Condensed Matter Theory
Alfred P. Sloan Fellow
University of Illinois at Urbana-Champaign;
Los Alamos National Laboratory
Professor Yu has a broad range of research interests which include
disordered systems, biophysics, noise, and quantum computing.
BIOPHYSICS OF INTRACELLULAR TRANSPORT: A cell is like a city. It has all the basic infrastructure that a city
has. For example, it has power plants (mitochondria), workers (proteins),
a library (genome), recycling centers (lysosomes), etc. A cell also
has a transportation system that works like container shipping.
There are interstate highways (microtubules) and local streets
(actin filaments) as well as trucks or motors (kinesin, dynein, and myosin)
that pull large cargo vesicles along the roads. We are working with
Steven Gross' group (UCI Dept. of Cell and Developmental Biology) to
understand how the motors and roads conspire to get cargo vesicles where
they need to go. The motion of the vesicles does not proceed smoothly
in one direction. Rather it can frequently reverse direction along
one road or switch roads as it diffuses through the cell.
So how does the cargo get to where it needs to go? To answer this
question, we are using a variety of theoretical techniques
including computer simulations, graph theory, time series analysis,
noise analysis, and chaos theory to analyze the motion.
DISORDERED SYSTEMS: Disordered systems such as glasses and spin
glasses. The physics of glassy systems is one of the most interesting
and least understood problems in condensed matter physics.
In the field of disordered systems, the Yu group is investigating several
topics including the glass transition, Coulomb glasses, dipolar glasses,
and the low temperature properties of glasses.
The Glass Transition: Is a glass is a liquid or a solid? Is the glass transition
a thermodynamic phase transition or a kinetic slowing down of the
molecules? No one knows the answers.
Professor Yu's group is currently studying the glass transition using
molecular dynamics simulations. They recently showed that the glass
transition as signaled by a peak in the specific heat can be the result
of insufficient sampling of the energy landscape. Another result of
insufficient sampling is that the specific heat displays frequency
dependence even in a system that shows no signs of aging.
Coulomb Glasses: A Coulomb glass is an insulator in which the electrons occupy randomly
placed sites, and interact with one another via a long-range Coulomb
potential. A practical realization of a Coulomb glass
is found in doped, compensated semiconductors where the disorder
is produced by the random placement of donor and acceptor impurities.
We have used simulations to show for the first time
that as the temperature is lowered,
the electrons undergoes a second order phase transition into a Coulomb
glass phase. We are currently exploring how this transition changes with
the amount of disorder.
The competition between interactions and disorder result in
glassy dynamics that are often associated with very long relaxation times
extending over many decades. One might not
expect the same to be true in an electronic system
since electrons typically respond very quickly.
However, in the presence of strong disorder such as that found in
a Coulomb glass, electrons can indeed have very long relaxation times.
In particular I have done a calculation where the Coulomb interaction between
electrons is suddenly turned on and I
follow the subsequent time development of the Coulomb gap (see above)
in the density of states and
show that it can occur over many decades of time due to slow electron
hopping and rearrangement. (In order for the ground state to be stable
to small perturbations such as single electron hops, Pollak, and
Efros and Shlovskii showed that
the zero temperature density of single-particle states
must vanish at zero energy, i.e., at the Fermi energy.
This is the origin of the Coulomb gap.) This is consistent with experiments.
Because of the competition between randomness and interactions,
the electrons exhibit glassy behavior at low temperatures with electron
hopping occurring over a broad range of times scales. We have
shown that these long relaxation times produce low frequency 1/f noise
at low temperatures. Even though 1/f noise is ubiquitous in conducting
devices, the microscopic mechanisms are not well understood. Our approach
was new and works much better than previous theories of 1/f noise
in Coulomb glasses. We used a microscopic model in which the
conduction electrons travel through a percolating network. The noise
is produced by electrons which occasionally hop between isolated clusters
and the extended network.
The Low Temperatures Properties of Glasses:
Glasses at low temperatures also present a challenge.
A bunch of molecules in a disordered jumble behaves very
differently from an ordered crystalline array of
those same molecules. This can be seen in
low temperature thermodynamic properties that
tend to be universal, independent
of the particular material and its chemistry. What is it
about the nature of disorder that gives rise to such universal
properties? This is the basic problem of disordered systems.
Professor Yu has studied this question with models in
which defects or tunneling centers interact with one another.
More recently her group has been concerned with the influence of
these two level systems on qubits.
QUANTUM COMPUTING QUBITS:
The basic unit of information for any computer is the bit. For a quantum
computer the quantum bit, or "qubit", is a wavefunction
describing a coherent superposition of the |0> and |1> state. Decoherence
of the wavefunction is one of the great obstacles facing the realization
of quantum computers. Josephson junction (JJ) qubits are a leading
candidate for making a quantum computer. A major obstacle to the
realization of quantum computers with Josephson junction qubits is
decoherence. The goal
of our research is to elucidate the microscopic sources of this decoherence and to suggest ways to eliminate or reduce these culprits.
We are working closely with experimentalists.
A Josephson junction consists of 2 superconducting electrodes separated
by a tunnel barrier that is often an insulator. The current passing
through a Josephson junction is superconducting. We are investigating
two level systems in the barrier produce noise and can lead to
decoherence of the qubit.
Frequency Dependence and Equilibration
of the Specific Heat of Glass Forming Liquids (with H. M. Carruzzo),
1/f Noise in Electron Glasses (with K. Shtengel), Phys. Rev. B 67,
Structural Probe of a Glass Forming Liquid: Generalized Compressibility,
(with H. M. Carruzzo), Phys. Rev. E 66, 021204 (2002).
Generalized Compressibility in a Glass Forming Liquid (with H. M. Carruzzo),
Phil. Mag. B 82, 125 (2002).
Slow Dynamics in Glassy Systems, Phil. Mag. B 81, 1209 (2001).
Viscoelasticity and Surface Tension
at the Defect--Induced First--Order Melting Transition of a Vortex Lattice
(with H. M. Carruzzo), Phys. Rev. B 61, 1521 (2000).
Time Dependent Development of the Coulomb Gap, Phys. Rev. Lett. 82, 4074
Absence of a Magnetic Field Induced Metal-Insulator Transition
in Kondo Insulators (with H. M. Carruzzo), Phys. Rev. B. 53, 15377 (1996).
Kondo Insulators Modeled by the One Dimensional Anderson Lattice: A Numerical Renormalization Group Study, (with M. Guerrero), Phys. Rev. B 51, 10301 (1995).
Non-EquilibriumDielectric Behavior in Glasses at Low Temperatures Evidence for Interacting Defects (with H. M. Carruzzo and E. R. Grannan), Phys. Rev. B 50, 6685 (1994).
A Numerical Renormalization Group Study of the One Dimensional Kondo Insulator, (with S. R. White), Phys. Rev. Lett. 71, 3866 (1993).
Critical Behavior of the Coulomb Glass, (with E. R. Grannan), Phys. Rev. Lett. 71, 3335 (1993).
Phase Transitions of Interacting Elastic Defects, Phys. Rev. Lett. 69, 2787 (1992).
Low Temperature Properties of Amorphous Materials: Through a Glass Darkly, (with A. J. Leggett) Comments on Condensed Matter Physics, 14, 231 (1988).
American Physical Society