This is an example of a) symmorphic symmetry vs. b) nonsymmorphic symmetry. CREDIT: Lukas Muechler.
In order to characterize a category of metals with fascinating electronic properties that can help to discover other, similarly endowed materials, researchers from Princeton, Yale, and the University of Zurich have put forward a theory-based approach.
The research describes a new category of metals based on their symmetry as well as a mathematical classification called topological number, which predicts special electronic properties. It has been published in the journal Physical Review X.
The exceptional research interest toward topological materials from the early 2000s has culminated in last year’s Nobel Prize in Physics being awarded to three physicists for their theoretical discoveries in the field. Princeton professor F. Duncan Haldane is one of them.
Topological classification is a very general way of looking at the properties of materials.
Lukas Muechler, Graduate Student, Princeton University
This abstract mathematical classification is often explained using breakfast items. According to topological classification, coffee cups and donuts are considered equivalent as they both have one hole and can be smoothly deformed into one another. However, donuts cannot be deformed into muffins, making them inequivalent.
Here, an example of a topological invariant is the number of holes, which is equal for the coffee cup and donut, but distinguishes the muffin from the donut.
“The idea is that you don’t really care about the details. As long as two materials have the same topological invariants, we can say they are topologically equivalent,” stated Lukas Muechler.
The curiosity of Muechler and team regarding the topological classification of the new category of metals was kindled by a unique finding in the neighboring laboratory of Princeton Professor Robert Cava.
When a crystal known as WTe2 was analyzed for superconductivity, the Cava lab accidentally discovered that the crystal had the ability to continually increase its resistance when increasingly stronger magnetic fields were applied. This property can be applied to construct a magnetic field sensor.
However, the origin of this property was mysterious.
This material has very interesting properties, but there had been no theory around it.
Lukas Muechler , Graduate Student, Princeton University
Initially, the arrangement of the atoms in WTe2 was taken into consideration. The symmetries, i.e. patterns of arrangement of the atoms, can be classified into different classes, namely, symmorphic and nonsymmorphic. These two classes are the reason for profound differences in electronic properties, e.g. transfer of current in an electromagnetic field.
Although WTe2 was made up of a number of atom layers stacked one over the other, Car and his colleagues discovered that a single layer possessed a unique nonsymmorphic symmetry in which the atomic arrangement remains unaltered overall when it is rotated and then translated by a fraction of the lattice period.
Once the researchers determined the symmetry, they then mathematically characterized every possible electronic state with this symmetry, ultimately classifying the states that can be smoothly deformed into one another as topologically equivalent, similar to a donut that can be deformed into a cup.
Using this classification, they discovered that the WTe2 crystal belonged to a new category of metals, which they named nonsymmorphic topological metals. These metals were established to have an electron number different from the previously analyzed nonsymmorphic metals.
In the case of nonsymmorphic topological metals, electrons that transfer current act like relativistic particles, that is, particles traveling at a speed close to speed of light. The fact that this property is not as susceptible to defects and impurities as ordinary metals renders them sought-out materials for electronic devices.
The researchers also used the abstract topological classification to explain some of the exceptional electronic properties of bulk WTe2, especially its perfect compensation, suggesting that it possesses equal number of electrons and holes. Muechler stated that the researchers also employed theoretical simulations to propose that this property can be attained by three-dimensional crystalline stacking of the WTe2 monolayers, a totally astonishing outcome.
Usually in theory research there isn’t much that’s unexpected, but this just popped out. This abstract classification directly led us to explaining this property. In this sense, it’s a very elegant way of looking at this compound and now you can actually understand or design new compounds with similar properties.
Lukas Muechler , Graduate Student, Princeton University
Some of the latest photoemission experiments have demonstrated that the electrons in WTe2 absorbed right-handed photons in a manner different from absorbing left-handed photons. The theory conceived by the researchers indicated that the photoemission experiments on WTe2 can be perceived based on the topological properties of the new category of metals.
Future research in this area should concentrate on analyzing whether such topological properties are also found in atomically-thin layers of these metals exfoliated from a larger crystal to fabricate electronic devices.
“The study of this phenomena has big implications for the electronics industry, but it’s still in its infant years,” stated Muechler.
This work received support from the Department of Energy (DE-FG02-05ER46201), the Yale Postdoctoral Prize Fellowship as well as the National Science Foundation NSF CAREER DMR-095242, ONR-N00014-11-1- 0635, MURI-130-6082, NSF-MRSEC DMR-0819860, Packard Foundation, Keck grant, "ONR Majorana Fermions" 25812-G0001-10006242-101, and Schmidt fund 23800-E2359-FB62.