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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.
The researchers’ model predicted topological semimetals in which the ends of two Fermi arcs would join at an angle or cross each other in a way that was previously unseen. Through a combination of intuition and simulation, Fang and Liu identified a material — a combination of strontium, indium, calcium, and oxygen — that, according to their theory, should exhibit such exotic Fermi arcs.
What uses, if any, these Fermi arcs may have is not clear. But topographical semimetals have such tantalizing electrical properties that they’re worth understanding better.
Of his group’s new work, however, Fu acknowledges that for him, “the appeal is its mathematical beauty — and the fact that this mathematical beauty can be found in real materials.”
“There are different kinds of semimetals, and the simplest one is called the Weyl semimetal,” says Ashvin Vishwanath, a professor of physics at the University of California at Berkeley. “The Fermi arcs are definitely stable for Weyl systems. But what Liang and his collaborators showed is that there is a class of so-called Dirac semimetals for which they are also stable. Dirac semimetals have a pair of these Fermi arcs, two copies that are opposite to each other and are superposed. You might expect that these would cancel out and give you something that looks simple. It was a bit of a surprise for me to see that these things are stable.”
“They’ve established that these Fermi-arc surface states may occur in a wider class of systems than previously believed, so from that point of view, it’s expanding the scope of the applicability of these ideas,” he adds. “The systems certainly have some nice properties that may make them attractive. For example, the electron has a spin, and the direction of motion of the Fermi arcs is governed by the spin. That could have potential applications to things like spintronics, where people use the electron spin to control electrical currents.”
