Until the 1980s, most researchers thought that long-range order in physical systems was impossible without periodicity. They believed that atoms were packed inside crystals in symmetrical patterns that were periodically repeated over and over again, and that this repetition was necessary to obtain a crystal.

However, in 1984, Daniel Shechtman of the Technion-Israel institute of Technology discovered quasicrystals – materials that have ordered but not periodic structures. Shechtman made his discovery while studying samples of an aluminium-manganese alloy and found that the atoms in these crystals were packed in an icosahedral pattern that could not be repeated but which had "10-fold" rotational symmetry.

A system is said to possess n-fold rotational symmetry if it looks the same after it has been rotated through 360/n degrees. A sample with 10-fold rotational symmetry therefore remains unchanged after being rotated through 360/10 = 36 degrees. Before Shechtman’s discovery, a periodic system was only supposed to have either 1-, 2-, 3-, 4- or 6-fold rotational symmetry, with anything else being forbidden by the laws of crystallography.

Since this time, scientists have discovered hundreds of different quasicrystals, including icosahedral quasicrystals that have 2-fold, 3-fold and 5-fold rotational symmetry. There are also octagonal (8-fold), decagonal (10-fold) and dodecagonal (12-fold) quasicrystals that show "forbidden" rotational symmetries within 2D atomic layers but that are periodic in the direction perpendicular to these layers.

36-fold rotational symmetry

Now, a team led by Teri Odom is saying that it can pattern quasicrystal nanostructures with a staggering 36-fold rotational symmetry using a new moiré nanolithography technique. Moiré patterns have been known for a long time and can be seen in the everyday world by placing two pieces of fine mesh one on top of the other and then rotating them to create new, more complicated patterns. As you keep on twisting, the patterns change like in a kaleidoscope.

Moiré nanolithography relies on the interference of two repeating patterns overlapped at a specific angle, explains Odom. Two-dimensional periodic patterns can be routinely fabricated by photolithography over large areas, but these arrangements have six-fold rotational symmetry at most – like a hexagonal lattice. Other high-rotational symmetry quasicrystals have become popular in recent years (the most well known and highest being the 12-fold symmetry ones), but these must be patterned through serial lithography methods, such as focused ion beam milling and electron-beam lithography, which are time consuming and expensive.

Multiple exposures

“We succeeded in making nanopatterns with rotational symmetries higher than any quasicrystals previously reported by performing two or more exposures through patterned poly(dimethylsiloxane) (PDMS) elastomeric masks,” Odom told nanotechweb.org. “Because we first make the patterns in a photoresist, we can then transfer the moiré pattern onto a wide range of materials, from silicon to metals. We can then fabricate omnidirectional reflectors or electrodes, for example, using these structures fairly easily.”

One area in which such high-symmetry moiré nanopatterns might have a huge impact is in photovoltaics, she adds. Thanks to their omnidirectional design, these patterns can trap light with nearly the same efficiency at all angles. This could come in handy for making solar panels, for example, that would not need sophisticated trackers to follow the position of the Sun during the day.

And that is not all; because the distances between the features in these high-rotational symmetry lattices are on the length scale of visible light, the patterns have the potential to manipulate the flow of light in new and exciting ways, explains Odom. “For instance, we are currently transferring these patterns onto metallic substrates that can trap, concentrate and slow down light via so-called surface plasmon waves. We are also looking at how nanohole arrays patterned with this moiré technique in metallic sheets can selectively transmit light at specific energies in the optical regime.”

The research is reported in Nano Letters.