Paths to least resistance

Room temperature superconductivity remains some way off, but researchers continue to attack the problem from multiple angles, writes Lou Reade

Years ago, as part of my physics A-level, I researched two projects. One on solar cells; the other on high-temperature superconductors. At the time, both were a distant dream. While solar energy is now part of the mainstream, high-temperature superconductivity is still confined to the laboratory. Despite this, high-temperature superconductivity is exhaustively researched. While solar cells are an important source of clean energy, cables made from high-temperature superconductors would allow this energy to be transferred over large distances without losses.

Superconductivity is already applied commercially, in devices such as MRI scanners. The problem is the equipment must be cooled with liquid nitrogen to temperatures of around -196°C. This is clearly impractical for applications such as electrical cables. A number of laboratory materials have ‘superconducted’ electricity at room temperature. The downside is, they only manage this at impossibly high pressures – typically 100 atmospheres or more. Again, not practical for everyday use.

But while a commercial superconducting electrical cable will not be arriving any time soon, progress continues. Researchers continue to identify materials – while also developing models and theories – that show potential routes to room-temperature superconductivity.

Hydride characterisation

Researchers at the University of Bayreuth in Germany have identified and characterised a number of ‘lanthanum hydride’ compounds that show potential as high-temperature superconductors. Several hydrides – including those of lanthanum, sulfur and yttrium – have previously been shown to exhibit superconductivity at temperatures above 200K and under high pressure. The team, with co-researchers from countries including the UK and Sweden, synthesised five new lanthanum hydrides, plus two that were previously known.

To accomplish this, lanthanum and a hydrogen reservoir – in this case, paraffin – were subjected to pressures of up to 1.74m atmospheres between two diamond anvils, at temperatures above 2000°C.[1] Varying the pressure and the amount of lanthanum led to the formation of different hydride variants. To characterise the atomic structure of the compounds, they were illuminated by an X-ray beam at two particle accelerators – in Germany and the US.

The interior of a diamond anvil cell, above, which is commonly used to produce superconducting materials under high pressure.
Image: Leonid Dubrovinsky

‘Based on single-crystal X-ray diffraction data, we can determine the crystal structure and chemical composition of these compounds,’ says Natalia Dubrovinskaia of the university’s Laboratory of Crystallography. ‘We have shown that the La-H system is very complex.’[2]

The synthesis never forms a single La-H compound – but creates hydrides with ‘a wide variability of the hydrogen content’, she says. In each case, the same framework of lanthanum atoms can be linked to different numbers of hydrogen atoms, in a variety of ways. The scientists say their research overturns an earlier hypothesis, which assumed that a certain number and arrangement of lanthanum atoms only allows one specific configuration of hydrogen atoms. The team has not tested the compounds for superconductivity, as Dubrovinskaia says it is critical to model the compounds first.

‘Without precise knowledge of a [potentially superconducting] material, measurements such as electrical resistivity – especially at high pressures – may be misinterpreted,’ she says, adding that the Bayreuth team has previously published similar research on sulfur hydrides, and is preparing a report on yttrium-hydride compounds.

‘In our search for superconductors with higher transition temperatures, theoretical models and calculations are indispensable,’ says Dubrovinskaia. ‘Hydrogen-containing solids are highly promising materials. It is important that our models do not make incorrect assumptions – leading to high transition temperature materials remaining undiscovered.’

Taking the strain

Modelling is also critical to recent Swedish research, which shows that stretching a particular material – rather than putting it under pressure – could boost its superconductivity. The material, magnesium diboride, has a relatively simple structure, meaning that modelling can concentrate on the superconducting properties, say the researchers. Unlike other substances, its superconductivity actually diminishes under increasing pressure.

