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Spatially Modulating Energy Gaps in Copper-Oxide Superconductors

Physicists have long been attempting to decode the electronic properties of high-temperature superconductors. It is believed that these materials can transform electronics and energy transmission because they have the potential to carry electric current without any energy loss, upon cooling below a specific temperature.

This schematic diagram maps out the binding energy (or superconducting energy gap) of individual electrons in a copper-oxide (cuprate) superconductor as measured by a sensitive microscope scanning across the surface. The size of the blue and yellow blobs surrounding individual atoms (red rods with arrowheads indicating their spin orientations) indicates the size of the energy gap (the larger the blobs the bigger the gap and stronger the electron-pair binding at that location). Note how when scanning across horizontal rows, the pattern increases to a maximum, then decreases to a minimum (no blobs), increases to another maximum with the opposite orientation (yellow and blue blobs switched) and then a minimum again, repeating this pattern every eight rows. These modulations are the first direct evidence of a “pair density wave,” a state of matter that coexists with superconductivity and may play a role in its emergence. Image Credit: Brookhaven National Laboratory.

Descriptions of the tiny electronic structure of “high-Tc” superconductors could expose the way the different phases, or states of matter, interact or compete with superconductivity. Superconductivity is a state where like-charged electrons bind together and flow freely, after overcoming their repulsion.

The ultimate aim of this study is to figure out how these materials can be made to behave as superconductors without the necessity for supercooling.

Currently, researchers focused on high-Tc superconductors at Brookhaven National Laboratory (Brookhaven Lab) of the U.S. Department of Energy, with a conclusive proof for the existence of a state of matter called pair density wave. The pair density wave was originally predicted by theorists about five decades ago.

Published in the Nature journal, the study results demonstrate that this phase exists jointly with superconductivity in a popular bismuth-based copper-oxide superconductor.

This is the first direct spectroscopic evidence that the pair density wave exists at zero magnetic field. We’ve identified that the pair density wave plays an important role in this material. Our results show that these two states of matter—pair density wave and superconductivity—coexist and interact.

Kazuhiro Fujita, Study Lead and Physicist, Brookhaven National Laboratory

The researchers arrived at the results by measuring the tunneling spectra of single electrons using advanced spectroscopic-imaging scanning tunneling microscope (SI-STM) in the OASIS laboratory of Brookhaven Lab.

What we measure is how many electrons at a given location ‘tunnel’ from the sample surface to the superconducting electrode tip of the SI-STM and vice versa as we vary the energy (voltage) between the sample and the tip,” added Fujita. “With those measurements we can map out the crystalline lattice and the electron density of states—as well as the number of electrons we have at a given location.”

When the material is not in a superconducting state, electrons subsist over a constant energy spectrum, with each electron propagating at its own special wavelength. However, when the temperature decreases, the electrons begin to interact—binding together as the material changes into the superconducting state.

When this phenomenon occurs, the researchers noted a gap in the energy spectrum, created by a lack of electrons inside that specific energy range.

The energy of the gap is equal to the energy it takes to break the electron pairs apart (which tells you how tightly bound they were),” added Fujita.

When the researchers scanned across the material surface, they identified spatially modulating energy gap structures. Such modulations in the energy gap structures exposed the difference in the strength of electrons’ binding—increasing to a maximum and then decreasing to a minimum; this pattern repeats for every eight atoms over the surface of the regularly arrayed crystal lattice.

The current study was based on earlier measurements that demonstrated that the electric current generated by pairs of electrons tunneling into the microscope also differed in the same periodic manner. These modulations in the electric current were the initial proof—albeit slightly incidental—that the pair density wave existed.

Modulations in the current of the paired electrons is an indicator that there are modulations in how strongly paired the electrons are across the surface. But this time, by measuring the energy spectrum of individual electrons, we succeeded in directly measuring the modulating gap in the spectra where pairing occurs. The modulations in the size of those gaps is direct spectroscopic evidence that the pair density wave state exists.

Kazuhiro Fujita, Study Lead and Physicist, Brookhaven National Laboratory

In addition, the results of the new study included proof from other major signatures of the pair density wave—such as defects known as “half-vortices”—and also its interactions with the superconducting phase.

The energy gap modulations also reflect the other studies performed by Brookhaven Lab, denoting the presence of modulating patterns of magnetic and electronic properties—at times known as “stripes”—that also take place with an eight-unit-cell periodicity present in specific high-Tc cuprate superconductors.

Together these findings indicate that the pair density wave plays a significant role in these materials’ superconducting properties. Understanding this state may help us make sense of the complex phase diagram that maps out how superconducting properties emerge under different conditions, including temperature, magnetic field, and charge-carrier density.

Kazuhiro Fujita, Study Lead and Physicist, Brookhaven National Laboratory

The study’s collaborators included Zengyi Du from Brookhaven Lab, Hui Li from Brookhaven Lab and Stony Brook University, Sang Hyun Joo from Seoul National University, and Elizabeth Donoway from Brookhaven Lab and the University of California, Berkeley).

Others included Jinho Lee from Seoul National University, J.C. Seamus Davis from the University College Cork, Ireland, and the University of Oxford, United Kingdom, and Genda Gu and Peter Johnson, both from Brookhaven Lab.

The Brookhaven Lab study was financially supported by the DOE Office of Science and Brookhaven Lab’s Supplemental Undergraduate Research Program.

Individual collaborators in the study also received support from Korea-based Institute for Basic Science, the National Research Foundation of Korea, the Institute of Applied Physics of Seoul National University, the European Research Council, and the Science Foundation of Ireland.

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