superconducting gap experiments

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• Published: 13 November 2024

Highly anisotropic superconducting gap near the nematic quantum critical point of FeSe 1− x S x

• Pranab Kumar Nag   ORCID: orcid.org/0000-0003-3689-8142 1 , 2   na1 ,
• Kirsty Scott   ORCID: orcid.org/0000-0002-4800-1710 1 , 2   na1 ,
• Vanuildo S. de Carvalho   ORCID: orcid.org/0000-0002-6141-7040 3 ,
• Journey K. Byland   ORCID: orcid.org/0000-0003-2391-6700 4 ,
• Xinze Yang   ORCID: orcid.org/0000-0003-4585-4133 1 , 2 ,
• Morgan Walker   ORCID: orcid.org/0009-0001-8728-5867 1 , 2 , 4 ,
• Aaron G. Greenberg   ORCID: orcid.org/0009-0004-2745-8844 1 , 2 ,
• Peter Klavins 4 ,
• Eduardo Miranda   ORCID: orcid.org/0000-0001-8833-1653 5 ,
• Adrian Gozar   ORCID: orcid.org/0000-0002-3233-0990 1 , 2 , 6 ,
• Valentin Taufour   ORCID: orcid.org/0000-0002-0024-9960 4 ,
• Rafael M. Fernandes   ORCID: orcid.org/0000-0002-3584-5180 7   nAff9 &
• Eduardo H. da Silva Neto   ORCID: orcid.org/0000-0001-6902-6100 1 , 2 , 4 , 8  

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• Electronic properties and materials
• Superconducting properties and materials

Nematic phases, in which electrons in a solid spontaneously break rotational symmetry while preserving translational symmetry, exist in several families of unconventional superconductors. Superconductivity mediated by nematic fluctuations is well established theoretically, but it has yet to be unambiguously identified experimentally. One major challenge is that nematicity is often intertwined with other degrees of freedom, such as magnetism and charge order. The FeSe 1− x S x family of superconductors provides an opportunity to explore this concept, as it features an isolated nematic phase that can be suppressed by sulfur substitution at a quantum critical point where the nematic fluctuations are the largest. Here we determine the momentum structure of the superconducting gap near the centre of the Brillouin zone in FeSe 0.81 S 0.19 —close to the quantum critical point—and find that it is anisotropic and nearly nodal. The gap minima occur in a direction that is rotated 45° with respect to the Fe–Fe direction, unlike the usual isotropic gaps due to spin-mediated pairing in other tetragonal Fe-based superconductors. Instead, we find that the gap structure agrees with theoretical predictions for superconductivity mediated by nematic fluctuations, indicating a change in the pairing mechanism across the phase diagram of FeSe 1− x S x .

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Data availability.

All data that support the findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

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Acknowledgements

We thank A. Chubukov, L. Glazman and P. Sukhachov for fruitful discussions during the preparation of this manuscript. E.H.d.S.N. acknowledges support from the National Science Foundation under grant number DMR-2034345. This work was supported by the Alfred P. Sloan Fellowship (E.H.d.S.N.). Sample synthesis was supported by the UC Lab Fees Research Program (grant number LFR-20-653926). R.M.F. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division, under award number DE-SC0020045 (theory work). E.M. acknowledges support from CNPq-Brazil under grant number 309584/2021-3 and Fapesp under grant number 2022/15453-0.

Author information

Rafael M. Fernandes

Present address: Department of Physics, University of Illinois Urbana-Champaign, Urbana, Illinois, USA

These authors contributed equally: Pranab Kumar Nag, Kirsty Scott.

Authors and Affiliations

Department of Physics, Yale University, New Haven, CT, USA

Pranab Kumar Nag, Kirsty Scott, Xinze Yang, Morgan Walker, Aaron G. Greenberg, Adrian Gozar & Eduardo H. da Silva Neto

Energy Sciences Institute, Yale University, West Haven, CT, USA

Instituto de Física, Universidade Federal de Goiás, Goiânia, Brazil

Vanuildo S. de Carvalho

Department of Physics and Astronomy, University of California, Davis, CA, USA

Journey K. Byland, Morgan Walker, Peter Klavins, Valentin Taufour & Eduardo H. da Silva Neto

Gleb Wataghin Institute of Physics, University of Campinas, Campinas, Brazil

Eduardo Miranda

Department of Physics, Fairfield University, Fairfield, CT, USA

Adrian Gozar

School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA

Department of Applied Physics, Yale University, New Haven, CT, USA

Eduardo H. da Silva Neto

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Contributions

P.K.N., K.S., M.W. and E.H.d.S.N. performed the STM measurements with the assistance of X.Y., A.G.G. and A.G. V.S.d.C., R.M.F. and E.M. performed theoretical calculations. X.Y. computed QPI simulations with assistance from A.G. and E.H.d.S.N. J.K.B. grew and characterized the FeSe 1− x S x crystals with support from P.K. and V.T. E.H.d.S.N., R.M.F., P.K.N., K.S., V.S.d.C., A.G. and E.M. wrote the manuscript with input from all other authors. E.H.d.S.N. conceived of the experiments and was responsible for overall project direction, planning and management.

