What is strange about high-temperature superconductivity in cuprates?

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1 International Journal of Modern Physics B Vol. 31, No. 25 (2017) (5 pages) c World Scientific Publishing Company DOI: /S What is strange about high-temperature superconductivity in cuprates? I. Božović,,, X. He,,, J. Wu, and A. T. Bollinger, Brookhaven National Laboratory, Upton, New York , USA Applied Physics Department, Yale University, New Haven CT 06520, USA bozovic@bnl.gov xhe@bnl.gov jwu@bnl.gov abolling@bnl.gov Accepted 11 July 2017 Published 18 August 2017 Cuprate superconductors exhibit many features, but the ultimate question is why the critical temperature (T c) is so high. The fundamental dichotomy is between the weakpairing, Bardeen Cooper Schrieffer (BCS) scenario, and Bose Einstein condensation (BEC) of strongly-bound pairs. While for underdoped cuprates it is hotly debated which of these pictures is appropriate, it is commonly believed that on the overdoped side strongly-correlated fermion physics evolves smoothly into the conventional BCS behavior. Here, we test this dogma by studying the dependence of key superconducting parameters on doping, temperature, and external fields, in thousands of cuprate samples. The findings do not conform to BCS predictions anywhere in the phase diagram. Keywords: High temperature superconductivity; cuprate; thin films; molecular beam epitaxy; superfluid density. 1. Introduction Extensive study of high-temperature superconductivity (HTS) in cuprates has brought about numerous intriguing questions about the nature and the role of the anomalous normal state, of the pseudogap, of competing instabilities such as spin and charge density waves, etc. 1,2 Nevertheless, we maintain that the foremost mystery is just why the critical temperature (T c ) is so high, reaching 165 K under high pressure. We have tried to probe this question by the following strategy, Corresponding author

2 I. Božović et al. focused on the overdoped side of the cuprate phase diagram. In this region, large Fermi surfaces have been depicted by angle-resolved photoemission spectroscopy (ARPES) as well as by the Fourier-transformed scanning tunneling microscopy (STM). Moreover, the thermal and electrical conductivity have been found related according to the standard Wiedemann Franz law. Hence, today it is almost universally believed that in cuprates the physics of strongly correlated fermions evolves smoothly upon overdoping into the conventional one in which the normal state is well described by Landau s Fermi Liquid theory and the superconducting state by the Bardeen, Cooper and Schrieffer (BCS) theory. If this is the case, then we have a well-understood fixed point from which to start our probing, and follow the evolution of the system as the doping is reduced toward the composition with the maximal T c, to see whether it flows smoothly and adiabatically all the way, or is perhaps interrupted by some jumps and singularities. With this motivation, we have embarked upon the task of synthesizing and studying a large set of cuprate samples, varying the doping level as continuously as possible, and testing whether the key superconducting parameters scale with doping and temperature as expected from the BCS theory. In line with our expectations, we have found that the evolution is quite smooth, without any apparent jumps. However, surprisingly, the findings do not conform to the BCS predictions anywhere in the phase diagram Experimental For film synthesis, we use a unique atomic-layer-by-layer molecular beam epitaxy (ALL-MBE) system equipped with state-of-the-art surface-science tools for realtime monitoring of film morphology, chemical composition, and crystal structure. 4 Using this technique, we synthesize cuprate films that are atomically smooth and perfect Each film is characterized by reflection high-energy-electron diffraction (RHEED), atomic force microscopy (AFM), and magnetic susceptibility measurements, and selected ones also by time-of-flight ion scattering and recoil spectroscopy (TOF-ISARS), X-ray diffraction (XRD), transport measurements, and Rutherford backscattering (RBS). As a representative HTS material, we choose La 2 x Sr x CuO 4 (LSCO), because it is the simplest, and we can dope all the way to overdoped nonsuperconducting metal. To determine the 2D superfluid density N s or the superfluid stiffness ρ s, we measure the magnetic penetration depth λ using the mutual inductance technique The later we have improved 20 to reach an absolute accuracy better than 1% and to extend the measurement range in both the frequency (up to ν = 50 MHz) and the temperature (down to T = 300 mk). To infer λ accurately from the measured inductance, it is important to know precisely the thickness of the superconducting layer. For this, we can leverage on our capability to engineer the samples at the atomic-layer level. For example, we can sandwich the active (superconducting) part of the sample between two passive protective layers. To eliminate any inter

