Pradeep Kumar
Professor of Physics

Department of Physics
University of Florida

VOICE: (352) 392-6690

EMAIL: pkumar@ufl.edu

HOMEPAGE: http://www.phys.ufl.edu/~kumar/

Research Interests

1. 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.

2. Competing/Conflcting 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.

In an unrelated project in collaboration with A. B. Saxena (Los Alamos) and
A. S. Bhalla (Penn State), we are also studying properties of coexisting
magnetism and ferroelectricity. In a homogeneous material, it becomes a
fundamental question of conflicting symmetries. The materials are
sometimes referred to as Multiferroics. In an inhomogeneous material,
for example in a nanophase composite, the material properties are affected
in a profound way.

3. 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.

We have also derived a Ginzburg-Landau like free energy which
describes a higher order phase transition. This free energy implies an
anomalous temperature dependence for the thermodynamic critical
field, as well as for the lower critical field. These results are in agreement
with experiments.

4. 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.

Recent Publications

1. "Thermodynamics of a Superconducting Phase Transition in Ba0.6K0,4 BiO3 ", P. Kumar, D. Hall and R. G. Goodrich, Phys. Rev. Lett. 82, 4532 (1999). cond-mat/9904288

2. "Magnetic Field Study of Ce0.8 La0.2Al3 ", R. Pietri, P. Kumar and B. Andraka, J. App. Phys. 87, 5129, (2000)

3. "Collective Mode in a dx2-y2+id xy Superconductor", A. V. Balatsky, P. Kumar and J. R. Schrieffer, Phys. Rev. Lett. 84, 4445 (2000) cond-mat/9910342

4. A Comment on ``Superconducting-Normal Phase Transition in (Ba1-xKx)BiO3 , x = 0.40, 0.47'' by B. F. Woodfield, D. A. Wright, R. A. Fisher, N. E. Phillips and H. Y. Tang, Phys. Rev. Lett. 83, 4622 (1999), P. Kumar, D. Hall and R. G. Goodrich, UF preprint (1999). cond-mat/9912164

5. "Clapping Modes in Unconventional Superconductors" by A. V. Balatsky, P. Kumar and J. R. Schrieffer, in Proceedings of the M2 S conference on High Tc Superconductivity, Houston, TX, preprint (2000). Physica C341, 807-810 (2000). cond-mat/0009111

6. "Thermodynamics of a Higher Order Phase Transition: Scaling Exponents and Scaling Laws", P. Kumar and A. B. Saxena, Philosophical Magazine B82, 1201-1209 (2002).cond-mat/0205002

7. "Phonon Modes and Heat Conductance in a Free-Standing Nanowire", S. E. Patamia and P. Kumar, preprint UF (2001).

8. "Field Induced Transition in the Specific Heat of CeIrIn5, B>30T", J. S. Kim, J. Alwood, P. Kumar and G. R. Stewart, Phys. Rev. B65, 174520 (2002).

9. "Specific Heat Anomaly for H>28.5 T in CeIrIn5", J. S. Kim, J.. Alwood, P. Kumar and G. R. Stewart, in Proceedings of the PPHMF-IV, ed. by G. Boebinger, Z. Fisk, L. P. Gorkov, A. Lacerda and J. R. Schrieffer, p. 104-107, World Scientifc, Singapore (2002).

10. "Specific Heat of URu2Si2 in Fields to 42 T:Clues to the ¡°Hidden Order", J. S. Kim, D. Hall, P. Kumar and G. R. Stewart, Phys. Rev. B67, 014404 (2003). cond-mat/0301234

11. "Theory of a Higher Order Phase Transition: Superconducting Transition in BKBO" P. Kumar, Phys. Rev. B68, 064505 (2003).cond-mat/0207373