日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or "Boys orbitals" as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.

Maximally-localized Wannier Functions: Theory and Applications

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

The axisymmetric time-dependent flow field in an evaporating sessile droplet whose contact line is pinned is studied numerically and using an analytical lubrication theory with a zero-shear-stress boundary condition on the free surface of the droplet at low capillary and Reynolds numbers. A finite element algorithm is developed to solve simultaneously the vapor concentration and flow field in the droplet under conditions of slow evaporation. The finite element solution confirms the accuracy of the lubrication solution, especially when terms of higher order in the droplet flatness ratio (the ratio of droplet height to radius, h/R) are included in the lubrication theory to account more accurately for the singular flow near the contact line.

Analysis of the microfluid flow in an evaporating sessile droplet.

We report that in addition to the fabrication of hollow nanomaterials, the Kirkendall-type diffusion can also be utilized in synthetic nanoarchitecture, through which low-dimensional nanobuilding blocks can be designed and organized chemically into complex geometrical conformations. Our approach may provide a new chemical alternative to materials self-organization. In principle, a great variety of inorganic “dandelions” and their nanocomposites can be tailored and fabricated through this type of total synthetic architecture.

Fabrication of ZnO dandelions via a modified Kirkendall process

CHCl3 and CHBr3 intercalated C60 have attracted particular interest after a superconductivity transition temperature ( T c) of up to 117 K was discovered. We have determined the structure using synchrotron x-ray powder-diffraction and found that the expansion of the lattice mainly takes place in one dimension (triclinic b axis), leaving planes of C60 molecules on an approximately hexagonal, slightly expanded lattice. We have performed tight-binding band structure calculations for the surface layer. In spite of the slight expansion of the layers, for the range of dopings where a large T c has been observed, the density of states at the Fermi energy is smaller for C60·2CHCl3 and C60·2CHBr3 than for C60. This suggests that the lattice expansion alone cannot explain the increase of T c.

https://science.sciencemag.org/content/sci/296/5565/109.full.pdf

Structure of haloform intercalated C60 and its influence on superconductive properties.

We study the influence of the lattice structure, the Jahn-Teller effect, and the Hund's rule coupling on a metal-insulator transition in ${A}_{n}{\mathrm{C}}_{60}$ $(A\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{K},\mathrm{Rb})$. The difference in the lattice structure favors ${A}_{3}{\mathrm{C}}_{60}$ (fcc) being a metal and ${A}_{4}{\mathrm{C}}_{60}$ (bct) being an insulator, and the coupling to ${H}_{g}$ Jahn-Teller phonons favors ${A}_{4}{\mathrm{C}}_{60}$ being nonmagnetic. The coupling to ${H}_{g}$ ( ${A}_{g}$) phonons decreases (increases) the value ${U}_{c}$ of the Coulomb integral at which the metal-insulator transition occurs. There is an important partial cancellation between the Jahn-Teller effect and the Hund's rule coupling.

/pdf/metal-insulator-transitions-influence-of-lattice-structure-thfbnia1ay.pdf

Metal-insulator transitions: influence of lattice structure, jahn-teller effect, and Hund's rule coupling

The Physics of Correlated Insulators, Metals, and Superconductors

We investigate the effect of electronic correlations on the coupling of electrons to Holstein phonons in the one-band Hubbard model. We calculate the static electron-phonon vertex within the linear response of Kotliar-Ruckenstein slave bosons in the paramagnetic saddle-point approximation. Within this approach the on-site Coulomb interaction $U$ strongly suppresses the coupling to Holstein phonons at low temperatures. Moreover, the vertex function does not show particularly strong forward scattering. Going to larger temperatures $kT\ensuremath{\sim}t$ we find that after an initial decrease with $U$, the electron-phonon coupling starts to increase with $U$, confirming a recent result of Cerruti, Cappelluti, and Pietronero. We show that this behavior is related to an unusual reentrant behavior from a phase separated to a paramagnetic state upon decreasing the temperature.

/pdf/renormalization-of-the-electron-phonon-coupling-in-the-one-4aj45gsq82.pdf

Erik Koch

Papers

Structure of haloform intercalated C60 and its influence on superconductive properties.

Metal-insulator transitions: influence of lattice structure, jahn-teller effect, and Hund's rule coupling

The Physics of Correlated Insulators, Metals, and Superconductors

Renormalization of the electron-phonon coupling in the one-band Hubbard model

Locality properties and Wannier functions for interacting systems