Weyl semimetals make way for super optics

In 2015, materials scientists made an unexpected discovery. In a compound of the metals tantalum and arsenic, they discovered a quasiparticle called a Weyl fermion. A quasiparticle is a packet of energy trapped in a system, like a giant cage of metal atoms, that in some ways moves around and interacts like a particle would. A fermion is a type of elementary particle that makes up matter; it includes electrons. A Weyl fermion, however, is a collection of electrons that behaves as if it is one big fermion – and as if it has no mass.

In June 2017, physicists reported that they had discovered another kind of Weyl fermion, dubbed a type-II Weyl fermion, in a compound of aluminium, germanium and lanthanum. It differed from other Weyl fermions in that it violated Lorentz symmetry. According to Wikipedia, Lorentz symmetry is the fact that “the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame”.

Both ‘regular’ and type-II Weyl fermions can do strange things. By extension, the solid substance engineered to be hospitable to Weyl fermions can be a strange thing itself. For example, when an electrical conductor is placed within a magnetic field, the current flowing through it faces more resistance. However, in a conductor conducting electricity using the flow of Weyl fermions, the resistance drops when a magnetic field is applied. When there are type-II Weyl fermions, resistance drops if the magnetic field is applied one way and increases if the field is applied the other way.

In the case of a Weyl semimetal, things get weirder.

Crystals are substances whose atoms are arranged in a regular, repeating pattern throughout. They’re almost always solids (which makes LCD displays cooler). Sometimes, this arrangement of atoms carries a tension, as if the atoms themselves were beads on a taut guitar string. If the string is plucked, it begins to vibrate at a particular note. Similarly, a crystal lattice vibrates at a particular note in some conditions, as if thrumming with energy. As the thrum passes through the crystal carrying this energy, it is as if a quasiparticle is making its way. Such quasiparticles are called phonons.

A Weyl semimetal is a crystal whose phonon is actually a Weyl fermion. So instead of carrying vibrational energy, a Weyl semimetal’s lattice carries electrical energy. Mindful of this uncommon ability, a group of physicists reported a unique application of Weyl semimetals on June 5, with a paper in the journal Physical Review B.

It’s called a superlens. A more historically aware name is the Veselago’s lens, for the Russian physicist Viktor Veselago, who didn’t create the lens itself but laid the theoretical foundations for its abilities in a 1967 paper. The underlying physics is in fact high-school stuff.

When light passes through a rarer medium into a denser medium, its path becomes bent towards the normal (see image below).

Credit: Wikimedia Commons
Credit: Wikimedia Commons

How much the path changes depends on the refractive indices of the two mediums. In nature, the indices are always positive, and this angle of deflection is always positive as well. The light ray coming in through the second quadrant (in the image) will either go through fourth quadrant, as depicted, or, if the denser medium is too dense, become reflected back into the third quadrant.

But if the denser medium has a negative refractive index, then the ray entering from the second quadrant will exit through the first quadrant, like so:

The left panel depicts refraction when the refraction indices are positive. In the left panel, the 'green' medium has a negative refractive index, causing the light to bend inward. Credit: APS/Alan Stonebraker
The left panel depicts refraction when the refraction indices are positive. In the left panel, the ‘green’ medium has a negative refractive index, causing the light to bend inward. Credit: APS/Alan Stonebraker

Using computer simulations developed using Veselago’s insights, the British physicist J.B. Pendry showed in 2000 that such mediums could be used to refocus light diverging from a point. (I highly recommend giving his paper a read if you’ve studied physics at the undergraduate level.

Credit: APS
Credit: APS

This is a deceptively simple application. It stands for much more in the context of how microscopes work.

A light microscope, of the sort used in biology labs, has a maximum zoom of about 1,500. This is because the microscope is limited by the size of the thing it is using to study its sample: light itself. Specifically, (visible) light as a wave has a wavelength of 200 nanometers (corresponding to bluer colours) to 700 nanometers (to redder colours). The microscope will be blind to anything smaller than these wavelengths, imposing a limit on the size of the sample. So physicists use an electron microscope. As waves, electrons have a wavelength 100,000-times shorter than that of visible-light photons. This allows electron microscopes to magnify objects by 10,000,000-times and probe samples a few dozen picometers wide. But as it happens, scientists are still disappointed: they want to probe even smaller samples now.

To overcome this, Pendry had proposed in his 2000 study that a material with a negative refractive index could be used to focus light – rather, electromagnetic radiation – in a way that was independent of its wavelength. In 2007, British and American physicists had found a way to achieve this in graphene, which is a two-dimensional, single-atom-thick layer of carbon atoms – but using electrons instead of photons. Scientists have previously noted that some electrons in graphene can flow around the material as if they had no mass. In the 2007 study, when these electrons were passed through a pn junction, a type of junction typically used between semiconductors in electronics, the particles’ path bent inward on the other side as if the refractive index was negative.

In the June 5 paper in Physical Review B, physicists demonstrated the same phenomenon – using electrons – in a three-dimensional material: a Weyl semimetal. According to them, a stack of two Weyl semimetals can be engineered such that the Weyl fermions from one semimetal compound can enter the other as if the latter had a negative refractive index. With this in mind, Adolfo Grushin and Jens Bardarson write in Physics:

Current [scanning tunnelling electron microscopes (STMs)] use a sharp metallic tip to focus an electron beam onto a sample. Since STM’s imaging resolution is limited by the tip’s geometry and imperfections, it ultimately depends on the tip manufacturing process, which today remains a specialised art, unsuitable for mass production. According to [the paper’s authors], replacing the STM tip with their multilayer Weyl structure would result in a STM whose spatial resolution is limited only by how accurately the electron beam can be focused through Veselago lensing. A STM designed in this way could focus electron beams onto sub-angstrom regions, which would boost STM’s precision to levels at which the technique could routinely see individual atomic orbitals and chemical bonds.

This is the last instalment in a loose trilogy of pieces documenting the shape of the latest research on topological materials. You can read the other two here and here.