Unresolved Questions in Cuprate Superconductivity: Mechanism, Pseudogap, and Intertwined Orders
Abstract
Abstract. Cuprate superconductors remain the central platform for studying high-temperature superconductivity, yet no single theory explains all major experimental observations. This mini-review summarizes four unresolved issues that continue to define the field: (i) the microscopic origin of pairing, (ii) the physical meaning of the pseudogap, (iii) the relationship between superconductivity and charge order, and (iv) the origin of strange-metal transport and the collapse of superconductivity on the overdoped side. The literature supports a picture in which strong electronic correlations are essential, while spin, charge, lattice, and topology-related effects remain entangled rather than fully separable. The main conclusion is that cuprate superconductivity should be treated as an emergent phenomenon of a doped correlated oxide, not as a simple extension of conventional BCS superconductivity. Keywords: cuprate superconductors; pseudogap; charge order; strange metal; high-Tc superconductivity; Introduction, Since the discovery of superconductivity in the Ba-La-Cu-O system in 1986, cuprates have remained the benchmark family of high-Tc materials [1]. Their importance is not only technological; they also expose the limits of established condensed-matter theory. Unlike conventional superconductors, the cuprates emerge from antiferromagnetic parent compounds with strong Coulomb correlations, low carrier density, pronounced anisotropy, and a phase diagram dominated by competing or intertwined electronic states [2,4]. Despite decades of work, several core questions remain unresolved. The most persistent ones concern the microscopic pairing interaction, the pseudogap, the status of charge order, and the anomalous metallic state that surrounds the superconducting dome [3-10]. Materials and Methods. This work is a focused narrative mini-review organized according to the IMRaD model. The literature set was deliberately restricted to ten peer-reviewed sources in order to maintain conceptual clarity and citation discipline. The selected papers represent four complementary categories: the original discovery of cuprate superconductivity [1], authoritative reviews of correlated-electron physics and momentum-resolved spectroscopy [2-5], studies of intertwined or charge-ordered phases [6-8], and key experimental or numerical papers on the overdoped and strange-metal regimes [9,10]. Sources were included if they directly addressed one of the unresolved questions and had established impact in the field. Highly specialized papers were excluded when their results did not substantially change the broader physical interpretation. First, the reviewed literature strongly supports the view that superconductivity in cuprates cannot be reduced to a weak-coupling phonon mechanism. The doped-Mott-insulator framework remains one of the most influential interpretive schemes because it explains why superconductivity develops from a strongly correlated antiferromagnetic background rather than from a simple metal [2]. Large-scale reviews likewise emphasize that spin fluctuations, short-range antiferromagnetism, and strong correlations are central to the problem, even though no universal microscopic pairing theory has been established [4]. Second, the pseudogap remains a defining unresolved phenomenon. ARPES-based studies have shown that the energy gap in cuprates evolves in a way that is not captured by a single order parameter [3,5]. In particular, the momentum dependence and doping evolution of the gap indicate that the pseudogap is not simply identical to superconductivity above Tc. Instead, the pseudogap appears as a partially gapped electronic state with its own energy and momentum scales, although its precise status - precursor, competitor, or distinct phase - remains debated [5]. Third, multiple studies now show that charge order is a robust part of the underdoped cuprate phase diagram. The theoretical language of intertwined orders has become particularly important because it avoids the oversimplified assumption that superconductivity and charge order are always independent or strictly antagonistic [6]. Resonant x-ray and related experiments demonstrate that charge order is widespread across several cuprate families and that its intensity, coherence, and field dependence are closely connected to superconductivity [7,8]. Fourth, the overdoped and strange-metal regimes remain difficult to reconcile with conventional metallic theory. On the overdoped side, the measured relationship between Tc and superfluid density does not fit the simplest mean-field expectation, implying that the disappearance of superconductivity is not a trivial return to a normal BCS-like metal [9]. In parallel, numerical work on the doped Hubbard model has reproduced strange-metal-like transport, including T-linear resistivity, strengthening the case that such behavior can emerge from strong electronic correlations without invoking an ordinary Fermi-liquid description [10]. Taken together, these results suggest that the unresolved questions of cuprate superconductivity are not independent puzzles. The pairing problem, pseudogap, charge order, and strange metallicity appear to be different manifestations of the same strongly correlated electronic environment. This is why no single experimental probe has settled the controversy: each technique highlights only one projection of a multiphase problem. The most defensible present-day position is therefore not that one candidate mechanism has already won, but that the correct theory must simultaneously accommodate Mott physics, momentum-selective gap formation, field-sensitive charge order, and non-Fermi-liquid transport [2-10]. A second implication is methodological. Future progress will likely depend on tighter integration between high-resolution spectroscopy, field-controlled experiments, and many-body numerical modeling. The field no longer lacks data; it lacks a framework that explains why these different datasets belong to the same organizing principle. For this reason, overly narrow explanations - whether purely phononic, purely magnetic, or purely band-structural - remain insufficient on their own. Conclusion. Cuprate superconductivity remains unresolved because it lies at the intersection of strong correlations, momentum-dependent electronic structure, and competing collective orders. The reviewed literature indicates that the central open problem is no longer whether cuprates are unconventional, but how their unconventional features are linked within a single quantitative theory. A professional and defensible summary of the field must therefore present the pairing mechanism, pseudogap, intertwined orders, and strange-metal transport as a connected research program rather than as isolated topics.