My research has focussed on materials in which the interactions
among the electrons are important, even for a qualitative
understanding of their
behavior. This is in contrast to the textbook examples of metals
and insulators, whose behavior is largely explicable in terms of
independent
electrons.
The particular systems I have worked on are the two-dimensional
electron gases that are realized in semiconductor
heterostructures,
superconducting fullerides, frustrated magnetic systems and the
cuprate superconductors. Issues that currently interest me
include:
Quantum Hall systems. Two-dimensional electron gases placed in
high magnetic fields exhibit the quantum Hall Effect, which
reflects an
underlying intricate set of novel phases. The excitations in
these phases have been of great interest for they are believed to
carry fractional quantum
numbers, i.e., charge and statistics. I'm interested in various
aspects of these excitations--whether they carry a third
fractional quantum number (an
intrinsic spin), under what circumstances the various quantum
numbers can be measured in the laboratory, and their internal
structure in various
limits.
For example, interesting variants of these excitations arise when
the spin of the electrons can fluctuate. In some cases the
excitations develop
topologically nontrivial spin order ("skyrmions") as a
consequence of geometric, or Berry, phases in the system. This
has led to questions about the
role of these geometric phases near the edges of quantum Hall
systems where yet another class of fascinating excitations lives
("edge states"), and
other electronic systems where local spin order and conduction
coexist.
Other problems of interest involve searching for possible new
phases in the quantum Hall regime, and the more theoretical
question of constructing
"better" field theories of the high-field dynamics.
Continuous quantum phase transitions. These are continuous phase
transitions that take place at absolute zero, i.e., in the ground
state of the
system, when some parameter other than the temperature is varied.
They are very interesting, for quantum effects are intrinsically
important to them,
most importantly in scrambling the dynamics with the
thermodynamics. Examples include transitions in magnetic systems,
superconductor-insulator
transitions, and transitions between quantum Hall states. I am
interested in very instructive analogies between the latter and
the transitions in
superconducting systems, understanding the seeming
superuniversality of these transitions, and looking for
experimental signatures that might shed
light on these issues.
There are also some general questions involving mechanisms of
dephasing and dissipation-near-zero temperature critical points
that are currently
unsettled and appear to be promising avenues of inquiry.
Frustrated Magnets. Classical frustrated magnets are primarily
identified by large ground state degeneracies, the Ising
antiferromagnet on a
triangular lattice being the canonical example of this phenomenon
and of the subclass of geometrically frustrated magnets.
Interesting new physics
can arise when quantum dynamics is introduced into these large
ground state manifolds on account of the singular nature of the
perturbation and a
fair amount of work has focussed on quantum Heisenberg models in
which the XY exchange is the quantum perturbation. I have been
interested
recently in simpler class of systems in which a transverse
magnetic field introduces a quantum dynamics into a frustrated
Ising magnet. The relative
simplicity allows much progress to be made, and the catalog of
results include examples of ``order by disorder'' such as the
triangular lattice
antiferromagnet as well as those of ``disorder by disorder''
(i.e. cooperative paramagnets) such as the kagome
antiferromagnet. One also obtains a
transparent connection to quantum dimer models which are in turn
connected to large-N antiferromagnets and to ideas on the origin of
superconductivity in the cuprates.
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