One of the great unsolved mysteries in science is the odd behavior exhibited by quantum critical points at absolute zero. A phase transition – a liquid getting cold and freezing, or a metal heating up and losing its magnetic properties for example – is usually accompanied by a change in temperature. Quantum Physicists are, however, puzzled by phase transitions occurring at absolute zero, where no temperature change is possible.
Absolute zero is pretty cold, -273°C in fact, and one might presume that nothing much happens at such a cold temperature. Perhaps not on a visible scale, but certainly on a quantum scale: a quantum critical point is the position in the phase diagram of a material where a continuous phase transition takes place at absolute zero. Such a point is usually achieved by a continuous suppression of a non-zero temperature phase transition to zero temperature by the application of a pressure, field, or through doping.
Researchers at the Institute of Solid State Physics at TU Wien (Vienna University of Technology) have been working towards a better understanding of such phenomena and hope to better describe quantum critical materials and the high-temperature superconductivity suspected to be closely related to quantum critical points.
Thermal fluctuations are usually responsible for phase transitions. Individual particles start to shake or rotate, for instance, completely at random. The higher the temperature, the more pronounced these fluctuations become, which can lead to a phase transition – causing a solid to melt, for example.
Dr Thomas Schäfer
As the temperature is reduced, the particles move around less and less until they reach absolute zero at which point they should stop moving – or so Scientists thought. They presumed that total calm would have been restored at absolute zero, but it isn’t that simple, says Professor Allessandro Toschi.
Quantum physics states that it is impossible for a particle to be fully at rest in a specific location. Heisenberg's uncertainty principle tells us that position and momentum cannot be ascertained with total precision. Therefore, a particle’s position and momentum can still change at absolute zero, even if classic thermal fluctuations are no longer present. These changes are known as quantum fluctuations.
Professor Allessandro Toschi
This means that when it is too cold for classic shaking and rotating movements, quantum physics guarantees that physically interesting things are still taking place – and this is why phase transitions at absolute zero are so captivating.
“What is crucial for the particles' behavior is how their momentum relates to energy,” explains Schäfer.
For a ball thrown through the air, the correlation is simple: the greater the momentum, the greater the kinetic energy, he continues. The energy increases as the square of momentum. But for particles in a solid, this relationship is much more complicated, and can look very different, depending on the direction in which the particle is moving. Therefore, this connection is modeled using ‘Fermi surfaces’, which are able to take on complex three-dimensional shapes.
Until now, it was thought the shape of these Fermi surfaces was not significant in terms of quantum phase transitions. We have been able to show that is not the case. Only if you take the shape into account can you accurately calculate certain physical effects – for example, the way in which a material’s magnetic properties will change as it approaches absolute zero.
Professor Karsten Held
The Researchers – who published their results in Physical Review Letters – hope to use this new tool to better describe quantum critical materials and maybe shed light on some of the great mysteries the Material Scientists have been striving to solve over the years.