# Viewpoint: A Tale of Two Domes

Physics 9, 38
Iron selenide films peppered with potassium atoms exhibit a high-temperature superconducting phase that emerges separately from a low-temperature superconducting phase.

Superconductivity describes the spectacular ability of electrons in some materials at low temperatures to form Cooper pairs and coherently carry charge without resistance. Creating superconductors that operate at room temperature has long been an unrealized dream. Of particular interest are copper- and iron-based superconductors, discovered in 1986 and 2008, respectively, that possess higher transition temperatures ( ${T}_{c}$ up to 135 K under ambient pressure) than most conventional superconductors. These “high- ${T}_{c}$” superconductors often exhibit a peak or “dome” behavior in the transition temperature: when doping or pressure is increased, ${T}_{c}$ rises until it reaches a maximum, and then it falls off. A new study of superconducting iron selenide $\left(\text{FeSe}\right)$ films has revealed a double-dome behavior as the doping of electrons is increased [1]. Can-Li Song and collaborators at Tsinghua University, China, argue that the two domes arise from distinct mechanisms for binding electrons together into Cooper pairs. The unexpected discovery strengthens recent suggestions that the conventional mechanism of phonon binding, which has, for three decades, been overshadowed by more exotic mechanisms, may yet have an important role to play in further enhancing ${T}_{c}$.

This is not the first surprise to come from $\text{FeSe}$. Until recently, $\text{FeSe}$ was a superconductor, with a modest ${T}_{c}$ of around 8 K. In 2012, however, researchers found that a single unit cell layer (“monolayer”) of $\text{FeSe}$ grown on strontium titanate ( ${\text{SrTiO}}_{3}$ or $\text{STO}$) exhibits high-temperature superconductivity [2], with ${T}_{c}$ skyrocketing to 109 K [3]. This boost appears localized near the interface, as, strangely, a second layer of $\text{FeSe}$ deposited on top exhibits semiconductor rather than superconductor behavior.

In their new study, Song et al. wanted to understand the giant enhancement of superconductivity in monolayer $\text{FeSe}∕\text{STO}$. However, $\text{STO}$ likely introduces multiple effects: strain from lattice mismatch, electron doping, and cross-interface coupling to phonons [4]. Furthermore, $\text{STO}$ is prone to oxygen deficiency and numerous surface reconstructions. Using a reductionist approach, Song et al. examined the role of electron doping in isolation. First, they eliminated the effect of strain by growing thin films of $\text{FeSe}$ on a graphitized silicon carbide $\left(\text{SiC}\right)$ substrate, which interacts only weakly via van der Waals forces with the $\text{FeSe}$ film. Second, they reproduced the charge transfer from $\text{STO}$ by depositing potassium $\left(\text{K}\right)$ atoms on top of the films. Like $\text{STO}$, potassium has the effect of electron doping—with the advantage that the number of $\text{K}$ atoms donating electrons can be controlled and precisely counted.

Using scanning tunneling microscopy, Song et al. observed the gap in the density of states, whose width is a measure of the binding energy between Cooper pairs. The gap energy typically scales with the transition temperature, so it acts as a proxy for ${T}_{c}$. As the researchers increased the electron doping by adding more $\text{K}$ atoms to the surface, they observed two widely separated domes in the gap energy. The first dome was associated with the superconducting phase of undoped $\text{FeSe}$ (called “L-SC” by the authors), which was rapidly suppressed by a small amount of electron doping. For intermediate doping, the film’s superconductivity was lost, only to be regained upon further doping, where a new superconducting phase (called “H-SC”) emerged (see Fig. 1).

