In this article I describe the embedding method and review its application to surface problems. In this method an embedding potential is added on to the Hamiltonian of the region of interest — here the surface — to take full account of the effect of the substrate. After deriving the method, applications to the electronic structure of several surfaces are reviewed, and adsorbate studies are described. The method can also be used to study confined electrons, and surface applications of this are given. Finally, the real space embedding method is related to embedding in the linear combination of atomic orbitals method.

The embedding method is a powerful theoretical and computational technique that is relevant to a great many technologically and scientifically important problems. This general nature encompasses many important and topical problems in for example surface and interface electronic structure, adsorption, physics of nanostructures, molecular electronics, plasmonics and photonics, and it has become an important tool for researchers in these fields. More recently it has also been extended into the time domain. Supplemented with demonstration programmes, code and examples, this book provides a thorough review of the method and would be an accessible starting point for graduate students or researchers wishing to understand and use the method, or as a single reference source for those already familiar with the subject and applying it in their research. Supplementary materials provided by the author to accompany the book are available within Book information.

The embedding method is a powerful theoretical and computational technique that is relevant to a great many technologically and scientifically important problems. This general nature encompasses many important and topical problems in for example surface and interface electronic structure, adsorption, physics of nanostructures, molecular electronics, plasmonics and photonics, and it has become an important tool for researchers in these fields. More recently it has also been extended into the time domain. Supplemented with demonstration programmes, code and examples, this book provides a thorough review of the method and would be an accessible starting point for graduate students or researchers wishing to understand and use the method, or as a single reference source for those already familiar with the subject and applying it in their research. Supplementary materials provided by the author to accompany the book are available within Book information.

A method of solving the time-dependent Schrödinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wavefunctions to the rest of space replaced by an embedding term added on to the Hamiltonian. This time-dependent embedding term is derived from the Fourier transform of the energy-dependent embedding potential, which embeds the time-independent Schrödinger equation. Results are presented for a one-dimensional model of an atom in a time-varying electric field, the surface excitation of this model atom at a jellium surface in an external electric field, and the surface excitation of a bulk state.

The photonic band structure of a linear array of metallic nanocylinders is calculated using the embedding method. The coupling to the vacuum on either side of the array is treated exactly, allowing the continuum states and plasmon broadening above the light-line to be treated accurately. In addition to the plasmon bands, which broaden at larger cylinder radius, there are two guided modes, with the character of surface plasmon polaritons. These split off the light-line at small wave-vector, becoming almost dispersionless as they enter the plasmon bands. The electric fields associated with the modes are calculated, and their symmetries are discussed. (C) 2013 Optical Society of America

The Dirac-Frenkel variational principle is used to derive the embedding method for solving the time-dependent Schrödinger equation. Embedding allows the time evolution of the wavefunction to be calculated explicitly in a limited region of space, the region of physical interest, the embedding potential ensuring that the wavefunction satisfies the correct boundary conditions for matching on to the rest of the system. This is applied to a study of the excitation of electrons at a metal surface, represented by a one-dimensional model potential for Cu(111). Time-dependent embedding potentials are derived for replacing the bulk substrate, and the image potential and vacuum region outside the surface, so that the calculation of electron excitation by a surface perturbation can be restricted to the surface itself. The excitation of the Shockley surface state and a continuum bulk state is studied, and the time structure of the resulting currents analysed. There is a distinction between emission from the localized surface state, where the charge is steadily depleted, and the extended continuum state, where the current emitted into the vacuum is compensated by current approaching the surface from the bulk. The time taken for the current to arrive outside the surface is studied.

This year marks the 20th anniversary of the launch of Journal of Physics: Condensed Matter in 1989. The journal was formed from the merger of Journal of Physics C: Solid State Physics and Journal of Physics F: Metal Physics which had separated in 1971. In the 20 years since its launch, Journal of Physics: Condensed Matter has more than doubled in size, while raising standards. Indeed, Journal of Physics: Condensed Matter has become one of the leading scientific journals for our field. This could not have occurred without great leadership at the top. No one has been more responsible for this growth in both size and quality than our Senior Publisher, Richard Palmer. Richard first started work at IOP in March 1971 as an Editorial Assistant with J. Phys. B After a few months, he transferred to J. Phys.C The following year, the Assistant Editor of J. Phys. C, Malcolm Haines, left suddenly in order to work on his family vineyard in France, and Richard stepped into the breach. In those days, external editors had a much more hands-on role in IOP Publishing and he had to travel to Harwell to be interviewed by Alan Lidiard, the Honorary Editor of J. Phys. C, before being given the job of Assistant Editor permanently. Since J. Phys. C and J. Phys. F re-merged to form Journal of Physics: Condensed Matter, Richard gradually shed his other journal responsibilities, except for Reports on Progress in Physics, to build up Journal of Physics: Condensed Matter. He has worked closely with four Editors-in-Chief of J. Phys. C and five of Journal of Physics: Condensed Matter. When Richard announced his retirement this past winter, we met it with a great deal of both happiness and sadness. Of course, we are happy that he is going to be allowed to enjoy his retirement, but we remain very sad to lose such a valuable member of our team, especially the one who had provided the heart and soul of the journal over its 20 years. We will be able to rely upon the team which Richard ably trained as we go into the future. The Executive Board decided to do this special issue, both to commemorate the 20th year of Journal of Physics: Condensed Matter and to honour Richard for his long years of service to IOP Publishing and Journal of Physics: Condensed Matter. This issue is dedicated to Richard for his many years of work and friendship with the journal board that has seen a great many changes over the years. This issue covers a very wide range of topics, since we approached all current and past members of the various boards of Journal of Physics: Condensed Matter in seeking papers for this special issue. The response has been very positive and this will be one of our larger special issues. The desire to honour Richard is widespread among these various boards, so that we have been almost overwhelmed with submissions, although many who wished to contribute could not because of other obligations. We hope that you, the readership, will enjoy these articles.

Matter is dedicated to him, with articles by friends, colleagues, and former students.By any standards,

Plasmon modes of a two-dimensional lattice of long conducting circular wires are investigated by using an embedding technique to solve Maxwell's equations rigorously. The frequency-dependent density of states is calculated for various values of the wave vector and the filling fraction. At low filling fractions, collective modes are all found to accumulate at the surface-plasmon frequency omega(p)/root 2, omega(p) being the bulk plasmon frequency. As the filling fraction increases, the interference between the electromagnetic fields generated by localized surface-plasmon polaritons leads to the presence of new resonances, whose frequency strongly depends on the interparticle separation. For touching wires, a number of multipole resonances fill the spectral range between dipole resonances, as occurs in the case of a three-dimensional packing of metal spheres.

First-principles electron field emission calculations have been performed on flat and stepped Pt and Pd surfaces. An increase in electron transmission is seen for well-defined stepped surfaces. This stems from the reduction in the work function caused by Smoluchowski electron-smoothing and an increased tunneling contribution from surface parallel wave vectors at the stepped surface. A reduced effective potential at the step site may also contribute to increased electron transmission.