Research Interests

Electronic Structure

Optical Properties

The energy levels and wavefunctions of electrons in an insulator are input to an understanding and computation of the linear and nonlinear susceptibilities and other optical properties that are of interest experimentally and technologically. There are several important concerns in implementing calculations based on the Local Density Approximation (LDA) treatment of band energies and wavefunctions.

Many-body corrections to conduction states

In the LDA description of band states the electron-electron interaction effects are approximated by the effective potential that depends on the local density. This fails to accurately represent the conduction (i.e., the unfilled) states. The next best approximation is believed to include an energy-dependent (self-energy) shift in the conduction electron energies. This so-called GW approximation -- involving the dynamical screened Coulomb interaction -- requires 1-2 orders of magnitude more computing. We are actively exploring three implementations of this `GW' approach.

Extended defects

Central to faster computing hardware is producing increasingly smaller line resolution in silicon chips. This is done by implanting ions such as boron. After the implantation, the material is annealed to restore the crystal structure and the high mobility. Unfortunately, the boron dopants show transient enhanced diffusion (TED) in which the boron diffusion `constant' is 1000 times its value in bulk for a transient but significant time in the annealing. Understanding this process has been identified a key step on the `highway' to continued improvement in computing hardware.

An extended defect in Si -- called the (311) defect due to its habit plane -- has been identified as a possible source/sink of Si interstitials believed to dominate boron diffusion. We are engaged in large-scale parallel simulations of extended defects in silicon. Essential to the treating 1000s of atoms is the use of the simpler, tight-binding Hamiltonian. Even so it is necessary to time-evolve a defect for a picosecond at 300-600 K to avoid being trapped in local minima. Then we fully relax the atomic positions by `steepest descent' until the atomic force on each atom is less than 0.1 eV/Angstrom and the effective temperature of the lattice is less than 0.1 K. Initial progress in identifying possible forms of the <311> defect has raised as many new questions as it offered possible answers to the original concerns that provoked the research.

Magnetic materials

Conventional electronic structure methods (LDA-based) fail to explain the magnetic transitions of the the 3d elements (Cr, Mn, Fe, Co, Ni). They both dramatically overestimate the transition temperature and fail to `predict' differing magnetic states for differing crystal structure of the same element. The so-called LDA + U method is a first attempt to add correlation effects to the band structure work. We have extended this approach to compute the temperature depended magnetic susceptibility with an effective electron-electron interaction computed with real electronic functions and including the effects of particle-particle and particle-hole (screening) scattering.

Strongly correlated systems

The quantitative understanding of atoms and molecules has continued to a theoretical challenge as the experimental resolution has always stayed ahead of theory. Mille-electron-volt resolution sets very high standards. The classic chemical approach of configuration interaction -- adding increasing numbers of excited states (as Slater determinant) to achieve increased accuracy. Our concerns are different from those of the chemists. We wonder whether these accurate approaches can be used to produce data set of correlation energies for atoms and molecules that can be used to produce a better LDA approximation for the effect of electron-electron interaction? Can we find faster ways of doing these calculations so as to permit their use in small clusters as models for solid surfaces?

Basic set reduction

The configuration-interaction approach suffers from the fact that computational time grows exponentially with the number of electrons. Furthermore the the number of configuration grows exponentially with the number of one-electron basis functions used to generate configurations. These problems are addressed in two ways.

(i)Partition of the basis. The partitioning takes advantage of so-called natural orbits to develop a basis set each of set of which as an occupancy an order of magnitude smaller than the next.

(ii)Many-electron state selection. The one-electron basis partitioning leads a division of the state space into an external and internal subspaces. A perturbative calculation of the external subspace can be combined with an exact treatment of the internal subspace to yield results comparable to those using the full state space.

