# Interview - How to realise transport of charge in an insulator

Building on work of his supervisor on charge transport in a particular kind of electrical insulators, Koen Schouten devised a protocol that is realistic for the first time. He converted his Bachelor’s thesis to a paper that was published in Physical Review A within half a year. It granted him a nomination for the Young Star Award 2021.

It was not difficult for Koen Schouten to select a topic for his Bachelor’s thesis. He studies physics and mathematics and his main interest is in condensed matter. From the possibilities that were offered for a combined research project, he chose to investigate a theoretical model of a particular kind of electrical insulators in which charge transport is possible. ‘Imagine a lattice of atoms, for instance metal atoms with empty places for electrons’, he explains. ‘Electrons can hop from one atom to a neighbouring one, so charge transport is possible. But when the lattice is saturated with electrons, they normally cannot go anywhere anymore, and the system is no longer conductive; it is now an insulator.’

## Adding energy must be eliminated

Still, charge transport in such saturated system is possible, dependent on the properties of the material, as the British Nobel Prize Winner David Thouless discovered about 40 years ago. To specify these properties, researchers characterize the system with parameters, and these parameters describe a space. After adjusting the parameters in such way that this space contains a so-called degeneracy point – imagine a hole – it is possible to pump electrons inside the corresponding insulator, Thouless showed. In other words: quantised charge transport, whereby electrons each shift exactly one place, can be realised. However, the frequency of pumping must be infinitely low. Schouten: ‘The reason is that pumping means adding energy, which must be eliminated. This takes an infinite amount of time, which makes the process infinitely slow and thus unrealistic.’

‘The charge transport that we predict can be measured in the lab’

Vadim Cheianov, Schouten’s supervisor, constructed a protocol to circumvent this problem. He used a simplified insulator model that represents a chain of two alternating kinds of atoms. Under certain criteria, quantized charge transport turned out to be possible at finite pumping frequencies, but now the system must be infinitely large. Schouten: ‘Again, this protocol is unrealistic.’

## Exploring how charge transport changes

At this point, his research started. ‘Using the simplified insulator model and its corresponding parameter space, I investigated how the pumping of charge would be affected when we put the insulator inside a potential, making it finite-sized. This potential can be compared to a well, in which the electrons get trapped, similar to how water is trapped inside a well’, he tells. Now, the possibility of quantised charge transport (electrons shifting places) turned out to be realistic for the first time. ‘By modelling and simulating, I explored how charge transport changed when the strength and position of the added field were varied. It yielded interesting results.’

These results motivated him to convert his thesis into an article during the summer break. The paper was peer reviewed, accepted and published in Physical Review A in December 2021.

Schouten liked his research: ‘It is fundamental science that entails both physics and mathematics, but it is less abstract than for instance string theory. The charge transport that we predict can be measured in the lab. That is not easy, though. It has been done only recently, a few times.’ He currently does a double Master’s program in Physics and Mathematics at the University of Amsterdam: ‘I hope to spend a lot more time doing research like this in the future.’