An international team of researchers
has predicted the existence of several previously unknown types of quantum
particles in materials. The particles—which belong to the class of particles
known as fermions—can be distinguished by several intrinsic properties, such as
their responses to applied magnetic and electric fields. In several cases,
fermions in the interior of the material show their presence on the surface via
the appearance of electron states called Fermi arcs, which link the different
types of fermion states in the material's bulk.
The research, published online this
week in the journal Science, was conducted by a team at Princeton
University in collaboration with researchers at the Donostia International
Physics Center (DIPC) in Spain and the Max Planck Institute for Chemical
Physics of Solids in Germany. The investigators propose that many of the
materials hosting the new types of fermions are "protected metals,"
which are metals that do not allow, in most circumstances, an insulating state
to develop. This research represents the newest avenue in the physics of
"topological materials," an area of science that has already
fundamentally changed the way researchers see and interpret states of matter.
The team at Princeton included Barry
Bradlyn and Jennifer Cano, both associate research scholars at the Princeton
Center for Theoretical Science; Zhijun Wang, a postdoctoral research associate
in the Department of Physics, Robert Cava, the Russell Wellman Moore Professor
of Chemistry; and B. Andrei Bernevig, associate professor of physics. The
research team also included Maia Vergniory, a postdoctoral research fellow at
DIPC, and Claudia Felser, a professor of physics and chemistry and director of
the Max Planck Institute for Chemical Physics of Solids.
For the past century, gapless fermions,
which are quantum particles with no energy gap between their highest filled and
lowest unfilled states, were thought to come in three varieties: Dirac,
Majorana and Weyl. Condensed matter physics, which pioneers the study of
quantum phases of matter, has become fertile ground for the discovery of these
fermions in different materials through experiments conducted in crystals.
These experiments enable researchers to explore exotic particles using
relatively inexpensive laboratory equipment rather than large particle
accelerators.
In the past four years, all three
varieties of gapless fermions have been theoretically predicted and
experimentally observed in different types of crystalline materials grown in
laboratories around the world. The Weyl fermion was thought to be last of the
group of predicted quasiparticles in nature. Research published earlier this
year in the journal Nature (Wang et al., DOI:
10.1038/nature17410) has shown, however, that this is not the case,
with the discovery of a bulk insulator which hosts an exotic surface fermion.
In the current paper, the team predicted and classified the possible exotic fermions that can appear in the bulk of materials. The energy of these fermions can be characterized as a function of their momentum into so-called energy bands, or branches. Unlike the Weyl and Dirac fermions, which, roughly speaking, exhibit an energy spectrum with 2- and 4-fold branches of allowed energy states, the new fermions can exhibit 3-, 6- and 8-fold branches. The 3-, 6-, or 8-fold branches meet up at points - called degeneracy points - in the Brillouin zone, which is the parameter space where the fermion momentum takes its values.
"Symmetries are essential to keep
the fermions well-defined, as well as to uncover their physical
properties," Bradlyn said. "Locally, by inspecting the physics close
to the degeneracy points, one can think of them as new particles, but this is
only part of the story," he said.
Cano added, "The new fermions know
about the global topology of the material. Crucially, they connect to other
points in the Brillouin zone in nontrivial ways."
During the search for materials
exhibiting the new fermions, the team uncovered a fundamentally new and
systematic way of finding metals in nature. Until now, searching for metals
involved performing detailed calculations of the electronic
states of matter.
"The presence of the new fermions
allows for a much easier way to determine whether a given system is a protected
metal or not, in some cases without the need to do a detailed
calculation," Wang said.
Verginory added, "One can just
count the number of electrons of a crystal, and figure out, based on symmetry,
if a new fermion exists within observable range."
The researchers suggest that this is
because the new fermions require multiple electronic states to meet in energy:
The 8-branch fermion requires the presence of 8 electronic states. As such, a
system with only 4 electrons can only occupy half of those states and cannot be
insulating, thereby creating a protected metal.
"The interplay between symmetry,
topology and material science hinted by the presence of the new fermions
is likely to play a more fundamental role in our future understanding of
topological materials - both semimetals and insulators," Cava said.
Felser added, "We all envision a future for quantum physical chemistry where one can write down the formula of a material, look at both the symmetries of the crystal lattice and at the valence orbitals of each element, and, without a calculation, be able to tell whether the material is a topological insulator or a protected metal."
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