E

*A
schematic illustration of a nanoscale circuit. A quantum dot (the yellow part)
is connected to two lead electrodes (the blue parts). Electrons tunneling into
the quantum dot from the electrodes interact with each other to form a highly
correlated quantum state, called “Fermi liquid”. Both nonlinear electric
current passing through the quantum dot and its fluctuations that appear as a
noise carry important signals, which can unveil underlying physics of the
quantum liquid. It is clarified that three-body correlations of the electrons
evolve significantly and play essential roles in the quantum state under the
external fields that break the particle-hole or time-reversal symmetry. Credit:
Rui Sakano.*

Osaka City
University scientists have developed mathematical formulas to describe the
current and fluctuations of strongly correlated electrons in quantum dots.
Their theoretical predictions could soon be tested experimentally.

Theoretical
physicists Yoshimichi Teratani and Akira Oguri of Osaka City University, and
Rui Sakano of the University of Tokyo have developed mathematical formulas that
describe a physical phenomenon happening within quantum dots and other
nanosized materials. The formulas, published in the journal Physical Review
Letters, could be applied to further theoretical research about the physics of
quantum dots, ultra-cold atomic gasses, and quarks.

At issue
is the Kondo effect. This effect was first described in 1964 by Japanese
theoretical physicist Jun Kondo in some magnetic materials, but now appears to
happen in many other systems, including quantum dots and other nanoscale
materials.

Normally,
electrical resistance drops in metals as the temperature drops. But in metals
containing magnetic impurities, this only happens down to a critical
temperature, beyond which resistance rises with dropping temperatures.

Scientists
were eventually able to show that, at very low temperatures near absolute zero,
electron spins become entangled with the magnetic impurities, forming a cloud
that screens their magnetism. The cloud's shape changes with further
temperature drops, leading to a rise in resistance. This same effect happens
when other external "perturbations," such as a voltage or magnetic
field, are applied to the metal.

Teratani,
Sakano and Oguri wanted to develop mathematical formulas to describe the
evolution of this cloud in quantum dots and other nanoscale materials, which is
not an easy task.

To
describe such a complex quantum system, they started with a system at absolute
zero where a well-established theoretical model, namely Fermi liquid theory,
for interacting electrons is applicable. They then added a 'correction' that
describes another aspect of the system against external perturbations. Using
this technique, they wrote formulas describing electrical current and its
fluctuation through quantum dots.

Their
formulas indicate electrons interact within these systems in two different ways
that contribute to the Kondo effect. First, two electrons collide with each
other,

forming
well-defined quasiparticles that propagate within the Kondo cloud. More
significantly, an interaction called a three-body contribution occurs. This is
when two electrons combine in the presence of a third electron, causing an
energy shift of quasiparticles.

"The
formulas' predictions could soon be investigated experimentally," Oguri
says. "Studies along the lines of this research have only just
begun," he adds.

The
formulas could also be extended to understand other quantum phenomena, such as
quantum particle movement through quantum dots connected to superconductors.
Quantum dots could be a key for realizing quantum information technologies,
such as quantum computers and quantum communication.