Topological insulators are a class of fascinating materials that have a unique property -when current is passed through them, the interior of the material acts like an insulator, while the surface acts like a conductor. With potential uses in quantum computing, superconductivity and electronics, topological insulators are the subject of much research in recent years.
From high school physics, we know that the flow of current across any material is actually the flow of electrons in the material. In insulators, electrons are in a bound state called the ‘valence band’ with a large energy ‘band gap’ to the conduction band, where the electrons are free to conduct. Without high-energy electrons that can cross the band gap, there is no current that flows in the insulators, making them bad conductors of electricity. In conductors, this gap doesn’t exist and there are no separate bands. Thus nearly all electrons are free to flow, making them good conductors of electricity. But what happens with topological insulators?
The answer to that lies in an effect known as ‘spin-orbit coupling’. Since the electron is charged, its motion in an orbit around the nucleus creates a small magnetic field just like a current-carrying wire. The interaction of this magnetic field with the electron itself is known as spin-orbit coupling. This imposes certain restrictions on the movement of electrons.
At the surface of topological insulators, extra-allowed energy states appear in the gap which make the material a conductor only at the surface. This effect was so far seen and expected only in crystalline substances - substances whose atoms/molecules are arranged in ordered patterns like in metals such as copper and silver. “If you place molecular sites randomly, the idea is that the system will be extremely disordered. This will lead to electrons getting localized and not being free to conduct”, says Adhip Agarwala, currently a post-doctoral researcher at the International Centre for Theoretical Science, Bengaluru, explaining the thought behind why only crystalline substances were thought to be topological insulators.
Now, in a recent study, Adhip, along with his doctoral guide Prof. Vijay Shenoy from the Indian Institute of Science, Bengaluru, has shown that even non-crystalline substances, also called amorphous substances, like glass, with random molecular arrangements, could be topological insulators too. This path-breaking study was recently published in one of the most prestigious journals -- the Physical Review Letters.
“Based on current theory, no one expected that glass-like materials could be topologically insulating materials. It was a surprise. Experimentally, people didn’t look for amorphous materials. Now there is a possibility that people can look for materials that are amorphous but can host topological properties”, remarks Adhip on this discovery, made during his time as a PhD student.
The researchers ran computer simulations of molecules placed in random positions, as opposed to an ordered arrangement, within a fixed volume. This simulated how molecules in an amorphous material are placed in reality. Additionally, the simulated interaction between the electrons of the molecules incorporated the restrictions from spin-orbit coupling. As Adhip explains, “There are models known as tight-binding models used to describe the properties of crystalline materials. Thinking about how it realistically should be, you can construct similar models for amorphous systems. These models can then be used to study the properties of simulated materials.”
At the end of the simulations, the researchers were thrilled to find traits resembling those of topological insulators. The bulk of the material behaved like an insulator with a clear band gap and at the boundaries, the characteristic additional topological states were seen.
They dug a little deeper into these results by calculating the conductivity of the simulated materials – a key characteristic that remains the same irrespective of the specific material and external conditions. They found that the conductivity at the boundary perfectly matched with the expected value of e2/h, where ‘e’ is the charge on an electron and h is the Planck constant, both fundamental constants of nature - a clear evidence for the fact that it was indeed a topological insulator.
Topological Insulators have myriad potential uses and there are extensive searches on across the world to identify more of these elusive materials. With the findings of this study, the search is no longer restricted to crystalline materials and should usher in a new series of searches in amorphous materials with a far wider scope. It would not be an understatement to say that a whole new field, experimentally and theoretically, has been created and perhaps the day when topological insulators are widely used is just that little bit closer to the present.