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M. Bonitz/Christian Albrechts Univ. |
Holes in the theory.
Even though a hole (red) is merely the absence of an electron (yellow)
in a material, holes can crystallize under the right conditions,
according to computer simulations. (See animations below.) |
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Ordinarily, a crystal is a regular array of particles, such as
atoms. But now a team of researchers has described the opposite--a
crystal made entirely of holes immersed in a sea of particles. In the 2 December PRL
they report computer simulations showing that, under the right
conditions, the holes within a semiconductor's electron "sea" can
crystallize. They suggest how such crystals could be coaxed to form and
note that similar crystals might occur naturally within stars and other
astronomical objects.
Metals and semiconductors are essentially crystals of
positively-charged ions arrayed in a sea of negatively-charged
electrons. The electron sea surrounding the ions is complex, with
several energy levels, or bands. An electron that jumps up from a lower
level to a higher one leaves behind a "hole".
Even though a hole is just the absence of an electron, it can act a
lot like a particle. Holes are positively charged, and they have an
apparent, or "effective," mass--just as electrons do--that reflects
their ability to move through a given material. A hole could be
effectively "heavy" if collisions with atoms in the material cause it
to respond sluggishly to an external electric field. Because holes can
act like particles, condensed matter physicists have hypothesized for
decades that they might be able to form crystals. Now Michael Bonitz of
the Christian Albrechts University in Kiel, Germany, and his
colleagues, have come up with the conditions such a "hole crystal"
would require.
The researchers calculated that a hole crystal could form
spontaneously in a semi-conductor if three requirements are met: The
material has to be cold enough to slow the holes, but not the
electrons--perhaps tens of degrees Kelvin--and the holes have to be
both numerous and heavy. To help them stay put in a crystal, the team
calculates the holes must be at least 80 times heavier than the
electrons.
The team envisions an experiment in which a laser zaps the
semiconductor, causing a bunch of electrons to hop up to a higher
energy band and leave holes behind. If there are enough holes, and the
semiconductor is cold enough, the slow, heavy holes should settle into
a lattice that lasts until the electrons fall back to their original
energies in a few microseconds. Very few semiconductors provide a hole
to electron mass ratio of 80 to 1, but Bonitz and his colleagues claim
it could be done with the right mix of elements. In fact, a few
experimentalists have already started trying, Bonitz says.
Hugh DeWitt of Lawrence Livermore National Laboratory in California
says that hole crystals and related phenomena occur in the super dense
cores of white dwarfs and neutron stars. "We're at the point where we
need to do serious quantum mechanical simulations of the interiors of
stars," and the models done by Bonitz's group are very good examples of
that, he says. Bonitz points out that hole crystals are not just
strange curiosities--most matter in the universe is made up of
positively and negatively charged particles like holes and electrons in
extreme conditions that might be right for crystals. The hole crystal
may be more common than we think.
----Kim Krieger
Kim Krieger is a freelance science writer in Washington, DC.
Videos
Two States of Holes Hole crystal: Electrons are yellow and blue; holes are red and pink. AVI (4.9 MB)
Hole gas. AVI (6.1 MB)
Video courtesy of M. Bonitz, Christian Albrechts University. Information
on viewing video files.
Related information:
Crystallization in two Component Coulomb Systems M. Bonitz, V. S. Filinov, V. E. Fortov, P. R. Levashov, and H. Fehske
Phys. Rev. Lett. 95, 235006
(issue of 2 December 2005)
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