The maximum observed gap energy in the H-SC phase is 14 meV, $7$ times larger than that of the L-SC phase (2 meV), and just shy of the value seen in monolayer $\text{FeSe}∕\text{STO}$ (up to 20 meV [2]). This comparison suggests that the ${T}_{c}$ enhancement in monolayer $\text{FeSe}∕\text{STO}$ is due primarily to electron doping, which is likely driven by oxygen vacancies in $\text{STO}$. The remaining portion of ${T}_{c}$ enhancement could arise from interface effects (see Fig. 1), such as coupling to a high-energy phonon mode in $\text{STO}$ [4]. These results complement recent photoemission experiments demonstrating similar ${T}_{c}$ enhancements induced by $\text{K}$ deposition, in $\text{FeSe}∕\text{STO}$ films [5] and bulk $\text{FeSe}$ crystals [6].

For H-SC, Song et al. additionally observed that the Cooper-pair binding energy was spatially homogeneous, despite a disordered distribution of $\text{K}$ atoms on the surface. The implications here are crucial. Anderson’s theorem states that a conventional superconductor, where electrons are bound together by phonons, should be robust against the disorder of nonmagnetic impurities like $\text{K}$. Not only is this property useful in allowing superconductivity to survive in dirty materials, it can also be turned around into a litmus test for the mechanism of superconductivity. Using the converse of Anderson’s theorem, Song et al. claimed that H-SC’s insensitivity to disorder implies conventional, phononic pairing.

Song et al.’s implication that $\text{FeSe}$ films attain high ${T}_{c}$ through the conventional phononic interactions places $\text{FeSe}$ in a special category and challenges the prevailing belief that high ${T}_{c}$ requires an unconventional mechanism [7]. Unconventional mechanisms such as magnetic fluctuations have found favor for several reasons. First, magnetic order often persists to high temperatures, implying a large underlying energy scale. Moreover, magnetic fluctuations flip the sign of the electron wave function, allowing larger separation between the paired electrons, which reduces the deleterious effects of Coulomb repulsion. In fact, all copper-based and most other iron-based superconductors exhibit unconventionality. Even the material ${\text{KFe}}_{2}{\text{As}}_{2}$, which was also observed to have two distinct superconducting phases [8], exhibits an unconventional electron pairing mechanism in both phases.

Despite the excitement of phononic high- ${T}_{c}$ superconductivity in $\text{FeSe}$, some caveats remain. First, beyond an optimal electron carrier concentration, the H-SC gap begins to diminish (this trend is also seen in Refs. [5, 6]). This dome evolution has been a hallmark of unconventional superconductors and is harder to explain with a conventional phonon scenario. Second, Song et al.’s use of the converse of Anderson’s theorem is not logically fool-proof. The H-SC insensitivity to $\text{K}$ atom disorder could be attributed simply to the fact that the $\text{K}$ atoms sit atop instead of within the $\text{FeSe}$, which reduces their ability to break electron pairs of any type. Finally, an even more exotic unconventional mechanism has been proposed—incipient sign-changing ${s}_{±}$ gap symmetry—where bands with no Fermi surface still participate in pairing and perhaps provide robustness against disorder in violation of Anderson’s theorem [9]. In the latter proposal, phononic and magnetic interactions work cooperatively to boost ${T}_{c}$ in $\text{FeSe}$ in a “best-of-both-worlds” scenario.

Beyond these caveats, Song’s argument for phononic pairing in $\text{K}$-doped $\text{FeSe}$ fits well with recent work suggesting the same for monolayer $\text{FeSe}∕\text{STO}$ [10]. Given these observations in $\text{FeSe}$, along with the recent discovery of phononic superconductivity up to 203 K in pressurized sulfur hydride $\left({\text{H}}_{3}\text{S}\right)$ [11], is it time to revisit our ideas of what it will take to reach room-temperature superconductivity? More surprises may be in store from $\text{FeSe}$, and lessons learned from this material may shape the future of superconductor searches more broadly.

This research is published in Physical Review Letters.

