Energy and volume of vector fields on spherical domains

We present in this paper a \boundary version" for theorems about minimality of volume and energy functionals on a spherical domain of threedimensional Euclidean sphere

System-size convergence of point defect properties: The case of the silicon vacancy

We present a comprehensive study of the vacancy in bulk silicon in all its charge states from 2+ to 2-, using a supercell approach within plane-wave density-functional theory, and systematically quantify the various contributions to the well-known finite size errors associated with calculating formation energies and stable charge state transition levels of isolated defects with periodic boundary conditions. Furthermore, we find that transition levels converge faster with respect to supercell size when only the Gamma-point is sampled in the Brillouin zone, as opposed to a dense k-point sampling. This arises from the fact that defect level at the Gamma-point quickly converges to a fixed value which correctly describes the bonding at the defect centre. Our calculated transition levels with 1000-atom supercells and Gamma-point only sampling are in good agreement with available experimental results. We also demonstrate two simple and accurate approaches for calculating the valence band offsets that are required for computing formation energies of charged defects, one based on a potential averaging scheme and the other using maximally-localized Wannier functions (MLWFs). Finally, we show that MLWFs provide a clear description of the nature of the electronic bonding at the defect centre that verifies the canonical Watkins model.Comment: 10 pages, 6 figure

The utility of surface magnetic field measurements in the MAGSAT program

To take full advantage of the global, vector, survey by the Magsat satellite, and international program of augmented surface measurements was proposed. For secular variation and upper mantle conductivity the proposed measurements are global. The repeat station measurements for secular variation should be occupied at 2-3 year intervals. A special observing period in November and December of 1979 is proposed during which simultaneous, continuous, global measurements for upper mantle conductivity studies are to be gathered. Finally, it is recommended that the networks in operation during the IMS extend their operation through the Fall of 1980 to provide correlative data useful for high latitude disturbance studies and for crustal conductivity studies

Effect of electron-nuclear spin interactions on electron-spin qubits localized in self-assembled quantum dots

The effect of electron-nuclear spin interactions on qubit operations is investigated for a qubit represented by the spin of an electron localized in a self-assembled quantum dot. The localized electron wave function is evaluated within the atomistic tight-binding model. The magnetic field generated by the nuclear spins is estimated in the presence of an inhomogeneous environment characterized by a random nuclear spin configuration, by the dot-size distribution, by alloy disorder, and by interface disorder. Due to these inhomogeneities, the magnitude of the nuclear magnetic field varies from one qubit to another by the order of 100 G, 100 G, 10 G, and 0.1 G, respectively. The fluctuation of the magnetic field causes errors in exchange operations due to the inequality of the Zeeman splitting between two qubits. We show that the errors can be made lower than the quantum error threshold if an exchange energy larger than 0.1 meV is used for the operation.Comment: 15 pages, 2 figure