Bengaluru: Upending current thought on the subject, physicists from the Indian Institute of Science have found that topological insulators – materials that conduct electricity only on their surface – needn’t always be crystals. Instead, using computer simulations, Adhip Agarwala and Vijay Shenoy, of the institute’s physics department, have obtained theoretical validation that amorphous substances, like certain forms of glass and powders, can also become topological insulators in the right conditions. As a result, “there are lots more places to look for them now than previously thought possible,” Shenoy told The Wire.
Since everything below the surface, i.e. the bulk of the material, is an insulator, this characteristic of a topological insulator affords the material some niche applications, such as in quantum computing and particle physics experiments.
A simplified way to understand why topological insulators conduct electricity only on their surface is in terms of the energies and momentums of the electrons in the material. The electrons that an atom can spare to share with other atoms – and so form chemical bonds – are called valence electrons. In a metal, these electrons can have various momentums, but unless they have a sufficient amount of energy, they’re going to stay near their host atoms – i.e. within the valence band. If they do have energies over a certain threshold, then they can graduate from the valence band to the conduction band, flowing throw the metal and conducting electricity.
In a topological insulator, the energy gap between the valence band and the conduction band is occupied by certain ‘states’ that represent the material’s surface. The electrons in these states aren’t part of the valence band but they’re not part of the conduction band either, and can’t flow throw the bulk. Their specialness is owed to a unique property.
The electrons’ spins (on their own axis) are coupled strongly with their motion around their host atoms. As a result, their spins become aligned perpendicularly to their momentum, the direction in which they can carry electric charge. Such coupling staves off an energy-dissipation process called Umklapp scattering, allowing the electrons to carry a current. Detailed observations have shown that the spin-momentum coupling necessary to achieve this is present only in a layer on the surface that is a few nanometres thick.
However, band theory is usually described with crystals in mind, wherein the material’s atoms are arranged in a well-defined pattern, forming a lattice. This allows physicists to determine, with some amount of certainty, how the atoms’ electrons interact and give rise to the material’s topological states. But in an amorphous material like glass, the constituent atoms are arranged randomly. How then can well-organised topological states form in it?
“Much of the current thinking about topological insulators is informed by the theory of electron motion in perfect crystals,” Shenoy said. “In the past ten or so years, a lot of effort have been invested in finding new topological insulators and all of these were guided, perhaps even constrained, by the theory of crystals.” And examining the theory led the pair to realise that nothing in it required the existence of a perfect crystal to realise a topological insulator. “Our finding is a simple result of curiosity.”
In their simulation, they created the right conditions in which the unique surface states are born – and not being concerned about whether the material was crystalline or not.
Apart from spin-momentum coupling, this requires time-reversal symmetry to be preserved.
There are many fundamental symmetries in nature. In particle physics, if a force acts similarly on left- and right-handed particles, it is said to preserve parity (P) symmetry. If the dynamics of the force are similar when it is acting against positively and negatively charged particles, then charge conjugation (C) symmetry is said to be preserved. Now, if you videotaped the force acting on a particle and played the recording backwards, the force must be seen to be acting the way it would if the video was played the other way, too. At least, if it did, it would be preserving time-reversal (T) symmetry.
The surface states of a topological insulator are protected by T symmetry. This is because the corresponding electrons’ wave-functions – the mathematical equations that describe some of the particles’ properties – do not ‘flip’ going backwards in time. As a result, a topological insulator cannot lose its surface states unless it undergoes some sort of phase transition that breaks the wave-functions’ T symmetry.
When scientists look for favourable materials, they are essentially looking for materials that have surface states, with spin-momentum coupling, that are protected by T symmetry. Then again, these conditions may not be sufficient, according to Shenoy.
So how did he and Agarwala achieve this? According to Michael Schirber writing in Physics magazine,
In their study, they assume a box with a large number of lattice sites arranged randomly. Each site can host electrons in one of several energy levels, and electrons can hop between neighbouring sites. The authors tuned parameters, such as the lattice density and the spacing of energy levels, and found that the modelled materials could exhibit symmetry-protected surface currents in certain cases. The results suggest that topological insulators could be made by creating glasses with strong spin-orbit coupling or by randomly placing atoms of other elements inside a normal insulator.
The duo’s paper was published in Physical Review Letters on June 8. It concludes, “The possibility of topological phases in a completely random system opens up several new avenues for experiments.” Agarwala and Shenoy also suggest that an “important challenge in these cases will be to engineer the bandwidth of such systems to make them useful for room temperature applications” – which is in fact not an uncommon challenge encountered in all condensed-matter physics. The arXiv preprint of the paper is available to read here.
Physicists also speculate that amorphous topological insulators will be amenable to the same kind of applications that crystalline ones are. But an advantage emerges on the fabrication side, said Shenoy: “Processing and making crystalline requires stringent care; amorphous systems should have an edge here.”
However, they don’t say which amorphous materials could be suitable topological insulators, beyond hoping that their work will help guide the hands of future quests. Even if they did find something, Shenoy said, “A science reporter will not be the first person with whom Adhip and I will discuss our ideas. A patent lawyer, may be…”
Parts of this article were originally published on Contra Diction and have been republished here with permission.