In copper oxides, as electron density increases, high-temperature superconductivity is destroyed. The currently prevailing understanding has been that this is just due to the increasing disorder. That explanation is refuted now in a recent paper by a research team lead by Dr. Ivan Božović from SHARPS. They showed that, on the contrary, under well-controlled experimental conditions, superconductivity can get stronger in more disordered samples. This means that a qualitatively different explanation is called for, but none are evident within the standard textbook theory of superconductivity.
High-temperature superconductors are among the most sought-after materials, due to their ability to carry electrical current without dissipation. The phenomenon reported in this paper may be more profoundly novel and disruptive than previously assumed, calling for a paradigm shift in how we search for new and better-performing superconductors.
Understanding high-temperature superconductivity (HTS) in cuprates is still one of the central open problems in condensed matter physics. The unconventional and anomalous nature of both the superconducting and normal states has been unearthed through inventive and meticulous experimentation, for which a unified and comprehensive theoretical explanation still needs to be provided. One striking observation was that ns0, the superfluid density extrapolated to T→0, decreases and vanishes as the doping level (the mobile carrier density per Cu atom) p is increased, closely tracking the critical temperature, Tc. Previously, the prevailing view has been that on the overdoped side of the superconducting dome, Tc decreases because of the weakening of the pairing interaction. In this case, the superconducting state should be well described by the weak-coupling Bardeen-Cooper-Schrieffer (BCS) theory. If so, as asserted by Legget’s Theorem, at T→0, all the electrons should be in the superfluid. Hence, ns0 should continue to increase as the doping level p increases. However, the experiments showed the opposite.
To resolve this discrepancy, several theoretical models were proposed. While they differ in detail, the common assumption is that, with increased dopant ion concentration, disorder increases, which causes pair breaking and depletes ns0. In principle, this hypothesis should be put to a direct experimental test, by varying the doping, measuring the resistivity and the magnetic penetration depth as a function of temperature, and studying the dependence of Tc and ns0 on some measurable quantities that capture the effects of disorder on electron transport. The main technical difficulty with such experiments is that different cuprate samples with nominally identical stoichiometry and chemical doping levels may have very different levels of disorder. The underlying causes are variations in chemical composition (impurities, vacancies, or deviations from stoichiometry) and crystal-structure defects (inter-site substitutions, interstitials, dislocations, etc.). This complicates a systematic study of the interplay between Tc, ns0, and disorder.
To alleviate this problem, in the present study, the team used ultrathin (5-unit-cell-thick) films of the prototypical cuprate, La2-xSrxCuO4-d (LSCO). The films were synthesized by atomic-layer-by-layer molecular beam epitaxy (ALL-MBE). This technique has been amply proven to produce atomically smooth films of highest quality and crystallinity. The doping level was modified by electrolyte gating; in this way, Tc and ns0 were varied in a single LSCO sample just by changing p. The dependence was studied of Tc and ns0 on the electron mobility m, the mean-free path l0, and the residual resistivity ratio RRR, the quantities commonly used to gauge the level of disorder and its effect on electron transport. The measured values of m, l0, and RRR varied because the defect screening improves with increased p. The samples were kept at relatively low temperatures, i.e., cycled between 300 K and 4 K, so one does not expect significant changes in the Sr2+ dopant concentration or the film crystallinity. At low-to-moderate gate voltages (Vgate), the oxygen content was not changed, either. This greatly reduced the uncertainties due to uncontrolled sample-to-sample variations in oxygen vacancy concentration and distribution, crystalline defects, etc., allowing for unambiguous conclusions.
The main finding was that as the doping decreased, m, l0, and RRR decreased, while Tc increased (see Figs. 1a and 1b) — precisely the opposite of what is expected from the dirty-d-wave-BCS scenario. The team also measured operando (upon electrolyte gating) the magnetic penetration depth l using the mutual inductance technique and determined the two-dimensional (2D) superfluid phase stiffness, ρs0 ≡ A/λ2, where A = ħ2d/4m0kBe2 = 4×10-12 m2K, kB is the Boltzmann constant, m* is the electron effective mass, ħ is the reduced Planck constant, m0 = 4p×10-7 N/A2 is the vacuum permeability, d is the layer thickness, and e is the electron charge. This phase stiffness is proportional to the 2D superfluid density ns2D = ρs(4kBm*/ħ2). Consistent with previous results, ρs0 decreased and tracked Tc as doping increased. In Fig. 1c, the gating-induced changes in ρs0 are plotted as a function of l0. In Fig. 1d, ρs0, l0, and m, are plotted as functions of the p. (To plot l0 and m on the same scale, both are normalized to their values at Vgate = 0.) As the doping decreased, ρs0 increased, as expected; however, both l0 and m decreased, indicating that disorder increased.
In summary, this study showed, experimentally, that Tc and ns0 increased with increased disorder. Hence, the cause of the demise of Tc and ns0 with overdoping must be something else. This brings back to the center stage the questions such as: Why does Tc decrease and vanish with overdoping? Why does ns0 track Tc? Why is the Tc(ns0) relation independent of the details of the band structure and even of whether the cuprate is underdoped or overdoped? The correct picture of HTS in cuprates should provide at least qualitative answers and explain the other observed departures from the standard textbook Landau Fermi-Liquid theory of metals and BCS-theory description of superconductors.
FIG. 1. Tuning the critical temperature, Tc, and the superfluid phase stiffness, ρs0, in overdoped LSCO(x=0.28) by electrolyte gating. a, Main panel: R(T) dependence measured for different values (color-coded) of the applied gate voltage Vgate. Inset: the same data, on log scale and zoomed on the superconducting transition to highlight a substantial change in Tc. b, The dependence of Tc on the residual resistance ratio, RRR ≡ R(T=295 K)/R0. c, The gating-induced changes of ρs0 as a function of the mean-free path l0. d, The dependence of ρs0 (blue diamonds), l0 (black squares), and the hole mobility m (red dots) on the doping level p. In all panels, Tc and ρs0 increase in the direction of increasing disorder (smaller RRR, l0, and m).
在铜氧化物中，随着电子密度的增加，高温超导性会遭到破坏。目前主流的解释认为，这仅仅是由于无序度的增加所致。近日，由上海前瞻物质科学研究院 Ivan Božović研究员领导的研究团队在最新的研究成果中反驳了这一解释。他们证明，恰恰相反，在良好受控的实验条件下，超导性在无序度更高的样本中反而可以变得更强。这意味着，需要一种在定性上截然不同的理论解释，但在标准教科书中的超导理论框架内，目前尚未看到明显的答案。
高温超导体由于能够无耗散地传输电流，属于最受追捧的材料之列 。该论文报道的现象可能比此前假设的更为新颖且具有颠覆性，或将促使我们在寻找新型、性能更优超导材料的过程中实现一次范式转变。相关成果于近日以“(Ir)Relevance of Disorder for Superconductivity in Cuprates”为题发表在《Physical Review Letters》期刊。文章链接：https://doi.org/10.1103/5nzl-fjmx
