Some butterflies have glistening, vividly coloured wings. From various angles you see different colors. This effect is called iridescence. How does it function? It turns out that these butterfly wings are made from very fancy substances! Light bounces around within these substances in a catchy way. Sunlight of different colours winds up reflecting off these materials in various directions. We’re beginning to comprehend the materials and create similar substances in the laboratory. They are called photonic crystals. They have excellent properties.
Here in the Centre for Quantum Technologies we’ve got people studying exotic materials of many kinds. Next door, there is a laboratory completely devoted to analyzing graphene: crystal sheets of carbon in which electrons can move as if they were massless particles! Graphene has a great deal of potential for constructing new technologies–that is why Singapore is pumping money into researching it.
A few physicists at MIT just demonstrated that one of the materials in butterfly wings might behave like a 3d kind of graphene. In graphene, electrons can only move readily in two directions. Within this brand new material, electrons can move in all three directions, acting like they had no mass. The pictures here show the microscopic arrangement of two materials found in butterfly wings:
The picture at left actually shows a sculpture produce by the mathematical artist Bathsheba Grossman. But it is a slice of a gyroid: a coating with a very complicated shape, which reproduces forever in 3 instructions. It’s referred to as a minimal surface because you can not shrink its area by tweaking it just a little. It divides space into two areas. The gyroid was found in 1970 with a mathematician, Alan Schoen. It’s a triply periodic minimal surfaces, meaning one that repeats itself in 3 different directions in space, like a crystal.
Schoen was working for NASA, and his thought was to utilize the gyroid for constructing ultra-light, super-strong structures. But that did not happen. Research does not proceed in predictable directions.
In 1983, people found that in certain mixtures of petroleum and water, the oil naturally forms a gyroid. The sheets of petroleum attempt to minimize their area, so it’s not surprising that they form a minimum surface. Something else makes this surface be a gyroid–I am not certain what.
Butterfly wings are made from a hard substance called chitin. About 2008, people found that the chitin in certain iridescent butterfly wings was created at a gyroid pattern! The spacing in this pattern is quite little, about one wavelength of visible light. This makes mild move through this substance at a complex manner, which is based on the light’s colour and the way it is moving.
So: butterflies have naturally evolved a photonic crystal based on a gyroid!
The world is awesome, but it isn’t magic. A mathematical pattern is amazing if it is a very simple remedy to at least one easy issue. That is the reason why beautiful patterns obviously bring themselves into lifestyle: they are the easiest ways for specific things to happen. Darwinian development helps out: it scans through trillions of possibilities and finds solutions to issues. Thus, we need to expect life to be packed with mathematically beautiful patterns… and it’s.
The picture at right above shows a ‘double gyroid’. Here it is again:
That really is two interlocking surfaces, displayed in blue and red. You can get them by composing the gyroid as a level surface:
f(x,y,z) = 0
and taking the two nearby surfaces
f(x,y,z) = \pm c
for some small value of c..
It turns out that if they’re still climbing, some butterflies have a double gyroid pattern in their own wings. This turns into a single gyroid when they develop! The new research at MIT studied how an electron would proceed through a double gyroid pattern. They calculated its dispersion terms: how the speed of the electron would depend on its energy and the direction it is moving.
A normal particle goes faster if it’s more energy. However a massless particle, like a photon, moves in exactly the same rate regardless of what energy it has. The MIT team revealed that an electron in a double gyroid pattern goes at a rate that does not depend much on its own energy. So, in a few ways this electron behaves as a massless particle.
Nonetheless, it’s rather different than the usual photon. It is really much more like a neutrino! You see, unlike photons, electrons and neutrinos are spin-1/2 particles. Neutrinos are nearly massless. A massless spin-1/2 particle can have an integrated handedness, turning in just 1 direction across its axis of movement. This type of particle is called a Weyl spinor. The MIT team revealed that an electron going through a double gyroid behaves approximately like a Weyl spinor!
How can this work? Well, the key truth is that the double gyroid has an integrated handedness, or chirality. It comes in a left-handed and sterile form. You can see the handedness quite obviously in Grossman’s sculpture of the ordinary gyroid:
Beware: no one has really made electrons behave like Weyl spinors in the laboratory yet. The MIT team just found a method which should work. Someday someone will actually make it happen, probably in under a decade. And later, someone will do wonders with this ability. I really don’t understand what. Perhaps the butterflies understand!