Surface modes are generally believed to be an undesirable feature of finite photonic crystals (PC), unlike point or line defect modes. However, it is possible to make the surface mode radiate by appropriate corrugation of the PC interface. In this paper we show theoretically that the coherent action of these surface indentations can be engineered to collimate within a few degrees the light exiting a PC waveguide, or to funnel light coming from free space into the waveguide.

We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay’s DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order ${\mathit{N}}_{\mathrm{atoms}}^3$ operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay’s scheme. A special ‘‘metric’’ and a special ‘‘preconditioning’’ optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order ${\mathit{N}}_{\mathrm{atoms}}^2$ scaling is found for systems containing up to 1000 electrons. If we take into account that the number of k points can be decreased linearly with the system size, the overall scaling can approach ${\mathit{N}}_{\mathrm{atoms}}$. We have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable. © 1996 The American Physical Society.

The electrical resistivity of Fe-Cr-Fe layers with antiferromagnetic interlayer exchange increases when the magnetizations of the Fe layers are aligned antiparallel. The effect is much stronger than the usual anisotropic magnetoresistance and further increases in structures with more than two Fe layers. It can be explained in terms of spin-flip scattering of conduction electrons caused by the antiparallel alignment of the magnetization.

We present a theory for tunneling between a real surface and a model probe tip, applicable to the recently developed ‘‘scanning tunneling microscope.’’ The tunneling current is found to be proportional to the local density of states of the surface, at the position of the tip. The effective lateral resolution is related to the tip radius R and the vacuum gap distance d approximately as [(2 Å)(R+d${\left)\right]}^{1/2}$. The theory is applied to the 2×1 and 3×1 reconstructions of Au(110); results for the respective corrugation amplitudes and for the gap distance are all in excellent agreement with experimental results of Binnig et al. if a 9-Å tip radius is assumed. In addition, a convenient approximate calculational method based on atom superposition is tested; it gives reasonable agreement with the self-consistent calculation and with experiment for Au(110). This method is used to test the structure sensitivity of the microscope. We conclude that for the Au(110) measurements the experimental ‘‘image’’ is relatively insensitive to the positions of atoms beyond the first atomic layer. Finally, tunneling to semiconductor surfaces is considered. Calculations for GaAs(110) illustrate interesting qualitative differences from tunneling to metal surfaces.

It is shown that the quantization of the Hall conductivity of two-dimensional metals which has been observed recently by Klitzing, Dorda, and Pepper and by Tsui and Gossard is a consequence of gauge invariance and the existence of a mobility gap. Edge effects are shown to have no influence on the accuracy of quantization. An estimate of the error based on thermal activation of carriers to the mobility edge is suggested.