Universal properties of cuprate superconductors: Tc phase diagram, room-temperature thermopower, neutron spin resonance, and STM incommensurability explained in terms of Chiral Plaquette Pairing

We report that four properties of cuprates and their evolution with doping are consequences of simply counting four-site plaquettes arising from doping, (1) the universal Tc phase diagram (superconductivity between∼0.05 and ∼0.27 doping per CuO2 plane and optimal Tc at ∼0.16), (2) the universal doping dependence of the room-temperature thermopower, (3) the superconducting neutron spin resonance peak (the “41 meV peak”), and (4) the dispersionless scanning tunneling conductance incommensurability. Properties (1), (3), and (4) are explainedwith no adjustable parameters, and (2) is explainedwith exactly one. The successful quantitative interpretation of four very distinct aspects of cuprate phenomenology by a simple counting rule provides strong evidence for four-site plaquette percolation in these materials. This suggests that inhomogeneity, percolation, and plaquettes play an essential role in cuprates. This geometric analysis may provide a useful guide to search for new compositions and structures with improved superconducting properties. SECTION Electron Transport, Optical and Electronic Devices, Hard Matter W e provide a simple explanation of the universal dependence of four properties of cuprate superconductors on doping (x) in the CuO2 planes: (1) the universal dependence of Tc (superconductivity between x ≈ 0.05 and 0.27 doping per CuO2 plane and optimal Tc at ∼0.16), (2) the room-temperature thermopower (Seebeck effect), (3) the neutron spin (π,π,π) resonance peak, and (4) the nondispersing conductance incommensurabilities in STM (observed thus far only for single-layer Bi-2201). It is hard to imagine four experiments that are more different. The Tc phase diagram is due to the nature of the superconducting pairing and its doping evolution, the universal thermopower is observed in the normal state near room temperature and relates simultaneous heat and charge transport, the neutron resonance probes spin fluctuations, and the STM measures local density of states (LDOS) variations on an atomic scale.We explain all four experiments here using simple counting arguments. It is well-known that the superconducting critical temperature, Tc, for all cuprates fits the expression (Tc/Tc,max) ≈ 1 82.6(x0.16),wherex is the hole doping per Cu in the CuO2 planes. This leads to the three universal doping values, where superconductivity first appears at x ≈ 0.05, is optimal at x≈ 0.16, and disappears above x≈ 0.27. This remarkable universality has not been explained. The room-temperature (290 K) thermopower, or Seebeck effect, for all cuprates decreases strongly with increased doping (from þ80 to -13 μV/K) with the same universal dependence. In addition, the temperature dependence at high temperatures is anomalous. Rather than S = BT, as expected from entropy transport due to electrons in metals (theMott formula), all cuprates have the formAþ BT, whereA is large and strongly doping-dependent while B is dopingindependent. The neutron spin inelastic scattering shows a very strong resonance near “41meV” at the AFwavevector (π,π) [(π,π,π) in bilayer materials] that is nearly the same for all cuprates, but doping-dependent while tracking Tc. 25,26 The peak occurs at the centerof an “hourglass”dispersionwith the highenergy sheet doping-independent and the lower sheet dopingand material-dependent. The recently observed doping-dependent STM incommensurability in single-layer Bi-2201 is anomalous because the wavelength increases with increasing doping rather than decreasing with increasing doping, as expected from the mean separation of holes. No theory has yet explained all four within a single framework. Electronic and small polaron models have been proposed for the Tc phase diagram 31-33 and spin-vortex and stripemodels for the neutron resonance.We show here that simple counting combinedwith a fewsimpleassumptions Received Date: February 24, 2010 Accepted Date: March 26, 2010