Researching Magnetic Matchmaking

ETH Zurich Department of Physics

Superconductivity is for couples only. That is, for conductance without electrical resistance to emerge in certain materials, the charge carriers involved have to pair up in order to perform their magic. In ‘conventional’ superconductors, the current consists of electrons and pairing is mediated by collective motions of the crystal lattice, known as phonons. This mechanism is well understood. However, in the past four decades, a steadily increasing number of materials have been discovered that defy explanation within this canonical theoretical framework. Leading theories for ‘unconventional’ superconductors posit that in such systems not phonons but magnetic fluctuations give rise to pairing — and surprisingly, magnetic interactions arise from the repulsive Coulomb interaction between electrons. But checking these models in experiments is fiendishly challenging. Hence the excitement as a team of scientists led by Sarah Hirthe, Prof. Immanuel Bloch and Dr. Timon Hilker at the Max Planck Institute of Quantum Optics in Garching (Germany), Dr. Annabelle Bohrdt at Harvard University (US), Prof. Fabian Grusdt at the Ludwig Maximilian University of Munich (Germany), and Prof. Eugene Demler in the Departement of Physics at ETH Zurich (Switzerland) now report experiments that confirm central predictions of these theories. Writing today in Nature, they show that in a synthetic crystal so- called holes — in essence empty sites in a lattice filled with fermions — can form pairs mediated by magnetic correlations.

The synthetic crystal that the team created consists of atoms trapped in complex optical structures formed by intersecting laser beams. In such crystals, the key parameters defining the properties and behaviour of the system can be controlled with a degree of precision and flexibility that is typically out of reach in real materials. Moreover, in the setup at Garching, individual atoms can be traced while also probing their interactions with the other atoms, thereby offering microscopic insight into the quantum many- body system at hand.

For the current experiments these capabilities were harnessed to realize a model system for magnetically mediated pairing that at first appears to be unphysical, in that the experiments start with a system in which fermions repel each other, making pairing energetically unfavourable. Still, in systems such as cuprates — the first class of unconventional superconductors, discovered in 1986 — electrons end up being paired, despite the repulsive interactions between them. How can that gap between models and observations be gapped? And more than that, how can this pairing be made strong enough, so that it would be observable in experiments?

The key is an approach that Grusdt and Demler (then at Harvard) introduced together with colleagues in 2018. They showed that there are clever ways of modifying a model of fermions with repulsive interactions such that strong pairing emerges. They dubbed their approach the mixed- dimensional (mixD) t–J model, extending works that reach back to the early 1990s, when a handful of researchers — including the group of Maurice Rice at ETH Zurich — formulated so- called t–J ladder models to explore magnetically mediated pairing. The key feature of the mixD model is that fermions can interact in two directions, while they can only move in one.

The remarkable experimental flexibility in creating synthetic crystals based on atomic quantum gases and light fields now enabled the first demonstration of such binding arising from repulsive interactions, as predicted for mixD systems. Owing to the tunability of the system, the physicists were able to also directly compare the mixD case with the standard scenario in which the repulsive interactions between holes prevent the emergence of tightly bound pair states. One of the encouraging results of that comparison, supported by numerical simulations performed by Bohrdt in Harvard, is that the binding energy can be boosted by one order of magnitude. This is important, as this energy scale sets as well the maximum temperate at which the system is still superconducting. In addition, the experiments suggest significant mobility of the bound hole pairs, which means that they might indeed be efficient carriers of currents.

These are inspiring findings that open up a vast playground for further explorations. On the one hand, the systems investigated so far are still relatively small in size, and larger systems should allow more detailed studies, providing in turn unique microscopic insight into the mechanisms underlying unconventional superconductivity. On the other hand, the knowledge gained by studying synthetic systems might be applied to solid- state materials and could in the future inform fresh approaches towards higher critical temperatures for superconductors.

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