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Research Interests:

At this point, I have quite a few research interests, but there are two main fields I am working in. The first is high temperature superconductivity. High temperature superconductors (HTS) are a family of materials which are very poor metals at room temperature (they are basically ceramics) but which superconduct at temperatures below roughly 100K (-170 C). This means that they can carry an electrical current with no resistance forever. Superconductors aren't new; even aluminum superconducts if it is cold enough (near 1K). What is unusual about the HTS is that they superconduct at a relatively high temperature. On the one hand, this makes them good for technological applications; on the other hand, there are lots of technical problems revolving around how to make wires out of a ceramic such that they won't break. The thing I care about, though, is what makes them tick. At present, there is no mathematical theory that explains the many strange properties of the HTS. I have studied a number of aspects of HTS. Recently, I was involved in a project to understand tunneling data in YBa2Cu3O7 [1,2]. I have also written a couple of papers [3,4] on coexisting phases in HTS, which has become quite a hot topic. A prominent theme in a lot of my work is the effect of disorder on the electronic structure of HTS. I have also recently trying to explain the low-magnetic-field vortex core expansion that has been measured in YBa2Cu3O7-d [8,9].










My second field of interest is disorder in strongly-interacting systems. Strongly-interacting materials (or, more correctly, strongly-correlated materials) are materials in which the interactions between electrons are quite strong relative to their kinetic energy. Whereas the kinetic energy dominates in a metal like aluminum (which is why free-electron theory works so well) there are many materials such as the transition metal oxides (for example, vanadium oxide) where the electron kinetic energy is reduced because the electrons are tightly bound to the host atoms. There is a lot of strange physics, much of which is still not really understood, which happens in this case. My current interest is in the interplay between disorder and strong-correlations in the highly disordered limit. This turns out to be a surprisingly rich problem. In a metal like aluminum, disorder (ie. impurities and imperfections) increase the electrical resistivity, but not much else happens. In strongly-correlated materials, it seems possible to drive the materials through a metal-insulator transition, and even to induce a magnetic glass phase, just by adding impurities. In particular, I want to understand how exactly the Mott-Anderson transition occurs. I have recently collaborated on a theoretical study of LiAlyTi2-yO4 [10], and have an ongoing interest in Anderson localization [5,6,7,14] and zero bias anomalies [11,12,13] in strongly-correlated materials .



ZBA

A zero bias anomaly (ZBA) is a peak or a dip in the density of states that is pinned to the Fermi energy. Most electronic properties of materials (electrical conductivity, for example) come from quantum states near the Fermi energy, and many of these properties are tied directly to the density of states. I am specifically interested in disorder-induced zero bias anomalies. In materials exhibiting a ZBA, there is a subtle interplay between disorder and electron-electron interactions that leads to a dramatic suppression of the density of states. The figure on the left shows the density of states calculated for the disordered Hubbard model within three different approximations: nonmagnetic Hartree-Fock (NMHF), unrestricted Hartree-Fock (UHF) and exact diagonalization (ED). Although the UHF and ED results look quite similar, we have been able to show that the reasons for the suppression are very different.[13]





Publications

A complete list of my publications can be found here.

A few recent notable publications:






Last update: February 28, 2011