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In the March 8 issue of Nature, researchers at
Stanford, Harvard and Israel's Weizmann Institute of Science reported
that they have built such a system in a semiconductor nanostructure.
By applying voltages to nanoscale electrodes, the scientists can tune
how strongly the magnetic atom couples to one set of electrons, or
channel, compared to the other set. Their system of correlated
electrons demonstrates a two-channel Kondo effect.
"We are observing and controlling how electrons
dance with each other," says David Goldhaber-Gordon, an assistant
professor of physics at Stanford who in 2001 with theorist Yuval Oreg
of Weizmann came up with the idea of how to build the two-channel
Kondo system. Their co-authors on the Nature paper are Ronald Potok, a
former graduate student at Harvard and Stanford, now at Advanced Micro
Devices, who set the stage for the measurements by designing and
fabricating the nanostructures and cooling electrons in those
nanostructures to unprecedentedly low temperatures; Ileana G. Rau, a
Stanford doctoral candidate in applied physics who together with Potok
performed the measurements and analysis; and Hadas Shtrikman, a senior
staff scientist at Weizmann who grew the materials on which the
nanostructures were based.
The work was supported by the U.S. National Science
Foundation, the Packard Foundation, the Sloan Foundation, the Research
Corporation, the U.S. Army Research Office, the U.S.-Israel Binational
Science Foundation, Deutsch-Israelische Projektkooperation (German-Israeli
Project Cooperation) and the Israel Science Foundation.
Building an artificial atom
"I've been interested for quite some time in
creating model quantum systems," says Goldhaber-Gordon. "Traditionally,
researchers would get excited about a particular theoretical construct
and would look for a material that might show the properties of this
construct. But maybe sometimes there's no material that shows these
properties. Can you then use nanotechnology to create an artificial
structure that will be a realization of this theoretical construct?"
Goldhaber-Gordon and colleagues set out to build an
artificial structure that could demonstrate the two-channel Kondo
effect. They used nanopatterning techniques to create an artificial
magnetic atom-basically a "box" containing an odd number of electrons.
To it they attached two reservoirs of mobile electrons. The
conductance they measured through the nanostructure was strikingly
different depending on which reservoir's electrons the artificial
magnetic atom paired with. The researchers then tuned the couplings to
intermediate values so that the artificial magnetic atom would be
equally happy to pair with electrons from either-but not both-of the
reservoirs. The frustrated two-channel Kondo state revealed itself in
a conductance that depended unusually strongly on electron energy.
The artificial magnetic atom and the two reservoirs
are built out of a semiconductor, gallium arsenide, also found in cell
phone transistors and laser pointers. Gallium arsenide makes up about
2 percent of the world's semiconductor market, according to
Goldhaber-Gordon. "That's important because it means that there's been
a lot of development that's gone into making the material perfect and
into tuning its properties with nanoscale electrodes," he says.
Gallium arsenide's perfection made it a better
starting material than the world's most famous semiconductor, silicon.
"To build computer chips you begin with a wafer of silicon, and you
grow a thin layer of glass-silicon oxide-on top of it,"
Goldhaber-Gordon says. "At the interface between those two, you can
form a sheet of electrons. But that interface is not so smooth because
silicon is a crystal and silicon oxide is amorphous; it doesn't have a
regular structure. So on the atomic scale, that interface is rough.
Electrons traveling along the interface feel that roughness, and that
causes them to jiggle around and not travel in straight lines."
In contrast, in a layered structure in which
gallium arsenide replaces silicon and aluminum gallium arsenide
replaces silicon oxide, both materials are crystals. Their interface
is smooth, so in the best structures electrons can travel as far as a
fraction of a millimeter, past millions of atoms, before getting
turned around. Such a perfect sheet of electrons is an ideal starting
point for further confining electrons to nanostructures such as that
used to study the two-channel Kondo effect.
In fact, the main theme of Goldhaber-Gordon's work
is confining electrons-to two-dimensional sheets, one-dimensional
wires and zero-dimensional "boxes" in which they're confined in all
directions. Besides building model systems like the two-channel Kondo
system, he hopes to explore the basic science of future transistors.
For example, how are familiar relations such as Ohm's law modified as
wires get narrower? If you apply a voltage to an electrically
conductive material, a current of electrons flows through the
material. According to Ohm's law, that current is proportional to the
voltage applied. If the wire narrows, the resistance-the ratio between
applied voltage and current-goes up. At some point-below about 50
nanometers for typical semiconductors-the wire is so narrow that
electrons, like cars in a traffic jam, can't get around each other and
instead must go through single file. Resistance is then predicted to
vary with voltage, becoming infinite at low voltage. By measuring
current-voltage relations, Goldhaber-Gordon can investigate how
electrons organize themselves in such narrow confines.
Graphene and beyond
Goldhaber-Gordon's group also is looking at novel
materials in which electrons can be confined. A low-tech material
they've looked to recently may seem an unlikely candidate for a new
conductor-it's pencil lead. Graphite is structured as sheets of packed
hexagons, like chicken wire, and the sheets slide off easily as a
pencil glides across a sheet of paper. Recently, scientists have
discovered how to peel off just a single sheet, called graphene. The
hexagonal bonding in graphene makes it an electrical conductor, and
this new material may have exotic properties akin to other hexagonally
bonded carbon materials, such as nanotubes and buckyballs.
"A lot of what I do I do because I want to
understand basic quantum mechanics," Goldhaber-Gordon says. "We've had
the equations of quantum mechanics for more than 70 years, and every
experimental test we've devised says that they're right, but
unfortunately we can't solve them except in very simple cases."
Undergraduates routinely calculate the quantum states of a hydrogen
atom, which has one electron, but a helium atom, with just two
electrons, is so complex that a full understanding of its excited
states requires sophisticated approximations and intensive computer
power.
"Now imagine 10 electrons or 100 electrons in a
semiconductor nanostructure," he says. "It's impossible to do a direct
calculation of how they behave, and yet because electrons repel each
other we know that they're going to be doing some rich and complicated
dances around each other to avoid each other. I want to understand
those dances." |
