispersive single-particle (inter-band) transitions fall in the same energy ranges, where they strongly influence each other.

We address the band-structure of two-dimensional crystals above the vacuum level in the context of discrete states immersed in the three-dimensional continuum. Scattering resonances are discovered that originate from the coupling of the in-plane and perpendicular motions, as elucidated by the analysis of an exactly solvable model. Some of the resonances turn into true bound states at highsymmetry k vectors. Ab initio scattering theory verifies the existence of the resonances in realistic graphene and shows that they lead to a total reflection of the incident electron below and total transmission above the resonance energy.

We calculate the optical spectra of silicon, germanium, and zinc blende semiconductors in the adiabatic time-dependent density-functional formalism, making use of kinetic energy density-dependent [meta-generalized-gradient-approximation (GGA)] exchange-correlation functionals. We find excellent agreement between theory and experiment. The success of the theory on this notoriously difficult problem is traced to the fact that the exchange-correlation kernel of meta-GGA supports a singularity of the form α/q(2) (where q is the wave vector and α is a constant), whereas previously employed approximations (e.g., local-density and generalized gradient approximations) do not. Thus, the use of the adiabatic meta-GGA opens a new path for handling the extreme nonlocality of the time-dependent exchange-correlation potential in solid-state systems.

We develop a scheme for building the scalar exchange-correlation ͑XC͒ kernel of time-dependent density functional theory ͑TDDFT͒ from the tensorial kernel of time-dependent current density functional theory ͑TDCDFT͒ and the Kohn-Sham current density response function. Resorting to the local approximation to the kernel of TDCDFT results in a nonlocal approximation to the kernel of TDDFT, which is free of the contradictions that plague the standard local density approximation ͑LDA͒ to TDDFT. As an application of this general scheme, we calculate the dynamical XC contribution to the stopping power of electron liquids for slow ions to find that our results are in considerably better agreement with experiment than those obtained using TDDFT in the conventional LDA.