From quantum gravity to strange metals

University of Amsterdam

What does a quantum theory of gravity have in common with electrons in a ‘strange’ metal? At first sight: not much, but this week in Nature a Dutch NWO consortium, including researchers Jake Ayres, Maarten Berben and Nigel Hussey (Radboud University), Jan Zaanen (Leiden University) and Erik van Heumen (University of Amsterdam) reports on new experimental findings that may point towards such a link after all.

strange metals
Artist’s impression: the description of electrons in strange metals (round particles) uses exactly the same mathematics as the description of spacetime in string theory (curved surface).

Superconductivity is a fascinating phenomenon in which, below a so-called critical temperature, a material loses all its resistance to electrical currents. In certain materials, at low temperatures, all electrons are entangled in a single, macroscopic quantum state, meaning that they no longer behave as individual particles but as a collective – resulting in superconductivity. The general theory for this collective electron behaviour has been known for a long time, but one family of materials, the cuprates, refuses to conform to the paradigm. It was long thought that for these materials the mechanism that ‘glues together’ the electrons must be special, but recently the attention has shifted and now physicists investigate the non-superconducting states of cuprates, hoping to find out their differences with normal superconductors.

Strange metals

Most superconductors, when heated to exceed their critical temperature, change into ‘ordinary’ metals. The quantum entanglement that causes the collective behaviour of the electrons fades away, and the electrons start to behave like an ordinary ‘gas’ of charged particles.

Cuprates are special, first of all because their critical temperature is considerably higher than that of other superconductors. On top of that, they have very special measurable properties even in their ‘metal phase’. In 2009, physicist Nigel Hussey observed experimentally that the electrons in these materials form a new type of structure, different from that in ordinary metals, and the term ‘strange metal’ was born.

At nearly the same time, originating in Stanford in the United States, physicists started applying the theoretical machinery of string theory – a theory for a very different phenomenon, the behavior of gravity at the quantum level – to the description of electrons in metals. Completely unexpectedly, this machinery turned out to be able to predict certain phenomena that experimentally were known to occur in cuprates and other strange metals. Theoretical physicists Jan Zaanen and Koenraad Schalm (Leiden University) were involved in the early stages of these developments and made important contributions. In 2017, the pioneering work was transformed into a national research programme funded by NWO: Strange Metals. The programme is a special collaboration that involves both experimental and theoretical groups.

Special behaviour at low temperatures

The higher the temperature of a material, the more ‘noise’ measurements will show. To make the special properties of the strange metal state clearly visible, one would like to study the material at a temperature that is as low as possible, at most 1 degree above the absolute temperature minimum of -273°C. The obstacle for this is superconductivity itself: most strange metals already turn into superconductors when cooled to temperatures around -200°C. For this reason, in the Strange Metals programme, the choice was made to focus exclusively on a material with the chemical name Bi2Sr2CuO6, also known as ‘Bi2201’. This material becomes superconducting at about 35 degrees above the absolute minimum temperature. That is still too ‘hot’ for good measurements, but now the researchers can use a trick: superconductivity can be suppressed by a magnetic field.

The general rule of thumb is: the larger the critical temperature of a material, the stronger the magnetic field required to suppress superconductivity. Since for Bi2201 the critical temperature is already quite low, the required magnetic field comes just within reach of the biggest magnets available in the Netherlands. This allowed PhD students Jake Ayres and Maarten Berben working within the groups of Hussey (HFML-FELIX, Bristol) and Van Heumen to eventually study the strange metal state of Bi2201 at various low temperatures and various magnetic field strengths.

In this domain, the differences between strange metals and ordinary metals become strikingly visible. For ordinary metals, for example, one expects the electrical resistance to increase quadratically with temperature: increase the temperature by a factor of two, and the resistance will grow by a factor of four. The same holds if it is not the temperature but the magnetic field that is increased. The Dutch/UK team has now shown that these golden rules do not hold for cuprates. In these materials a new phase exists where the resistance depends linearly on the temperature and field strength: if one of these increases by a factor of two, so does the resistance. Contrary to what was observed before, the group discovered that this behaviour persists for a large range of the parameters.

At the moment, there are two widely accepted theories that could explain the linear behaviour of the resistance. The first theory assumes that the linear behaviour only occurs near very specific values of the temperature and magnetic field strength. With the new measurements, this theory has now come under considerable pressure. The second theory is the theory of extreme quantum entanglement that comes from the string theoretic approach. Within this theory it is possible to observe the linear behavior for a large range of parameters. Surprisingly, therefore, it seems that to describe strange metals, one truly needs a theory that can also be used to describe quantum gravity!

Quantum gravity in the lab

The link between strange metals and quantum gravity has special observable effects. In an extensive analysis, the team shows that within the conventional models of electrical transport, it is absolutely impossible to properly explain the data. Their analysis shows that there exists a previously unobserved mechanism that makes the electrons lose energy. This loss occurs at extremely short time scales related to a fundamental constant of nature in quantum mechanics: Planck’s constant. According to general theory, this is the shortest time scale at which a quantum system can lose energy – something which moreover is only possible when the system is maximally entangled. This fingerprint of quantum gravity behaviour in the data excites many supporters of the link with string theory: it would be a first clue of physics far beyond the usual model of metals.

To shed further light on the tension between ‘normal’ and ‘strange’ behaviour of metals, further experiments are needed. In that respect, promising developments still lie ahead within the Strange Metals program. Using a technique called ‘optical spectroscopy’, Van Heumen expects to be able to provide new details soon, and the groups of Mark Golden (Amsterdam) and Milan Allan (Leiden) are also working on results that could cause new surprises when it comes to the mysterious relation between quantum gravity and strange metals.

Publication

Incoherent transport across the strange metal regime of overdoped cuprates, J. Ayres, M. Berben, M. Čulo, Y.-T. Hsu, E. van Heumen, Y. Huang, J. Zaanen, T. Kondo, T. Takeuchi, J. R. Cooper, C. Putzke, S. Friedemann, A. Carrington and N. E. Hussey. Nature 2021.

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