Our main interest has been in first principles electronic structure calculations of solids, surfaces and interfaces that provide us information pertaining to the ground state crystal structure, electronic and magnetic structures, elastic properties, compound formation, surface and interface induced changes etc. These calculations use a basis set to expand a one electron wave function and are based on the local (spin) density approximation (L(S)DA). The basis sets we have employed in the past include augmented plane waves, augmented Slater type orbitals, augmented Bessel or Hankel functions and simple plane waves, as in the pseudopotential approaches. These state-of-the-art techniques have been applied to metallic elements and alloys in order to successfully predict ground state properties without using significant experimental input. In my opinion, the LDA has worked better than it should have, even in describing certain ground state properties of materials. However, there are clear problems in the LDA that have to be addressed in order to have better first principles predictions of complex materials.
We are also interested in Quantum Monte Carlo (QMC) as well as Molecular Dynamics (MD) calculations. The auxiliary field QMC method is used in studies of many-body Hamiltonians such as the Hubbard Hamiltonian. MD can be used to understand the dynamical properties of solids and liquids such as diffusion and melting. An essential part in a MD simulation is the force on a given atom and it is now possible to calculate this from first principles, and carry out MD simulations of cells containing several hundreds of atoms. An important limitation in these simulations is the relatively small size of the cells that can be studied compared to traditional MD work . Parallel computing is turning out to be quite useful here with regard to studying larger cells. However, methods that can extract out the first principles information in a reliable way, leading to quality interatomic potentials will provide the most efficient means of carrying out large scale MD simulations, at least in the near future.
Some basic problems in condensed matter physics that we have addressed using the above mentioned techniques include; chemisorption on transition metals, surface magnetism, phase stabilities and related energetics of (3d, 4d, 5d) transition metals and their compounds, diffusion in simple metals from first principles, surface electronic structure of actinides, orbital magnetism, supermodulus effect in Cu/Pd multilayers, structural phase transitions in zirconia and ferromagnetism and related issues in hard magnets.
We have also improved some of the analytical and computational aspects of these calculations; for example, utilizing group theoretical techniques for symmetrization, improving the basis functions, building in spin-polarization, spin-orbit terms, calculating all the non spherical pieces of the charge density, potential, improving iterative schemes for Molecular Dynamics schemes, etc. There is a clear need for more efficient algorithms in first principles dynamics. Also, there are fundamental problems that have to be addressed and made computationally efficient. As an example, although the LDA has been quite successful with respect to structural and other ground state properties, improvements beyond LDA such as better treatments of correlations and computationally efficient ways (such as O(N) methods) of handling the electronic structure problem are necessary, especially when studying correlated electron systems or (real) materials with nonlocal defects.
There are several projects currently underway. One of them is identifying and studying "Organic Dirac Materials." Topological properties of 2- and 3-dimensional materials, spin-Hall effect and (Rashba) spin-orbit effects are being studied by us. In addition, we are interested in magnetic interactions in rare-earth/transition metal compounds in order to understand various enhancements in magnetic properties of these materials.
Structural Phase Transitions of certain ceramic materials are being studied in order to understand the underlying changes in electronic structure and to try and build better interatomic potentials using the first principles output.
Fundamental aspects of electronic structure are being examined in order to go beyond various approximations necessary in first principles studies.
Over the last few years, we have worked on exact solutions to small Hubbard clusters combined with statiscal mechanics. These calculations have yielded several fascinating results related to charge and spin pairing, phase separation, especially at one hole off half filling in the repulsive Hubbard model. We believe that these results provide significant clues to understanding high temperature superconductors as well as other inhomogeneous systems.
We are currently using national computer facilities at the CFN (center for functional nanomaterials) at Brookhaven National Laboratory.
Most of the projects mentioned above have been collaborative efforts, with the condensed matter theory groups at Brookhaven and Los Alamos National Laboratories, Nordita (Sweden), experimental and other groups at UConn, and other universities. These collaborations have been very fruitful, and we intend to continue these during the years ahead.