Configuration interaction (CI) with non-orthogonal determinants

Typically the basic set reduction approach would reduce the 10^8 number of states in full CI to 10^5. This approach produces the same answer with 10^2 states.
The orthogonal basis functions in each determinant are different so that determinants are not orthogonal. This severely slows down the calculation of matrix elements.
The small number of determinants making up the state allows for a better understanding of the correlations.

Fast time dynamics in quantum dots

Basis reduction allows an accurate calculation of the correlated state in a sufficiently short time that it is feasible to consider the time evolution of the state. An atoms in a femtosecond pulse could be computed at subfemtosecond intervals to accurately track the evolution of various excited states.

More interestingly, almost all the object-oriented software can be adapted to study semiconductor quantum dots in a laser pulse. It turns out that one can readily identify effects demonstrating important correlations in the dots -- that is, easy to measure experimentally. This is such a new area that it is difficult to predict where it is going. But effective probes of correlation in strongly interacting systems are few. This could be an important new probe.

Nanoscale physics

The technology responsible for high-speed computing allows physicists to create structures more often seen in quantum mechanics text books: tunneling between two quantum wells, a periodic array of square wells. This ideality permits comparison between analytic calculations and actual measurements. Three areas of interest are described below. Others are in Many-body physics section.

Magnetic heterostructures

A long term development in dilute magnetic semiconductors has entered the nanostructure era. The groups Awschalom at UCSB and Samarth at Penn State make and measure layers of magnetic atoms (Mn) by probing the decay of a gas of magnetic excitons created with a fast laser pulse. The magnetization and decay in an applied magnetic field exhibit a range of phenomena never seen before. We are developing models to qualitatively and quantitatively understand these effects.

Dynamic localization

The dynamics in a one dimensional array of potential wells -- forming a so-called miniband -- offers a range of predicted phenomena: Bloch oscillations, Stark shifts, dynamic localization. The latter corresponds to a localization of the wavefunction when the quantity, (applied electric field)(well spacing)/frequency, is equal to zeros of the first Bessel function. We are calculating properties that would most dramatically exhibit this effect.

Fast time dynamics

The example above are just a few of the possible femtosecond effects. We are developing a formalism for treating electron-electron and electron-phonon effects in these short time scales. Other non-equilibrium formalism are devised to work in the steady state or long-time limit. Here we want to describe the initial phenomena before the long-time decay process set. This is the relevant time regime of many experiments.

Many-body physics

Since the 60's physicist have been studying strongly interacting systems. The initial success in study translational invariant models for 3D systems has encouraged efforts to study correlations in real materials and in materials of restricted dimensionality. For example, in one dimension, the interactions between electrons are strongly modified by the restricted motion: one particle cannot get around another.

Electron-electron scattering in two dimensions

A very early prediction that the electron-electron scattering rate at low temperature of T^2 in 3D would change to T^2 log(T) in two dimensions. Only recently in layered electron gasses has experimental verification been possible. Deviation from the prediction have sent us back to considered contribution to the rate that cannot be understood in the terms of the Fermi Golden Rule. These so-called vertex corrections should be larger due to the restricted motion in lower dimensions and should effect them magnitude of the rate.

Optical absorption in Peierls 1-D systems

A one-dimension periodic array of atoms in a half-filled band is unstable to dimerization: alternating short-long atomic spacings which opens a gap in the spectra. This is called the Peierls effect. Measurement of the absorptivity do not see this gap clearly, the absorptivity turns on over smoothly. However, in one dimension the zero-point motion is enhanced; so much so that the atoms provide a disorder potential to scatter the electrons. Including this idea in the conductivity lead to good agreement with published data. More interesting is the possibility of unusual states in the Peierls gap: soliton and polarons. Since the detection of solitons was strong evidence for the Peierls transition, it is important to predict the absorptivity spectrum of solitons in the zero-point-motion disordered state to see if the experimental shapes can be explained.

Your comments and suggestions are appreciated.
[OSU Physics] [College of Mathematical and Physical Sciences] [Center for Materials Research] [Ohio State University]
Edited by: [October 1996]