Research
Thrusts
..... Nanostructures
..... Biomimetics
..... Bio-Nano
Pradeep Kumar - My research has been in the theory of Condensed Matter Physics.
- Magnetism and Superconductivity:
Recent specific interest lies in magnetism and superconductivity, especially in a coexistence of these phenomena. In magnetism I continue to work on the special features of nuclear magnetism, whether in Solid 3He or due to the nuclear moments in metals. The coexistence of magnetism and superconductivity in heavy fermion compounds (these are compounds of rare earth materials which have anomalously large specific heat in the normal state and are also superconducting) is in close collaboration with my experimentalist colleagues G. Stewart and B. Andraka.
- Competing/Conflicting Order:
In a superconductor, there may be coexisting order of differing symmetries. Starting with our work on doped UBe13, where we had proposed an order parameter consisting of an s-wave component and a d-wave component, there has been a longstanding interest in this subject. Much of the recent work has been to study the high Tc Copper oxides, in particular the Y-based 123 compounds. By invoking a gradient coupling (following the suggestions of Brand, Doria and Pleiner), Ting et al have suggested a complex core structure of vortices with an s-wave precore and an unusual distribution of angular momentum. In a recent paper, with Balatsky and Schrieffer, we have studied a field induced mixing of a dxy component to a dominant dx2-y2 component. We have derived a mode corresponding to a clapping like motion of the two order parameters.
- Higher Order Phase Transitions
It appears that the transition to superconductivity in Ba(1-x)KxBiO3 may be of order 4 in the original classification of phase transitions by Ehrenfest. In collaboration with Donavan Hall (NHMFL) and R. G Goodrich we have noted the anomalous experimental results in the measurement of magnetization. A higher order ( say of order n) phase transition is where the nth derivative of the free energy with respect to temperature and/or a mechanical variabe such as magnetic field is discontinuous. For example for a 2nd order phase transition, the specific heat is found to be discontinuous. Often the discontinuity is replaced by a weak (nearly logarithmic) divergence characterized by scaling exponents and the exponents in turn, satisfy scaling laws. In a higher order transition, the first singular derivative of the free energy can be associated with exponents. We have derived scaling relations between these exponents.
- Phonon Modes and Heat Conductance in a Nanowire:
My student S. Patamia, is carrying out an extensive study of lattice vibrations in meso/nano structures. In small systems, boundary effects play an important role in determining the shape dependent density of states of elastic excitations which in turn influence the thermodynamic and transport properties. Because there are lower symmetry surfaces, there are modes corresponding to surfaces, edges and corners. We have developed a mathematical formalism to calculate the phonon density of states for an arbitrary shaped object. Concurrently, we have a collaboration with A. B. Saxena (Los Alamos) to study mechanical properties of a nanoscale system using molecular dynamics simulation.