Calculus on surfaces with general closest point functions

The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs

Circuit model for spin-bottleneck resistance in magnetic-tunnel-junction devices

Spin-bottlenecks are created in magnetic-tunnel-junction devices by spatial inhomogeneity in the relative resistances for up and down spins. We propose a simple electrical circuit model for these devices which incorporates spin-bottleneck effects and can be used to calculate their overall resistance and magnetoresistance. The model permits a simple understanding of the dependence of device magnetoresistance on spin diffusion lengths, tunneling magnetoresistance, and majority and minority spin resistivities in the ferromagnetic electrodes. The circuit model is in a good quantitative agreement with detailed transport calculations.Comment: 4 pages, 3 figures, submitted to Phys. Rev.

Imaging interstitial iron concentrations in boron-doped crystalline silicon using photoluminescence

Imaging the band-to-band photoluminescence of silicon wafers is known to provide rapid and high-resolution images of the carrier lifetime. Here, we show that such photoluminescence images, taken before and after dissociation of iron-boron pairs, allow an accurate image of the interstitial iron concentration across a boron-doped p-type silicon wafer to be generated. Such iron images can be obtained more rapidly than with existing point-by-point iron mapping techniques. However, because the technique is best used at moderate illumination intensities, it is important to adopt a generalized analysis that takes account of different injection levels across a wafer. The technique has been verified via measurement of a deliberately contaminated single-crystal silicon wafer with a range of known iron concentrations. It has also been applied to directionally solidified ingot-grown multicrystalline silicon wafers made for solar cell production, which contain a detectible amount of unwanted iron. The iron images on these wafers reveal internal gettering of iron to grain boundaries and dislocated regions during ingot growth.D.M. is supported by an Australian Research Council QEII Fellowship. The Centre of Excellence for Advanced Silicon Photovoltaics and Photonics at UNSW is funded by the Australian Research Council

Magnetic domains in III-V magnetic semiconductors

Recent progress in theoretical understanding of magnetic anisotropy and stiffness in III-V magnetic semiconductors is exploited for predictions of magnetic domain characteristics and methods of their tuning. We evaluate the width and the energy of domain walls as well as the period of stripe domains in perpendicular films. The computed stripe width d = 1.1 um for Ga_0.957Mn_0.043As/In_0.16Ga_0.84As compares favorably to the experimental value 1.5 um, as determined by Shono et al. [Appl. Phys. Lett. 77, 1363 (2000)].Comment: 4 RevTex pages, 2 figures spelling of author's names corrected in abstract pag

Theory of inter-edge superexchange in zigzag edge magnetism

A graphene nanoribbon with zigzag edges has a gapped magnetic ground state with an antiferromagnetic inter-edge superexchange interaction. We present a theory based on asymptotic properties of the Dirac-model ribbon wavefunction which predicts $W^{-2}$ and $W^{-1}$ ribbon-width dependencies for the superexchange interaction strength and the charge gap respectively. We find that, unlike the case of conventional atomic scale superexchange, opposite spin-orientations on opposite edges of the ribbon are favored by both kinetic and interaction energies.Comment: 4 pages 8 figure

Competing Ordered States in Bilayer Graphene

We use a perturbative renormalization group approach with short-range continuum model interactions to analyze the competition between isotropic gapped and anisotropic gapless ordered states in bilayer graphene, commenting specifically on the role of exchange and on the importance of spin and valley flavor degeneracy. By comparing the divergences of the corresponding susceptibilities, we conclude that this approach predicts gapped states for flavor numbers N=1,2,4. We also comment briefly on the related gapped states expected in chiral (ABC) trilayer graphene.Comment: 12 pages, 7 figures and 1 tabl