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John O | July 2018

Wallpaper patterns lead to new insulating material with metallic surface


By Josh Perry, Editor
[email protected]

 

An international team of researchers from Princeton University (Princeton, N.J.), the University of Pennsylvania (Philadelphia, Pa.), Sungkyunkwan University (Seoul, South Korea), Freie Universität Berlin (Germany), and the Max Planck Institute of Microstructure Physics (Halle, Germany) has discovered a new insulating material with a metallic surface using new analytical methods that rely on mathematical properties like symmetry that are used in the repeating patterns of wallpaper.

 


This new insulating material is based on the symmetrical model of wallpaper.
(Wikimedia Commons)

 

According to a report from Princeton, the researchers believe this new material can be used to make more efficient electronics or advance the study of quantum computing.

 

The discovery of this new form of lead-strontium (Sr­2Pb3), which combines the electronic properties of graphene and 3-D topological insulators, a phase of matter that was originally discovered in 2005, ends more than a decade of study for these scientists.

 

“The new work demonstrates how the symmetries of certain two-dimensional surfaces, known as the 17 wallpaper groups for their wallpaper-like patterning, constrain the spatial arrangement (topology) of three-dimensional insulators,” the article explained.

 

Typically, in 3-D topological insulators each 2-D layer has a single group of states with cone-like dispersion. In graphene these are called Dirac cones and give the material its specific electronic transport characteristics. Graphene is also unusual because its four Dirac cones are paired that are “glued” together.

 

Researchers “suspected that with crystal symmetries, a second kind of topological insulator could exist with a single pair of glued Dirac cones.”

 

Based on the idea of a graduate assistant at Princeton, researchers “recognized that a glued pair of Dirac cones could be stabilized on crystal surfaces that have two intersecting lines along which the surfaces look identical after being flipped and turned perpendicularly. These lines, known as glide reflections, characterize the so-called nonsymmorphic wallpaper groups, and thus provide the namesake of this new phase, which the team dubbed a ‘nonsymmorphic Dirac insulator.’”

 

This understanding quickly led to a mathematical methodology for outlining the bulk topology of 3-D crystals and will help scientists design surface and interface states to meet their specific needs.

 

“To identify the Dirac insulating phase in nature, the researchers calculated the electronic structures of hundreds of previously synthesized compounds with surfaces with two glide lines (wallpaper groups pgg and p4g) before identifying the novel topology in lead-strontium,” the article added.

 

The research was recently published in Science. The abstract stated:

 

“Materials whose gapless surface states are protected by crystal symmetries include mirror topological crystalline insulators and nonsymmorphic hourglass insulators. There exists only a very limited set of possible surface crystal symmetries, captured by the 17 ‘wallpaper groups.’

 

“Here we show that a consideration of symmetry-allowed band degeneracies in the wallpaper groups can be used to understand previously described topological crystalline insulators and to predict phenomenologically distinct examples.

 

“In particular, the two wallpaper groups with multiple glide lines, pgg and p4g, allow for a topological insulating phase whose surface spectrum consists of only a single, fourfold-degenerate, true Dirac fermion, representing an exception to a symmetry-enhanced fermion-doubling theorem. We theoretically predict the presence of this phase in Sr2Pb3 in space group 127 (P4/mbm).”

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