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Cuprates Show their Stripes

Superconducting technology has given us highly-detailed medical imaging, particle accelerators, and high-speed trains, but exactly what gives rise to this property is still a mystery. To help answer that question, Assistant Professor Steve Johnston and colleagues have used sophisticated calculations to learn more about the intrinsic physics of superconducting cuprates. The results are published in “Numerical Evidence of Fluctuating Stripes in the Normal State of High-Tc Cuprate Superconductors,” in the December 1, 2017 issue (Volume 358) of Science magazine.

Scientists have known for more than a century that in certain materials electric current can travel with no resistance. Superconductivity, as this is known, typically only shows itself at extremely low temperatures. Thirty years ago physicists discovered compounds comprising copper and oxygen (cuprates) were superconducting at much higher temperatures, albeit still well below the freezing point of water ( ~130° Kelvin, or -225 °F). Since the 1980s, researchers have worked with different materials and scenarios and seen promise in superconductivity at higher transition temperatures (Tc), all the while working to pinpoint why it occurs. Applications have already found their way into fields like medicine, where superconducting magnets make it possible for magnetic resonance imaging machines to give doctors exceptionally detailed images of soft tissue. With potential benefits of resistance-free current (such as drastically improved power grids), tailoring materials capable of sustained superconductivity at room temperature or above has long been a goal for scientists and engineers. Johnston and his collaborators went looking for signals in cuprates to see what gives rise to this valuable property. In doing so, they literally got these materials to show their true stripes.

Physics logoMore of Steve Johnston's research on superconductivity has been featured in Physics Viewpoint: online news and commentary about papers selected from APS journals.

Physics Viewpoint: Order on Command
A current of electrons with aligned spins can be used to modify magnetic order and superconductivity in an iron-based superconductor.

The paper, "Switching Magnetism and Superconductivity with Spin-Polarized Current in Iron-Based Superconductor," was published in Physical Review Letters and was also chosen as an Editor's suggestion.

Searching for a Signal

In certain materials, the addition of an electron (or a space where an electron should be) causes the charge carriers and their spins to organize into patterns called stripes.

“We know (stripes) exist in a static form in certain cuprates,” Johnston said. “And the question has always been are these intrinsic to the cuprate superconductors or is the material specific so that it only occurs in a couple of them?”

In other words, are stripes a more universal phenomenon relevant to all cuprates, rather than just a handful? To help answer this question he and fellow scientists from Stanford University looked for a signal in a model of a copper-oxide plane. They used two calculation techniques: determinant quantum Monte Carlo (DQMC) and density matrix renormalization group (DMRG). The first is done at finite temperatures with periodic boundary conditions, or as Johnston explained, “If you think of the system as a very small cluster, it’s like a Pac-Man board where you can go in on one side and come back in on the other. It’s meant to approximate the two-dimensional infinite system because you’ve got this periodicity in both directions. The other technique, DMRG, is a zero-temperature technique but it is only really very accurate in one dimension.”

Both techniques revealed stripes: fluctuating, or delocalized, stripes in one method (DQMC) and static stripes pinned by the open boundaries in the DMRG simulation.

“These stripes have been seen in techniques like DMRG before, but there’s always been this worry that the way that you handled the boundaries might be biasing the solution,” Johnston said.

Johnston explained it’s becoming more common for scientists to benchmark different techniques against each other, especially in a scenario such as this where fluctuating stripes are extremely close to other states in terms of energy.

“Doing these comparisons is really good for sorting out those issues. Are you really seeing genuine physics or are you seeing something your technique is biased toward seeing?,” he explained, adding that the observation of fluctuating stripes in this work may explain why other studies may have missed this physics if they were only looking for a static signal.

“This paper was taking the three-band Hubbard model, which is one of the minimal models to describe high-Tc cuprates, and asking the question do we see evidence for stripe formation in these models,” he said.

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