Homogeneous materials that conduct electricity and insulate at the same time: These are just some of the paradoxical properties encountered by physicist Titus Neupert as he models the atomic structure of solids on the computer.
Titus Neupert’s lab is in his own head. With the help of mathematics and quantum mechanics, the 33-year-old theoretical physicist seeks out crystals with interesting physical properties. And he’s taking a completely new tack. These kinds of materials, highly sought-after in science and technology, used to be tracked down by investigating naturally occurring crystalline structures and studying their properties. Scientists such as Titus Neupert have turned this approach on its head, first thinking up exciting quantum mechanical states, and then finding materials existing in the physical world that behave similarly to abstract models with the appropriate characteristics.
An interesting example is crystals that insulate but conduct electricity at their surface. At first this might sound pretty paradoxical, at least from the point of view of classic solid-state physics. But seen through the lens of of quantum physics, where weird and paradoxical phenomena are the order of the day, so-called topological materials of this sort become possible. This is precisely what the young professor does when he sits in front of the computer doing his calculations. More and more often it turns out that the structures he calculates have pretty bizarre properties, especially at the edges where the familiar order suddenly breaks down. Here quantum physics, you could say, does somersaults that classic chemistry and metallurgy can’t explain. These somersaults are Titus Neupert’s specialty. In 2017, the physicist received one of the EU’s prized ERC Starting Grants for his research.
Now he’s joined forces with colleagues in the United States, Spain and Germany to investigate a new class of so-called topological materials that can conduct electricity not at the surface, but at the edges of the crystal. They’re particularly interesting because the conductive edges are extremely robust. The current of electrons can’t be stopped by disorder or impurities in the crystal – the current simply flows around the impurity.
Not only that, but the crystal edges don’t have to be specially prepared to conduct electrical current. If the crystal breaks, the new edges automatically also conduct. “The most exciting aspect is that electricity can at least in theory be conducted without any dissipation,” says Titus Neupert. “You could think of the crystal edges as a kind of highway for electrons. They can’t simply make a U-turn.” This property of dissipationless conductance, otherwise mainly known from superconductors at low temperatures, isn’t shared by the previously known topological insulator crystals with conducting surfaces.
All possible thanks to bismuth
Now Neupert and his fellow researchers have found the first crystals with conductive edges in the real world. Elemental bismuth long held little interest for experts: “topologically trivial,” as they put it. But when Neupert and his colleagues worked it through precisely in terms of quantum mechanics, they discovered this unique “edge conductivity,” which experiments then actually confirmed. The researchers systematically searched for crystalline structures with what quantum physicists called “free modes” at their edges.
These free modes permit the flow of electrons, but only at the ends of such a quantum mechanical system; inside everything stays “shut.” This property is so firmly written into the crystal that it can’t be changed from the outside, for example by impurities or scratches. “You’d have to rejig the entire inner structure to destroy this property,” explains Neupert.
In the best case these structures would have such perfect quantum physical properties that these edges would conduct without dissipation. But so far that’s mere theory. “We haven’t yet found a material where it really functions, especially not at room temperature.” Even so, the relevant databases of materials contain around 10,000 potential candidates that could be further fine-tuned by making alloys.
The most exciting possibilities for topological materials are likely to be in quantum computing (see box). Shortly after they’d published their work, says Neupert, the first proposals for electronic components containing bismuth had been submitted. The newly-discovered property of bismuth might really turn out to be an easy option for creating a pseudoparticle. Which takes us back to the strange world of quantum physics: A world where particles can be conjured up that are only mathematical phenomena, but have very useful qualities – and which are usually only sought in the big particle accelerators.
One of these particles, which goes by the name of the Majorana fermion, is seen as one of the hottest candidates for creating a real-life quantum computer. Model calculations suggest that it could serve as a simple and easy-to-handle switch, a so-called qubit. And just this kind of special fermion could suddenly crop up in solid states if bismuth were incorporated appropriately. But there’s plenty of research to be done before that can happen. “We’ll need a lot of creativity,” says Neupert. One thing’s for sure: The physicists have no shortage of ideas.
Counting on half-truths
The quantum world is full of shades of gray, describing states as superimpositions rather than in terms of black and white.
This is complex, but perfectly manageable from a mathematical point of view. Applying the model to IT could yield major gains. A quantum computer wouldn’t compute in bits – ones and zeros with nothing in between. Instead, its circuits would recognize and compute with ambiguous states – half-truths, if you like.
This process would bring undreamed-of benefits for many computing tasks, for example factoring a number into prime factors. Quantum computers promise to operate whole orders of magnitude faster than anything that can be built with silicon chips – in theory at least. But as promising as the future of quantum computing may sound, all the ideas proposed so far work in small experimental model systems at best. It’ll be a while yet before we see the reliable “solid-state” application of quantum mechanical circuits.