A description (a bit outdated) of my research projects is given below.
In this work, we studied the ordering of dipolar molecules when trapped in an optical lattice. Dipolar molecules in a rotational eigenstate will not have a net dipole moment. One method of inducing dipolar interactions between molecules is to use an external electric field which will align the dipoles to point in the same direction which has been considered in the literature. In this work, we describe an alternative method of inducing such long-range dipolar interactions which involves creating a mixture of states in the lowest and first excited rotational levels. We describe the various Mott insulating and superfluid states that can result for such a system in an optical lattice.
(Figure courtesy of W. Yin and W. Ku from Brookhaven).
Despite being one of the earliest class of materials found to exhibit a charge-density wave at sufficiently low temperatures, many properties of the 2H-transition metal dichalcogenides are still not understood. One of the most interesting puzzles is found from photoemission experiments: seemingly no gap opens on the nested region of the fermi surface going against conventional CDW wisdom. We have provided a qualitative model which explains how such gapless excitations can exist in the CDW phase.
While the properties of larger radius nanotubes can be deduced from the properties of graphite by applying the so-called zone folding method, we find that this method does not work well for nanotubes of sufficiently small radius. More specifically, the large curvature makes some of these nanotubes metallic with a large density of states at the Fermi energy and leads to unusual electron-phonon interactions, with the dominant coupling coming from the out-of-plane phonon modes.
With quantities calculated from microscopic models, we developed a method to find the parameters of the effective Frohlich Hamiltonian by combining the frozen-phonon approximation with the RPA analysis of the giant Kohn anomaly. Including a model for the residual electron-electron Coulomb interaction, we can determine the temperatures at which Fermi surface instabilities, namely superconductivity and charge-density wave, occur. We find that larger radius nanotubes (>7 Angstroms in diameter) are stable at all experimentally relevant temperatures while tubes with smaller radii can have either a CDW or SC instability depending on the details of their specific chirality. This work is relevant to experimental studies of superconductivity in carbon nanotubes which have been the subject of some controversy.
I've also collaborated with J. Xu's group at Brown and M. Tinkham's group at Harvard (both experimental groups) studying the effect of gating on CNT phonon frequencies.
In the first phase of this project we used a density-functional theory based method to calculate the electronic structure of DNA stretched up to 90% of its natural length. It is found that DNA is an insulator with band gap around 3 eV, and for all cases the valence states are centered on the purine bases (A, G) while the conduction states are centered on the pyrimidine bases (C, T). Next we took the results from the all-atom calculation and derived effective tight-binding models for DNA at different stretching magnitudes. We find that adding a disorder potential in line with that from the dipole moment of stray water molecules, the electronic states which were originally extended across thousands of base pairs, become localized as the molecule is stretched. This is in line with recent experimental studies (Heim et al., Appl. Phys. Lett. (2004)).