J. Ihm

Momentum-space formalism for the total energy of solids

A momentum-space formalism for calculating the total energy of solids is derived. This formalism is designed particularly for application with the self-consistent pseudo- potential method. In the present formalism, the total energy is obtained through band- structure calculations without involving additional integrations. The Hellman-Feynman theorem is derived, as is a modified virial relation for the pseiidopotential Hamiltonian which provides an alternative way of calculating forces and total energies. The calculation of the total energy of solids and related derivatives with respect to structural degrees of freedom has been an ongoing problem since the early days of solid state physics (Wigner and Seitz 1933, 1934, Fuchs 1935). Quantum-mechanical calcu- lations on molecules suggest that correlation effects might sometimes be responsible for most of their binding energy (Schaefer 1972). The solid state approaches have concentrated on efforts to include most of these effects through an effective potential I/corr(p(r, Y)) (Hohenberg and Kohn 1964, Kohn and Sham 1965), rather than by complicated wave- function-related configuration interactions or many-electron perturbation techniques. Besides the problem of considering correlation effects, the self-consistent solution of the Schrodinger equation within a desired accuracy is quite difficult ; typically, the experi- mental binding energy of elemental solids is 10-4-10-5 times the total energy. These difficulties have inspired a large set of total-energy calculations that circumvents the complete solution of the Schrodinger equation (Harrison 1966, Heine and Weaire 1970). It is based on various approximations to the nearly-free-electron representation and may include the effect of more localised electrons (e.g. d states in transition metals) through specific interaction models (Moriarty 1974, 1977). As the variational self-consistent charge density remains unspecified in this approach, various forms of linear dielectric screening of the basic Coulomb interactions are introduced (Harrison 1966, Heine and Weaire 1970). Another set oftotal-energy calculations is based on direct solutions ofthe Schrodinger equation within a given interaction model : for example, Hartree-Fock (Harris and Monkhorst 1971, Wepfer et al 1974), density-functional (Ching and Callaway 1974,

Broken symmetry and pseudogaps in ropes of carbon nanotubes

Since the discovery of carbon nanotubes, it has been speculated that these materials should behave like nanoscale wires with unusual electronic properties and exceptional strength. Recently, ‘ropes’ of close-packed single-wall nanotubes have been synthesized in high yield. The tubes in these ropes are mainly of the (10,10) type, which is predicted to be metallic. Experiments on individual nanotubes and ropes, indicate that these systems indeed have transport properties that qualify them to be viewed as nanoscale quantum wires at low temperature. It has been expected that the close-packing of individual nanotubes into ropes does not change their electronic properties significantly. Here, however, we present first-principles calculations which show that a broken symmetry of the (10,10) tube caused by interactions between tubes in a rope induces a pseudogap of about 0.1u2009eV at the Fermi level. This pseudogap strongly modifies many of the fundamental electronic properties: we predict a semimetal-like temperature dependence of the electrical conductivity and a finite gap in the infrared absorption spectrum. The existence of both electron and hole charge carriers will lead to qualitatively different thermopower and Hall-effect behaviours from those expected for a normal metal.

Quantum mechanical force calculations in solids: The phonon spectrum of Si

Abstract Quantum mechanical force calculations with a realistic charge distribution for Si are reported here. Using the momentum-space expression for the Hellman-Feynman theorem, forces on displaced Si atoms corresponding to Γ, L, and X phonon modes are calculated. This frozen phonon model, based on the Born-Oppenheimer approximation, gives results within 5% of the experimental phonon frequencies. Anharmonic effects are briefly discussed using the calculated force constants.

Valence charge distribution and electric field gradients in GaAsAlAs mixed crystals

Abstract Electric field gradients at the arsenic sites in the GaAsue5f8AlAs mixed compounds are calculated using the self-consistent pseudo-potential method. The result is in good agreement with recent nuclear quadrupole resonance (NQR) experiments and supports the interpretation that the NQR splittings arise from an Al ion relacing one of the four Ga ions near an As site.