Physicists predict novel phenomena in exotic materials

June 06, 2016

Discovered just five years ago, topological semimetals are materials with unusual physical properties that could make them useful for future electronics.

In the latest issue of Nature Physics, MIT researchers report a new theoretical characterization of topological semimetals' electrical properties that accurately describes all known topological semimetals and predicts several new ones.

Guided by their model, the researchers also describe the chemical formula and crystal structure of a new topological semimetal that, they reason, should exhibit electrical characteristics never seen before.

"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 the new paper. "What's special about these topological materials is they have some very robust properties that are insensitive to these perturbations. That's attractive because it makes theory very powerful in predicting materials, which is rare in condensed-matter physics. Here, we know how to distill or extract the most essential properties, these topological properties, so our methods can be approximate, but our results will be exact."

Semimetals are somewhat 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 instantiate the logic of 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 the much-studied 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.

Parking-garage graphs

The term "topological" is a little more oblique. Topology is a branch of mathematics that treats geometry at a high level of abstraction. Topologically, any object with one hole in it -- a coffee cup, a donut, a garden hose -- is equivalent to any other. But no amount of deformation can turn a donut into an object with two holes, or none, so two-holed and no-holed objects constitute their own topological classes.

In a topological semimetal, "topological" doesn't describe the geometry of the material itself; it describes the graph of the relationship between the energy and the momentum of electrons in the material's surface. Physical perturbations of the material can warp that graph, in the same sense that a donut can be warped into a garden hose, but the material's electrical properties will remain the same. That's what Fu means when he says, "Our methods can be approximate, but our results will be exact."

Fu and his colleagues -- joint first authors Chen Fang and Ling Lu, both of whom were MIT postdocs and are now associate professors at the Institute of Physics in Beijing; and Junwei Liu, a postdoc at MIT's Materials Processing Center -- showed that the momentum-energy relationships of electrons in the surface of a topological semimetal can be described using mathematical constructs called Riemann surfaces.

Widely used in the branch of math known as complex analysis, which deals with functions that involve the square root of -1, or i, Riemann surfaces are graphs that tend to look like flat planes twisted into spirals.

"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. This is exactly what happens for the surface states of topological semimetals. If you move around in momentum space, you find that the energy increases, so there's this winding."

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.

Cross sections

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."
-end-
Additional background

ARCHIVE: Researchers find unexpected magnetic effect http://news.mit.edu/2016/unexpected-magnetic-effect-thin-film-materials-0509

ARCHIVE: Long-sought phenomenon finally detected http://news.mit.edu/2015/Weyl-points-detected-0716

ARCHIVE: New findings could point the way to "valleytronics" http://news.mit.edu/2014/valleytronics-2-d-microchip-different-electron-properties-1215

ARCHIVE: New 2-D quantum materials for nanoelectronics http://news.mit.edu/2014/2-d-quantum-materials-for-nanoelectronics-1120

Massachusetts Institute of Technology

Related Electrons Articles from Brightsurf:

One-way street for electrons
An international team of physicists, led by researchers of the Universities of Oldenburg and Bremen, Germany, has recorded an ultrafast film of the directed energy transport between neighbouring molecules in a nanomaterial.

Mystery solved: a 'New Kind of Electrons'
Why do certain materials emit electrons with a very specific energy?

Sticky electrons: When repulsion turns into attraction
Scientists in Vienna explain what happens at a strange 'border line' in materials science: Under certain conditions, materials change from well-known behaviour to different, partly unexplained phenomena.

Self-imaging of a molecule by its own electrons
Researchers at the Max Born Institute (MBI) have shown that high-resolution movies of molecular dynamics can be recorded using electrons ejected from the molecule by an intense laser field.

Electrons in the fast lane
Microscopic structures could further improve perovskite solar cells

Laser takes pictures of electrons in crystals
Microscopes of visible light allow to see tiny objects as living cells and their interior.

Plasma electrons can be used to produce metallic films
Computers, mobile phones and all other electronic devices contain thousands of transistors, linked together by thin films of metal.

Flatter graphene, faster electrons
Scientists from the Swiss Nanoscience Institute and the Department of Physics at the University of Basel developed a technique to flatten corrugations in graphene layers.

Researchers develop one-way street for electrons
The work has shown that these electron ratchets create geometric diodes that operate at room temperature and may unlock unprecedented abilities in the illusive terahertz regime.

Photons and electrons one on one
The dynamics of electrons changes ever so slightly on each interaction with a photon.

Read More: Electrons News and Electrons Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.