Superconducting vortex matters

In a recent study, HFML researchers discovered an anomalous vortex state in several families of cuprate superconductors at high magnetic fields. This new state, believed to be caused by an intricate interplay between the superconducting vortex state and charge order, may be essential to understand the evolution of the cuprate phase diagram. The research, performed at HFML in Nijmegen and NHMFL in Tallahassee, was published in the journal Proceedings of the National Academy of Sciences of the United States of America (PNAS).

Vortices in a superconductor

A magnetic field creates vortices — circulating loops of charge around a quantized magnetic flux — inside a superconductor. In a perfect superconductor with no defects, vortices are fluid and free to move in a way that leads to dissipation at any field strength. This state is known as the vortex liquid. In a real superconductor, however, defects in the material can act to pin down the vortices, forming a vortex solid, and maintain the perfect conduction to a much higher field strength. Paradoxically, defects make a better superconductor for application purposes.

Fragile superconductivity at extreme conditions

When the magnetic field become so strong that the vortices start to overlap, superconductivity is destroyed. This field scale, known as the upper critical field Hc2, is one of the most fundamental properties of a superconductor. Therefore it might be somewhat surprising that the Hc2 scale in high-temperature cuprate superconductors is still debated. The issue is that, unlike the clear-cut superconducting transition in zero magnetic field, the resistive transition (due to vortex motion) becomes very broad in a magnetic field and the definite signature of a transition from vortex to normal state is far from clear.

The research project itself was led by Dr. Yu-Te Hsu, a postdoctoral researcher at HFML within the Correlated Electron Systems group. During his PhD in Cambridge, Dr. Hsu and his colleagues found that the region of vortex liquid in YBa2Cu3O6+x extends far higher than previously reported. Their trick was to use a very low excitation current of micro-Amperes to measure the resistance — and only then could the vortex liquid manifest itself by exhibiting a highly non-linear resistivity up to field scales that were more than double previous estimates. Even more surprisingly, they found quantum oscillations coexisting with a state of zero resistivity. This discovery, also published in PNAS this week, challenges the established wisdom that quantum oscillations can only be found in a metal and suggests the existence of an exotic vortex state.

Extraordinary claim requires extraordinary evidence. A much simpler explanation would be that the non-stoichiometric nature of YBa2Cu3O6+x gives rise to the fragile superconductivity surviving to such high field strength. Is the unusual vortex state an intrinsic phenomenon due to exotic cuprate physics, or a trivial byproduct due to the imperfect chemistry of this particular material?

A tale of two maglabs

At the HFML in Nijmegen, Dr. Hsu set out to get to the bottom of this puzzle. He selected single crystalline samples from three different cuprate families with very different crystal structures, defect levels and more importantly, covering a broader range of doping. These characteristics proved to be crucial to draw a definite conclusion of the nature of this anomalous vortex state. And because the state appears only at the lowest temperatures, where the superconductivity is the strongest, the team needed to travel to the National High Magnetic Field Laboratory at Tallahassee in order to use their 45 T hybrid magnet. A similar magnet is currently under construction in Nijmegen and due for completion this year.

Exotic vortex matter

Yu-Te duly found that this anomalous vortex state is only present in a regime of temperature-doping phase  where superconductivity and charge order coexist. As the magnetic field increases, superconductivity is weakened while charge order is strengthened and become long-ranged (see figure bwlow). It is in this low-temperature high-field region, where the long-range charge order and the vortex solid state coexist, that the anomalous vortex liquid emerges. The group’s findings thus suggest that the two competing orders in the cuprates are intertwined under certain conditions, and the anomalous vortex liquid may be a manifestation of some form of exotic superconductivity. “The cuprates are such a rich system,” says Hsu, “You can always find something new when you dig a little deeper. Even with an experiment conceptually as simple as measuring resistance with varying electrical currents like ours. One might think that vortex liquid is just a state of nuisance. Still, it matters.”

Phase diagram

Schematic magnetic field-temperature phase diagram of charge-ordered cuprates. The increase of magnetic filed and/or temperature melt the superconducting vortex solid into vortex liquid. An anomalous vortex liquid emerges in the low-temperature high-field region where vortex solid and long-range charge order coexists.


Anomalous vortex liquid in charge-ordered cuprate superconductors, Yu-Te Hsu, Maarten Berben, Matija Čulo, Seiji Adachi, Takeshi Kondo, Tsuneshiro Takeuchi, Yue Wang, Steffen Wiedmann, Stephen M. Hayden, Nigel E. Hussey, PNAS118, 7 (2021)  doi:10.1073/pnas.2016275118

Unconventional quantum vortex matter state hosts quantum oscillations in the underdoped high-temperate cuprate superconductors, Yu-Te Hsu et al., PNAS 118, 7 (2021) doi:10.1073/pnas.2021216118

More information

Nigel Hussey
Yu-te Hsu