Quantum percolation in cuprate high-temperature superconductors

Abstract

Although it is now generally acknowledged that electron-phonon interactions cause cuprate superconductivity with Tc values Ϸ100 K, the complexities of atomic arrangements in these marginally stable multilayer materials have frustrated both experimental analysis and theoretical modeling of the remarkably rich data obtained both by angle-resolved photoemission (ARPES) and highresolution, large-area scanning tunneling microscopy (STM). Here, we analyze the theoretical background in terms of our original (1989) model of dopant-assisted quantum percolation (DAQP), as developed further in some two dozen articles, and apply these ideas to recent STM data. We conclude that despite all of the many difficulties, with improved data analysis it may yet be possible to identify quantum percolative paths.dopant ͉ superconductivity P ercolation in strongly disordered materials cannot be treated analytically, and early discussions of percolation focused on lattice model simulations. Recent discussions are much more sophisticated, and include many off-lattice effects connected with nanoscale phase separation, especially in glassy materials (1-7). The case of cuprate electronic high-temperature superconductive (HTSC) glasses (disordered dopants in a crystalline host) is especially intriguing, as scanning tunneling microscopy (STM) measures local gaps directly. Long ago, we suggested (8) that the dopants (usually oxygen interstitials), added to the insulating host crystal to make it metallic, should not be regarded as donating carriers to the cuprate planes (the most common theoretical model in the early days), but should instead be regarded as electronic bridges connecting metallic nanodomains separated by insulating domain walls generated by planar lattice buckling. This model has several advantages: it recognizes the lattice instabilities that are ubiquitous in perovskite and pseudoperovskites, and the dopants can function as centers of strong electron-phonon interactions.The foregoing dopant-assisted quantum percolation (DAQP) model, with its roots in materials science, initially enjoyed little popularity, because many theorists found more exotic models (not involving attractive electron-phonon interactions at all) more suitable (9-11). However, as we analyzed in many articles (12), the accumulation of data showing large strain effects (13) provided little support for exotic models. There is now a complete picture of the phase diagrams of lattice instabilities (pseudogaps) and superconductive gaps within the DAQP model (14). Nevertheless, the intriguing question of whether these percolation paths can actually be identified in cuprate planes studied by STM remains open. Why has this problem proved to be so difficult?There are several answers to this question. Distinguishing between strain-related pseudogaps and superconductive gaps with only a local probe is difficult, because both gaps are pinned by the Fermi line, and both are intrinsically nonlocal. This means that studies with a local STM probe inevitably see only the projec...

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“…In the course of establishing this novel sample preparation route, we have also observed that the YBa 2 Cu 3 O ∇x film exhibits twin-free properties, i.e., behavior comparable to that observed for twin-free YBa 2 Cu 3 O x single crystals under uniaxial stress. We have also found new novel evidence furthering the already well established link between oxygen, electronic, and structural ordering [18][19][20]48,56,57 in the form of local oxygen content stabilization against the annealing thermal gradient at the p ≈ 1/7 level, and to a lesser extent at the p ≈ 1/8 level as well. We believe that the evolving electronic and structural nature of the YBa 2 Cu 3 O x films make them ideal for carrying out new novel experiments which could potentially discriminate TABLE I. c-axis length c(nm) calculated from x-ray data, inferred hole doping content p using Eq.…”

“…47,[52][53][54] (2b) The intrinsic instabilities within the lattice, and the percolative nature of the superconducting path which is embeded in a poor metallic background. [55][56][57] (3a) The highly correlated nature of electronic charge doping in the CuO 2 plane and oxygen ordering in the Cu-O chains noted above in Refs. [18 -20].…”

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