‘This makes it different to the main trend of high-temperature superconductivity,’ says Bjorn Alling, co-author of a paper on the discovery.[3]

Alling is a senior lecturer in the division of theoretical physics at Linkoping University and director of its National Supercomputer Centre. He says the superconductivity mechanism in MgB₂ may be different to that seen in other substances. Alling’s team found that when magnesium diboride is ‘stretched’, this pulls the molecules apart, causing their vibration frequency to change. This affects a phenomenon called electron-phonon coupling, which is critical to superconductivity.

‘This coupling is killed when you increase temperature,’ says Alling. ‘But here, the strain helps to overcome this.’ The simulations show that this could lead to the ‘critical temperature’ at which MgB₂ superconducts increasing from 39K to 77K.

These magnesium diboride properties are so far only theoretical calculations, but Alling’s team has devised a way in which it might stretch or strain the crystals. ‘Putting tensile strain on a crystal is unfeasible in many ways – because you can’t just increase its volume,’ he says.

If a substance is grown as a thin film on a surface, it can be strained in two dimensions – but he says this does not have much effect on the superconductivity of MgB₂.

‘To maximise the effect, you need three strain axes,’ he says. The way to achieve this, he adds, is to grow it in a ‘co-deposition’ with a second substance, such as chromium or yttrium diboride.

‘This way, you get two structures that strain each other,’ he notes. ‘This is known from different applications in semiconductors or metal growth systems, for example. If the second diboride is larger, it will apply the strain.’

The technique has been borrowed from metallurgy – and previous work from Alling’s background in hard coatings. Here, there is a need to ‘twin-strain’ the material’s structure, he says. ‘We’ve taken science from one place and applied it to another,’ he emphasises. ‘With perfect strain, we think we could reach liquid nitrogen temperatures.’ Alling’s team is working with two others – one in Latvia, the other in Sweden – to produce these materials.

‘They’re being made now; I think we’ll see results – positive or negative – within a year.’

If experimental results match the simulations, this will create more confidence in the models, he says. ‘The problem is that theoretical models for predicting whether a material has a high critical temperature have low accuracy. Theoretical principles work well for mechanical properties – but we’ve not yet got that for superconductivity.’

Beyond this, he believes that theoretical calculations – if they prove robust and accurate – could be used to re-examine previously ‘discarded’ candidate materials. Many will have been tested under high pressure but may have seen no increase in superconductivity, so were probably not publicised as they were seen as ‘failed’ experiments.

‘Some of them might behave like MgB₂ – so should be tested again,’ Alling says.

The problem is that theoretical models for predicting whether a material has a high critical temperature have low accuracy. Theoretical principles work well for mechanical properties – but we’ve not yet got that for superconductivity.
Bjorn Alling Senior Lecturer in the division of theoretical physics, Linkoping University, Sweden.

Strange behaviour

Researchers at Chalmers University of Technology in Sweden, meanwhile, have developed an explanation for a feature of high temperature superconductors – called the ‘strange metal state’. The phenomenon got its name because its behaviour when conducting electricity seems far too simple, say the researchers. In an ordinary metal, many temperature-dependent processes affect electrical resistance – such as electrons colliding with the atomic lattice, with impurities, or with themselves. Total resistance is then a complicated function of temperature. However, the resistance of ‘strange’ metals has a linear relation with temperature.

‘Such simple behaviour begs a simple explanation based on a powerful principle,’ says Ulf Gran, a professor of physics at Chalmers University, and co-author of a paper in Science.[4] ‘For this type of quantum material, the principle is believed to be quantum entanglement.’

Quantum entanglement is what Einstein called ‘spooky action at a distance’, he says – a way that electrons interact that has no equivalent in classical physics. ‘To explain the properties of the strange metal state, all particles need to be entangled with each other, leading to a soup of electrons in which individual particles cannot be discerned, and which constitutes a novel form of matter,’ he says.