3 What is strange about HTS in cuprates? face contributions, Sr doping can be graded in the transition layers, which can be additionally δ-doped with Zn to quench any residual interface superconductivity. 3 Most importantly, we have studied a very large sample set we have measured inductance in over 2000 LSCO films, which was critical for the success of this study. Cuprates are complex compounds and they have complex phase diagrams that contain dozens of stable phases. This makes preparation of clean, single-phase samples extremely difficult, calling for an exquisite stoichiometry control and some sophisticate materials science. Our large statistics allows us to identify clear trends and discern intrinsic behavior. 3. Results We now outline the results for the whole battery of samples, 3 covering densely the entire overdoped LSCO region with the hole concentration varied from p = 0.16 all the way to p c2 = In Fig. 1, we display the doping dependence of N s (T ). Our main observations are as follows. (i) The N s (T ) curves are for the most part linear, N s (T ) = N s0 AT with A = const. (ii) The evolution of the superconducting state with doping, from optimal all the way to overdoped nonsuperconducting metal, appears monotonous and smooth. (iii) When p p c2, both T c 0 and N s0 0. (iv) The T c (N so ) dependence is linear but with a clear offset, T c = T 0 + αn s0, where T 0 = (7 ± 0.1) K and α = (2.5 ± 0.1) 10 2 K, except very close to the origin (i.e., for N s0 < 0.02) where it fits to T c = γ N s0, with γ = (1.1 ± 0.1) 10 2 K. (v) The superfluid stiffness ρ s0, which can be viewed as the temperature scale at which thermal phase fluctuations destroy superconductivity, is extremely low and comparable to T c. This should be contrasted with what is observed in conventional BCS superconductors such as e.g., Nb, where the ρ s0 /T c ratio is three orders of magnitude larger. Fig. 1. The ρ s(t ) (left scale) and N s(t ) (right scale) curves for the one hundred most homogeneous LSCO films grown by ALL-MBE. For the most part, the T -dependence is essentially linear

4 I. Božović et al. 4. Discussion Our key experimental findings (i) (v) are very specific, and clearly at variance with numerous proposed models and scenarios for HTS in cuprates. First, they are at odds with the BCS theory in any variant, clean or dirty. Within the clean BCS theory, one would expect the superfluid density at low-temperature should be essentially equal to the total free carrier density. 21,22 As shown in Fig. 2, the experimental data refute this prediction spectacularly; the discrepancy exceeds two orders of magnitude for the samples with lowest measured T c. As for the dirty BCS picture, it cannot account for the observation (i) above, that N s (T ) stays linear down to very low T to 1 K in the best samples. Indeed, if we deliberately add a tiny amount (1/200) of pair-breaking (Zn) impurities, the N s (T ) curves turn parabolic. We can rule out the presence of a large density of pair-breaking impurities or structural defects, of electronic or chemical phase separation, and of a broad distribution of gap values, etc., since T c is sharp and uniform to ±0.1 K in the best films. In our LSCO films, the superconducting fluid appears to be quite homogeneous. In passing, let us emphasize that although the temperature range of thermal superconducting phase fluctuations is thousand times broader than in the conventional BCS superconductors, we see no evidence of the Berezinskii Kosterlitz Thouless (BKT) transition, even when the superfluid is confined to a single CuO 2 plane. On the other hand, the so-called dynamic BKT transition is seen at very high (MHz) frequencies. 9,19 Fig. 2. The dependence of N s0 on doping, compared to the dependence expected within a BCS picture (which also incorporates the d-density wave, DDW, a postulated competing instability), across the entire overdoped region. The disagreement seems irreconcilable

5 What is strange about HTS in cuprates? 5. Conclusion and Outlook We have determined the dependence of the magnetic penetration depth, λ(t, p), on temperature and doping, covering densely the entire optimally-doped to overdoped side of the LSCO phase diagram. Our experimental observations disagree with the BCS predictions qualitatively and quantitatively, the discrepancy reaching a few orders of magnitude. Thus, cuprates are very unusual ( strange ) superconductors not just because of the exceptionally high T c but also in that the nature of the superconducting state seems quite unlike that in the conventional, low T c, BCS superconductors. Acknowledgments The research was done at BNL and was supported by the U.S. Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division. X.H. is supported by the Gordon and Betty Moore Foundation s EPiQS Initiative through Grant GBMF4410. References 1. J. Zaanen et al., Nat. Phys. 2, 138 (2006). 2. B. Keimer et al., Nature 518, 179 (2015). 3. I. Božović et al., Nature 536, 309 (2016). 4. I. Božović, IEEE Trans. Appl. Supercond. 11, 2686 (2001). 5. A. Gozar et al., Nature 455, 782 (2008). 6. G. Logvenov, A. Gozar and I. Božović, Science 326, 699 (2009). 7. I. Sochnikov et al., Nat. Nanotechnol. 5, 516 (2010). 8. J. Wu et al., Nat. Mater. 12, 877 (2013). 9. L. S. Bilbro et al., Nat. Phys. 7, 298 (2011). 10. M. P. M. Dean et al., Nat. Mater. 11, 850 (2012). 11. X. Shi et al., Nat. Mater. 12, 47 (2013). 12. D. H. Torchinsky et al., Nat. Mater. 12, 387 (2013). 13. M. P. M. Dean et al., Nat. Mater. 12, 1019 (2013). 14. A. F. Hebard and A. F. Fiory, Phys. Rev. Lett. 44, 291 (1980). 15. J. H. Claassen, M. E. Reeves and R. J. Soulen Jr., Rev. Sci. Instrum. 62, 996 (1991). 16. J. R. Clem and M. W. Coffey, Phys. Rev. B 46, (1992). 17. S. J. Turneaure, E. R. Ulm and T. R. Lemberger, J. Appl. Phys. 79, 4221 (1996). 18. S. J. Turneaure, A. A. Pesetski and T. R. Lemberger, J. Appl. Phys. 83, 4334 (1998). 19. V. A. Gasparov and I. Božović, Phys. Rev. B 86, (2012). 20. X. He et al., Rev. Sci. Instr. 87, (2016). 21. R. B. Laughlin, Phys. Rev. Lett. 112, (2014). 22. R. B. Laughlin, Phys. Rev. B 89, (2014)