## References

1. C.-L. Song, H.-M. Zhang, Y. Zhong, X.-P. Hu, L. Wang, K. He, X.-C. Ma, and Q.-K. Xue, “Observation of Double-Dome Superconductivity in Potassium-Doped FeSe Thin Films,” Phys. Rev. Lett. 116, 157001 (2016).
2. Q.-Y. Wang et al., “Interface-Induced High-Temperature Superconductivity in Single Unit-Cell FeSe Films on SrTiO3,” Chin. Phys. Lett. 29, 037402 (2012).
3. J. Ge, Z.-L. Liu, C. Liu, C. Gao, D. Qian, Q. Xue, Y. Liu, and J.-F. Jia, “Superconductivity Above 100 K in Single-Layer FeSe Films on Doped SrTiO3,” Nature Mater. 14, 285 (2014).
4. J. J. Lee et al., “Interfacial Mode Coupling as the Origin of the Enhancement of ${T}_{c}$ in FeSe Films on SrTiO3,” Nature 515, 245 (2014).
5. Y. Miyata, K. Nakayama, K. Sugawara, T. Sato, and T. Takahashi, “High-Temperature Superconductivity in Potassium-Coated Multilayer FeSe Thin Films,” Nature Mater. 14, 775 (2015).
6. C. H. P. Wen et al., “Anomalous Correlation Effects and Unique Phase Diagram of Electron-Doped FeSe Revealed by Photoemission Spectroscopy,” Nature Commun. 7, 10840 (2016); Z. R Ye et al., “Simultaneous Emergence of Superconductivity, Inter-Pocket Scattering and Nematic Fluctuation In Potassium-Coated FeSe Superconductor,” arXiv:1512.02526.
7. I. I. Mazin, “Superconductivity Gets an Iron Boost,” Nature 464, 183 (2010).
8. F. F. Tafti, A. Juneau-Fecteau, M-È. Delage, S. René de Cotret, J-P. Reid, A. F. Wang, X-G. Luo, X. H. Chen, N. Doiron-Leyraud, and L. Taillefer, “Sudden Reversal in the Pressure Dependence of ${T}_{c}$ in the Iron-Based Superconductor KFe2As2,” Nature Phys. 9, 349 (2013).
9. X. Chen, S. Maiti, A. Linscheid, and P. J. Hirschfeld, “Electron Pairing in the Presence of Incipient Bands in Iron-Based Superconductors,” Phys. Rev. B 92, 224514 (2015).
10. Q. Fan et al., “Plain $s$-Wave Superconductivity in Single-Layer FeSe on SrTiO3 Probed by Scanning Tunnelling Microscopy,” Nature Phys. 11, 946 (2015).
11. A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Ksenofontov, and S. I. Shylin, “Conventional Superconductivity at 203 kelvin at High Pressures in the Sulfur Hydride System,” Nature 525, 73 (2015).

Dennis Huang is a graduate student researcher in the Department of Physics at Harvard University. He holds a B.Sc. in physics and mathematics from the University of British Columbia, Canada, and an A.M. in physics from Harvard University. His research interests include the growth and imaging of quantum materials, such as superconducting iron selenide, using molecular beam epitaxy and scanning tunneling microscopy.

Jenny Hoffman is a Professor at Harvard and at the University of British Columbia. She earned her Ph.D. in physics from the University of California, Berkeley, in 2003, and was a postdoctoral fellow at Stanford before joining the Harvard faculty in 2005. Dr. Hoffman’s experimental research is motivated by the idea that layer-by-layer growth and nanoscale imaging of materials can uncover new physics and applications that are inaccessible via bulk synthesis and probes. Her laboratory combines molecular beam epitaxy and scanning probe microscopy to image and manipulate the electronic and magnetic properties of quantum materials. Dr. Hoffman has been named a 2006 PECASE Fellow, a 2008 NSF Career Fellow, a 2010 Sloan Research Fellow, a 2013 Radcliffe Fellow, a 2014 Moore Foundation Experimental Investigator, and a 2015 Canada Excellence Research Chair. She is grateful to work with outstanding students like Dennis.

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