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MIT researchers are working on a new theoretical characterization of topological semimetals’ electrical properties that predicts several potential new uses in electronics and computing.
In a topological semimetal, the word “topological” describes the graph of the relationship between the energy and the momentum of electrons in the material’s surface.
“Generally, the properties of a material are sensitive to many external perturbations,” says Liang Fu, an assistant professor of physics at MIT and senior author on a new paper on the research.
“What’s special about these topological materials is they have some very robust properties that are insensitive to these perturbations,” said Fu.
Discovered just five years ago, semimetals work like semiconductors, which are at the core of all modern electronics. Electrons in a semiconductor can be in either the “valence band,” in which they’re attached to particular atoms, or the “conduction band,” in which they’re free to flow through the material as an electrical current. Switching between conductive and nonconductive states is what enables semiconductors to use binary computation.
Bumping an electron from the valence band into the conduction band requires energy, and the energy differential between the two bands is known as the “band gap.” In a semimetal — such as carbon sheets known as graphene — the band gap is zero. In principle, that means that semimetal transistors could switch faster, at lower powers, than semiconductor transistors do.
Fu and his colleagues have showed that the momentum-energy relationships of electrons in the surface of a topological semimetal can be described using mathematical constructs called Riemann surfaces.
“What makes a Riemann surface special is that it’s like a parking-garage graph,” Fu says. “In a parking garage, if you go around in a circle, you end up one floor up or one floor down.
The researchers showed that a certain class of Riemann surfaces accurately described the momentum-energy relationship in known topological semimetals. But the class also included surfaces that corresponded to electrical characteristics not previously seen in nature.
The momentum-energy graph of electrons in the surface of a topological semimetal is three dimensional: two dimensions for momentum, one dimension for energy. If you take a two-dimensional cross section of the graph — equivalent to holding the energy constant — you get all the possible momenta that electrons can have at that energy. The graph of those momenta consists of curves, known as Fermi arcs.
What uses, if any, these Fermi arcs may have is not yet clear, however topographical semimetals have such tantalising electrical properties that they’re worth understanding better.