A team of scientists, including physicist Eugene Demler from ETH Zurich, for the first time, closely observed how magnetic correlations play a role in mediating hole pairing.
Superconductivity only occurs in pairs. Therefore, in order for conductance without electrical resistance to take place in specific materials, the charge carriers must pair up. In traditional superconductors, the current is made up of electrons and pairing is facilitated by the collective movements of the crystal lattice, referred to as phonons. This mechanism is well understood. However, in recent decades, a growing number of materials have been found that don’t fit within this conventional theoretical framework.
The leading theories for unconventional superconductors suggest that magnetic fluctuations, not phonons, lead to pairing in these systems, — and surprisingly, magnetic interactions arise from the repulsive Coulomb interaction between electrons. However, verifying these models in experiments is extremely difficult.
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 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.
Pairing up for exciting physics
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 behavior 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 a 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 unfavorable. 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.
From theoretical abstraction to an experimental playground
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 at 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 toward higher critical temperatures for superconductors.
Reference: “Magnetically mediated hole pairing in fermionic ladders of ultracold atoms” by Sarah Hirthe, Thomas Chalopin, Dominik Bourgund, Petar Bojović, Annabelle Bohrdt, Eugene Demler, Fabian Grusdt, Immanuel Bloch and Timon A. Hilker, 18 January 2023, Nature.
The study was funded by the European Research Council, the Max Planck Society, the Max Planck Harvard Research Center for Quantum Optics, the German Federal Ministry of Education and Research, Excellence Strategy Germany, Alexander von Humboldt-Stiftung, the European Research Council, the National Science Foundation, the Army Research Office, and the Air Force Office of Scientific Research.
hmmm this doesn’t really explain how the binding works just that it does … bummer
One consequence of having electron pairs side-by-side is the spins can oppose and form a substantially closed magnetic circuit, which can eliminate any drag from magnetic coupling to the rest of the lattice. Paired electrons in a lattice will presumably jump together, possibly creating and eliminating paired holes, thus moving the holes in jumps, which is apparently the only way holes can move.
“The leading theories for unconventional superconductors suggest that magnetic fluctuations, not phonons, lead to pairing in these systems, — and surprisingly, magnetic interactions arise from the repulsive Coulomb interaction between electrons.”
Coulomb interactions (electrons repel each other by charge) are of course basically eliminated by the lattice providing a surrounding environment of electrons.
Phonon effects may correspond to an electron pair with one electron acting as a leading edge, where both electrons spin in the same way along a shared axis. I’ll call this an “end-to-end” mode here. It’s possible an electron pair can also rotate between “side-by-side” pairing, where shared magnetic field is most tightly exclusive and most particle-like, and the “end-to-end” pairing where the effective field is relatively extended with some coupling to the pair’s surroundings, where (if I recall a published example video correctly) lattice bulk elasticity (phonon action) supposedly enforces a regular spacing between the electrons of the pair and supposedly pushes on the lagging electron to keep it in line.