## Research Topics

The broad focus of Prof. Baranger's group is **the interplay of electron-electron interactions and quantum interference at the nanoscale**.
Fundamental interest in nanophysics - the physics of small, nanometer
scale, bits of solid - stems from the ability to control and probe
systems on length scales larger than atoms but small enough that the
averaging inherent in bulk properties has not yet occurred. Using this
ability, entirely unanticipated phenomena can be uncovered on the one
hand, and the microscopic basis of bulk phenomena can be probed on the
other. Additional interest comes from the many links between
nanophysics and nanotechnology. Within this thematic area, our work
ranges from projects trying to nail down realistic behavior in
well-characterized systems, to more speculative projects reaching
beyond regimes investigated experimentally to date. Currently, 5 topics
are being actively pursued:

** 1. Kondo Effect in Nanoscale Systems **

The Kondo effect is a classic of many-body physics involving the
correlation of an electron in an isolated level with a bulk Fermi sea.
In contrast, we consider a finite size Fermi sea and so treat the
non-zero level-spacing in the lead. The relevant experimental situation
is two quantum dots connected by tunneling, a very small one to supply
the electron in an isolated level and a large one to act as a nanoscale
Fermi sea. [with R. Kaul, D. Ullmo, and Prof. S. Chandrasekharan]

** 2. Molecular Electronics **

We have established a state-of-the-art program to calculate the
electric current through single molecules. This involved substantial
program development in previous years; we are now concentrating on
studying various systems. For instance, we carried out an extensive
study of molecules containing *cobaltocene*,
a sandwich molecule consisting of a Co atom between two 5-member carbon
rings. Cobaltocene has spin 1/2, and manipulation of this spin strongly
affects the electrical conduction. Thus we have introduced the first
examples of true *molecular spintronics* - a spin filter, spin valve, and spin switch. [with R. Liu, S.-H. Ke, and Prof. W. Yang]

** 3. Quantum Computing: Decoherence in Quantum Error Correction **

We focus on the effects of *decoherence* - processes which break
the quantum mechanical coherence at the basis of this type of
computation. A key question is how decoherence scales as the computer
becomes larger, that is, as the number of qubits increases so that the
states of the computer become increasingly more complicated entangled
states. Initial pessimistic estimates were circumvented by *quantum error correction*,
a clever encoding of a single logical qubit using several physical
qubits. We are studying how decoherence due to correlated noise scales
in a computer using error correction. [with E. Novais and Prof. E.
Mucciolo]

** 4. Toward Strong Interactions in Circular Quantum Dots **

The “electron gas” model of electrons in solids – in
which the conduction electrons interact via Coulomb forces but the
ionic potential is neglected – has been a key paradigm of solid
state physics. Quantum mechanically, the physical properties change
dramatically depending on the balance between the strength of the
Coulomb interaction and the kinetic energy. The limiting cases are well
understood: for very weak interactions the particles are delocalized
while for very strong interactions they localize in a Wigner crystal.
The physics at intermediate densities is surprisingly rich and remains
at the forefront of research. We are studying the *intermediate density electron gas* confined to various nanostructures by using quantum Monte Carlo techniques. [with A. Ghosal, D. Guclu, and Prof. C. Umrigar]

** 5. Quantum Phase Transitions **

We are studying models of strongly interacting systems in which there
is a quantum (zero temperature) phase transition as a function of
disorder strength. The models are chosen so that there is a cooperative
many-body ground state (superconductivity or ferromagnetism), and the
disorder introduces inhomogeneity through quantum interference. As the
inhomogeneity in the system grows, the cooperative state is eventually
killed at a quantum phase transition. Through careful study using
recently developed algorithms, we identify a bosonic
superconductor-insulator transition which has new critical exponents
which sharply disagree with previous theoretical prejudices. [with A.
Priyadarshee and Prof. S. Chandrasekharan]