Percolative theories of strongly disordered ceramic high-temperature superconductors

Abstract

Optimally doped ceramic superconductors (cuprates, pnictides, etc.) exhibit transition temperatures T c much larger than strongly coupled metallic superconductors like Pb (T c ¼ 7.2 K, E g ∕kT c ¼ 4.5) and exhibit many universal features that appear to contradict the Bardeen, Cooper, and Schrieffer theory of superconductivity based on attractive electron-phonon pairing interactions. These complex materials are strongly disordered and contain several competing nanophases that cannot be described effectively by parameterized Hamiltonian models, yet their phase diagrams also exhibit many universal features in both the normal and superconductive states. Here we review the rapidly growing body of experimental results that suggest that these anomalously universal features are the result of marginal stabilities of the ceramic electronic and lattice structures. These dual marginal stabilities favor both electronic percolation of a dopant network and rigidity percolation of the deformed lattice network. This "double percolation" model has previously explained many features of the normal-state transport properties of these materials and is the only theory that has successfully predicted strict lowest upper bounds for T c in the cuprate and pnictide families. Here it is extended to include Coulomb correlations and percolative band narrowing, as well as an angular energy gap equation, which rationalizes angularly averaged gap∕T c ratios, and shows that these are similar to those of conventional strongly coupled superconductors. percolation | theoryA ll known microscopic theories of metallic superconductors are based on the isotropic Bardeen, Cooper, and Schrieffer (BCS) model of Cooper pairs formed by attractive electronphonon interactions that overwhelm repulsive Coulomb interactions, yet many features of electron-phonon interactions in the BCS theory that are confirmed in metals appear to be weak or absent in the infrared spectra of ceramic layered high temperature superconductors (HTSC) (1). The ceramics often exhibit multiple phases and must be doped to be not only superconductive but even metallic. By contrast layered undoped MgB 2 with T c ∼ 40 K is an "ideal" example of a metallic BCS crystalline superconductor where T c can be calculated quite accurately (2). When MgB 2 is substitutionally doped with ∼10% Al (on the Mg sites) or C (on the B sites), T c decreases drastically to ∼10 K (3). Many authors have invoked residual spin interactions in the doped state, left over from the magnetic undoped states, as a source of this difference (1). However, it has been known for a long time that electron-spin interactions (for instance, with magnetic impurities) drastically suppress T c by breaking S ¼ 0 Cooper pairs (4), and more generally that the insulating antiferromagnetic (AF) and metallic Cooper pair four-particle plaquette channels are completely independent (5). While ceramics often exhibit multiple phases, recently the data have shifted overwhelmingly in favor of phonon exchange as the only attractive interaction cor...

Optimum inhomogeneity of local lattice distortions in La 2 CuO 4+ y

“…Our quantitative results should be tested against theories of composite, granular superconductors proposed for cuprates (10,14,15,25,(30)(31)(32)(55)(56)(57)(58)(59)(60)(61)(62). The X-ray data indicate that these theories must take into account not only the usual superconducting proximity effects, but also the effects of the strains the two components exert on each other.…”

“…1. The lattice complexity of superconducting copper oxides was neglected by most popular theories of high T c superconductivity, while percolative theories for granular superconductors were invoked because of the relevance of lattice disorder for electronic properties (10).…”

Packing and the structural transformations in liquid and amorphous oxides from ambient to extreme conditions

“…For instance, the limit of stability for tetrahedral units in SiO 2 or GeO 2 glass corresponds to the packing fraction found for an RLP of hard spheres, with the majority of datasets pointing to a maximum packing fraction that is comparable to the RCP limit (24)(25)(26)(27). This structural map (34)(35)(36), in which n O A is classified in terms of η O , allows for several properties of disordered oxides to be rationalized, and leads to predictive power for estimating the likely regimes of topological change.…”

Scale-invariant magnetic textures in the strongly correlated oxide NdNiO3

“…Nowadays, there is overwhelming evidence of domain pattern formation for an array of emergent phenomena, including metal-insulator transitions [7][8][9][10][11], charge/magnetic ordering [12][13][14], and unconventional superconductivity [15][16][17]. Several studies have identified these spatial textures as essential underpinnings for novel phenomena in TMOs and other correlated electron [5,13,[18][19][20][21].Rare earth nickelates (RENiO 3 ) are a fertile platform to realize and explore the emergent physics brewing in proximity to electronic symmetry-breaking phenomena, thanks to the cooperative action of the coupled charge, spin, and lattice degrees of freedom. In this family of compounds, the dominant structural/electronic instability sets the stage for a first-order transition (P2 1 /n to Pbnm) to a bond-disproportionated phase, that is accompanied by a concurrent insulator-to-metal transition (IMT).…”