Computational approaches to the electronic structure of matter have emerged as a powerful tool for understanding and predicting the properties of materials. They also provide a tool for clear thinking, and a number of theoretical developments have come out of the effort to understand a given physical phenomenom well enough
to the point of being able to "ask" the computer to produce a number for it. Through this line of inquire it has been found that many basic properties of crystalline solids, such as the dielectric polarization of ferroelectrics, the localization of electrons in insulators, and the orbital magnetization of ferromagnets, are related to certain geometric and topological properties of the electronic wavefunctions (Berry's phases and related quantities).
My recent work has focused on exploring such properties through first-principles calculations, particularly those which are associated with magnetism, spin-orbit coupling, and broken time-reversal symmetry. This ongoing work involves developing new and efficient algorithms and applying them to specific materials.
The following are two representative examples of recent and ongoing research projects.
Anomalous Hall effect: When a current is driven through a metallic plate exposed to a perpendicular magnetic field, a voltage (Hall voltage) is set up across the third direction. Surprisingly, in ferromagnets such Hall voltage is generated even in the absence of an external magnetic field. This puzzling behavior has become known as the "anomalous" Hall effect. Recently it has been clarified that it can be attributed to a subtle "Berry-curvature" correction to the group velocity of electron wavepackets moving through the periodic crystal structure. First-principles calculations of the Berry curvature turned out to be exceedingly demanding, typically requiring the calculation of the electronic wavefunctions over millions of points in the Brillouin zone. We have developed an interpolation scheme, based on the used of Wannier functions (localized molecular orbitals), which reduces by orders of magnitude the cost of performing the needed Brillouin zone or Fermi-surface integrals. The anomalous Hall conductivity of simple ferromagnets can now be computed in a few hours on a home computer, whereas before it required weeks of computer time.
Orbital magnetization and magnetic circular dichroism: The magnetization of matter has contributions from the spin of the electrons and from their orbital motion. When expressed in terms of localized Wannier functions, the orbital magnetization can be thought of as a sum of two parts, one "localized", the other "itinerant": (i) the self-rotation of the Wannier orbitals around their centers; (ii) the circulation arising from the motion of the centers of mass of the Wannier functions (think of the rotation of a planet around its axis and the orbital motion around the sun: both carry angular momentum). The net sum of those two contributions, i.e., the total orbital magnetization, can be measured using gyromagnetic experiments, as discovered by Einstein and others. It was however not known how to measure the individual contributions (i) and (ii). It turns out that this can be done by complementing gyromagnetics with magneto-optical experiments, such as magnetic circular dichroism (MCD). MCD is the differential absorption of left- and right-circularly-polarized light by magnetic materials. We have found that by integrating the measured MCD spectrum over all frequencies one obtains, through an optical sum rule, essentially the term (i) above. Since the sum (i)+(ii) is known from gyromagnetics, the value of term (ii) can be inferred. We are planning to carry out first-principles calculations of the orbital magnetization of ferromagnets, diamagnets, and paramagnets, in order to elucidate the relative importance of the two contributions and make testable predictions.
"Fermi-surface calculation of the anomalous Hall conductivity" Xinjie Wang, David Vanderbilt, Jonathan R. Yates, Ivo Souza (arXiv:0708.0858)
"Spectral and Fermi surface properties from Wannier interpolation" Jonathan R. Yates, Xinjie Wang, David Vanderbilt, and Ivo Souza, Phys. Rev. B 75, 195121 (2007)
"Ab initio study of the nonlinear optics of III-V semiconductors in the terahertz regime" Eric Roman, Jonathan R. Yates, Marek Veithen, David Vanderbilt, and Ivo Souza, Phys. Rev. B 74, 245204 (2006)
"Electron-Phonon Interaction via Electronic and Lattice Wannier functions: Superconductivity in Boron-Doped Diamond Reexamined" Feliciano Giustino, Jonathan R. Yates, Ivo Souza, Marvin L. Cohen, and Steven G. Louie, Phys. Rev. Lett. 98, 047005 (2007)
"Ab-initio calculation of the anomalous Hall conductivity by Wannier interpolation" Xinjie Wang, Jonathan R. Yates, Ivo Souza, and David Vanderbilt, Phys. Rev. B 74, 195118 (2006)