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Correspondence to Eduardo H. da Silva Neto .

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Extended data

Extended data fig. 1 comparison to other tetragonal fe-based superconductors..

Polar plots comparing ∣ Δ ( θ ) ∣ , the superconducting gap, in FeSe 0.81 S 0.19 (outer hole pocket, full circles) and in various tetragonal FeSCs (reproduced from 35 , 36 ). The gaps for the largest (stars 35 ) and middle (crosses 36 ) pockets at Γ in LiFeAs, which has three pockets, are depicted. For the other materials, open (full) symbols represent ∣ Δ ( θ ) ∣ for outer (inner) hole pockets. For FeSe 0.81 S 0.19 the line represents the fit to the form in Eq. ( 1 ) of the paper (see Fig. 4 ). For the largest hole pocket of LiFeAs, the line follows \(\varDelta ={\varDelta }_{0}+{\varDelta }_{1}\cos (4(\theta +\Phi ))\) , with Δ 0 = 2.6 meV, Δ 1 = 0.4 meV and Φ = π /4 as reported 35 . For all other materials the lines are constant Δ curves, with their radii determined from the average experimental Δ ( θ ).

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Supplementary Figs. 1–11 and Notes I–VIII.

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Source data fig. 1e.

Data points for each curve plotted in Fig. 1e.

Source Data Fig. 2k

Data points for each curve plotted in Fig. 2k.

Source Data Fig. 3g

Data points for each curve plotted in Fig. 3g.

Source Data Fig. 4a–c

Data points for curves and data plotted in Fig. 4a–c.

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Nag, P.K., Scott, K., de Carvalho, V.S. et al. Highly anisotropic superconducting gap near the nematic quantum critical point of FeSe 1− x S x . Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02683-x

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Experiment supports existence of a new type of superconductor

by Jim Shelton, Yale University

A Yale-led team has found the strongest evidence yet of a novel type of superconducting material, a fundamental science breakthrough that may open the door to coaxing superconductivity—the flow of electric current without a loss of energy—in a new way.

The discovery also lends tangible support to a long-held theory about superconductivity—that it could be based upon electronic nematicity, a phase of matter in which particles break their rotational symmetry.

Here is what that means. In iron selenide crystals mixed with sulfur, iron atoms are positioned in a grid. At room temperature, an electron in an iron atom cannot distinguish between horizontal and vertical directions. But at lower temperatures, the electron may enter a "nematic" phase, where it begins to prefer moving in one direction or the other.

In some instances, the electron may start to fluctuate between preferring one direction, then the other. This is called nematic fluctuation.

For decades, physicists have attempted to prove the existence of superconductivity due to nematic fluctuations, with little success. But the new study, a multi-institutional effort led by Yale's Eduardo H. da Silva Neto, offers promise.

The findings appear in the journal Nature Physics .

"We started on a hunch that there was something interesting happening in certain iron selenide materials mixed with sulfur, relating to the relationship between superconductivity and nematic fluctuations," said da Silva Neto, who is assistant professor of physics in Yale's Faculty of Arts and Sciences and a member of the Energy Sciences Institute at Yale's West Campus.

"These materials are ideal because they display nematic order and superconductivity without some of the drawbacks, such as magnetism, that can make it difficult to study them," da Silva Neto said. "You can detach magnetism from the equation."

But it's not easy. For the study, the researchers chilled iron-based materials down to a temperature of less than 500 millikelvins over a period of several days. To track the material, they used a scanning tunneling microscope (STM)—which takes images of the quantum states of the electrons at the atomic level.

Focusing their studies on the iron selenides with maximum nematic fluctuations, the researchers looked for a "superconducting gap"—a well-established proxy for the existence and strength of superconductivity. The STM images enabled the researchers to find a gap that was an exact match for superconductivity caused by electronic nematicity.

"This has been elusive to prove, because you have to do the challenging STM measurements at very low temperatures to be able to measure the gap accurately," da Silva Neto said. "The next step is to look even more closely. If we keep increasing the sulfur content, what will happen with the superconductivity ? Will it die? Will spin fluctuations return? Several questions come up that we will explore next."

Co-lead authors of the study are Yale graduate students Pranab Kumar Nag and Kirsty Scott. Additional co-authors from Yale include Xinze Yang and Aaron Greenberg, as well as researchers from the University of California, Davis; the University of Minnesota; Universidade Federal de Goiás in Brazil; the University of Campinas in Brazil; and Fairfield University.

Journal information: Nature Physics

Provided by Yale University

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