The researchers found that charge density waves (CDW) – ripples of electric charge generated by patterns of electrons in the material lattice – destroy the strange metal effect. However, by straining nanoscale samples of superconducting yttrium barium copper oxide, the effect returned. This shows a close connection between the emergence of charge density waves and the breaking of the strange metal state. In addition, the results suggest a potential new avenue of research, the researchers say – using strain control to manipulate quantum materials.

Chalmers University researchers believe that quantum entanglement enables the strange metal phase (and superconductivity) in a material called YBCO (top left) – the effect disappears when charge density waves appear (top right).
Image: Yen Strandqvist/Chalmers University of Technology

Twisted behaviour

Quantum physics also helps to explain why graphene becomes a superconductor when it is ‘twisted’ at a particular angle, according to US-based researchers. Scientists have been trying to explain the effect since it was first seen in 2018 when researchers from the Massachusetts Institute of Technology aligned two sheets of graphene – a single layer of carbon atoms – at a ‘magic angle’ of 1.08 degrees.

‘Conventional theory doesn’t work in this situation – so we did a series of experiments to understand the origins of why this material is a superconductor,’ says Marc Bockrath, Professor of physics at Ohio State University, and co-author of a paper in Nature.[5]

In a metal, high-speed electrons are responsible for conductivity. However, twisted bilayer graphene has an electronic structure known as a ‘flat band’, where electrons move very slowly – with a speed approaching zero at the ‘magic angle’. The conventional theory of superconductivity says that electrons moving this slowly should not even be able to conduct electricity – yet it actually exhibits superconductivity.

‘We can’t use the speed of electrons to explain how the twisted bilayer graphene is working – so we had to use quantum geometry,’ says Bockrath. Quantum geometry is complex, he adds – and based on the principle that an electron exists as both a particle and a wave. It means that a quantum effect, such as that behind quantum tunnelling microscopy, is the reason for the behaviour.

Conventional flow of electrons accounted for almost none of the superconductivity and quantum effects were responsible for around 90% of it. The effect only takes place at very low temperatures, though the researchers want to understand the factors that lead to high-temperature superconductivity – which could make it potentially useful in areas such as electrical transmission and communication.
‘It’s a long way off, but this research is taking us forward in understanding how it could happen,’ says Bockrath.

In its element

While many superconductors are compounds, several elements in solid form – including calcium and titanium – also show superconducting properties at low temperatures. Niobium has a superconducting transition temperature of around 9K, while its alloy, NbTi, also exhibits superconductivity. Now, researchers from China and the US have found superconducting behaviour at around 30K, in what they call ‘densely compressed scandium’. The research is detailed in an arXiv paper, meaning it has not yet been peer-reviewed.[6]

‘Elemental superconductors attract special and growing attention due to the simplicity of their singular composition,’ according to the researchers, most of whom are from Beijing National Laboratory for Condensed Matter Physics in China.

Previous work has shown that scandium’s crystal structure changes as greater pressure is applied, which explains the change in conductivity. In the process, it moves progressively from Sc(II) to Sc(V).

In a series of experiments, a maximum pressure of 283GPa produced superconductivity at 30K. The researchers say this is the only known case of an elemental superconductor working at a temperature as high as 30K. They also note the material showed no sign of ‘saturation’ – meaning that it may superconduct at higher temperatures as more pressure is applied.

Identifying a roadmap for high-temperature superconductors is tricky, because current research covers such a disparate range of materials, theories and approaches.

It’s impossible to know whether any of these promising ideas will one day be realised commercially. What seems likely is that room-temperature superconductivity will come about due to successive layers of research – possibly including some of those mentioned here – rather than a sudden, explosive breakthrough.

References
1 Nature Commun., doi: 10.1038/s41467-022-34755-y
2 Nature Communications, doi: 10.1038/s41467-022-34755-y
3 Journal of Applied Physics, doi: 10.1063/5.0078765
4 Science, doi: 10.1126/science.abc8372
5 Nature, doi: 10.1038/s41586-022-05576-2
6 arXiv, doi: 10.48550/arXiv.2303.01062