We present an experimental review of the nature of the pseudogap in the cuprate superconductors. Evidence from various experimental techniques points to a common phenomenology. The pseudogap is seen in all high-temperature superconductors and there is general agreement on the temperature and doping range where it exists. It is also becoming clear that the superconducting gap emerges from the normal state pseudogap. The d-wave nature of the order parameter holds for both the superconducting gap and the pseudogap. Although an extensive body of evidence is reviewed, a consensus on the origin of the pseudogap is as lacking as it is for the mechanism underlying high-temperature superconductivity.

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The pseudogap in high-temperature superconductors: an experimental survey

The case for dx2 − y2 pairing in the cuprate superconductors

We examine the effect on the superconducting transition temperature ${(T}_{\mathrm{c}})$ of chemical inhomogeneities in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$ and ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ single crystals. Cation disorder at the Sr crystallographic site is inherent in these materials and strongly affects the value of ${T}_{\mathrm{c}}.$ Partial substitution of Sr by Ln (Ln = La, Pr, Nd, Sm, Eu, Gd, and Bi) in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{1.6}{\mathrm{Ln}}_{0.4}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$ results in a monotonic decrease of ${T}_{\mathrm{c}}$ with increasing ionic radius mismatch. By minimizing Sr site disorder at the expense of Ca site disorder, we demonstrate that the ${T}_{\mathrm{c}}$ of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ can be increased to 96 K. Based on these results we discuss the effects of chemical inhomogeneity in other bulk high-temperature superconductors.

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Effect of chemical inhomogeneity in bismuth-based copper oxide superconductors

The universe is so much bigger than the bit we can see in our observable bubble   and we know nothing about what lies out there in the cosmos. The challenge is so  much bigger than is shown on this chart and it is evident that we really only  understand a tiny fraction of the whole cosmos.  Theories ​for Dark Energy have been around for a long time but we still have no  satisfactory explanation. None of the theories are adequate, some are clearly wrong    – an error of 10^120 is a really big miss!  Scott Dodelson of Carnegie Mellon University, one of the lead scientists behind the  Dark Energy Survey’s new map of cosmic structure says:

Dark Energy

In materials with strong local Coulomb interactions, simple defects such as atomic substitutions strongly affect both macroscopic and local properties of the system. A nonmagnetic impurity, for instance, is seen to induce magnetism nearby. Even without disorder, models of such correlated systems are generally not soluble in 2 or 3 dimensions, and so few exact results are known for the properties of such impurities. Nevertheless, some simple physical ideas have emerged from experiments and approximate theories. Here, we first review what we can learn about this problem from 1D antiferromagnetically correlated systems. We then discuss experiments on the high Tc cuprate normal state which probe the effect of impurities on local charge and spin degrees of freedom, and compare with theories of single impurities in correlated hosts, as well as phenomenological effective Kondo descriptions. Subsequently, we review theories of impurities in d-wave superconductors including residual quasiparticle interactions, and compare with experiments in the superconducting state. We argue that existing data exhibit a remarkable similarity to impurity-induced magnetism in the 1D case, implying the importance of electronic correlations for the understanding of these phenomena, and suggesting that impurities may provide excellent probes of the still poorly understood ground state of the cuprates.

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Defects in correlated metals and superconductors

We have measured the temperature dependence of the transverse relaxation time of 63 Cu(2) nuclear spin in YBa 2 Cu 3 O 6.98 , YBa 2 ( 63 Cu) 3 O 7 , and YBa 2 Cu 4 O 8 . After subtraction of the T 1 process, the decay curve of the spin-echo envelope for YBa 2 Cu 4 O 8 in a strong H 1 followed a single Gaussian form from 280 K to 4.2 K, while for YBa 2 Cu 3 O 6.98 it follows only above T c . The absolute value and the temperature dependence of the decay rate 1/ 63 T G could be understood by the combined contributions of the direct dipole-dipole and the temperature-dependent indirect nuclear spin-spin coupling via χ( q ). From the temperature dependence of 1/ 63 T G for YBa 2 Cu 4 O 8 below T c , we considered that χ( Q ) even below T c remains enhanced. In a viewpoint of the 63 Cu(2) nuclear spin-spin relaxation experiments, so far as YBa 2 Cu 4 O 8 is concerned, the high- T c superconductivity seems to exhibit the d -wave pairing.

63Cu(2) Nuclear Spin-Spin Relaxation in YBa2Cu3O6.98, YBa2(63Cu)3O7-δ, and YBa2Cu4O8

We observed the pseudo spin-gap behavior of spin excitations in lightly doped single- CuO 2 -layer HgBa 2 CuO 4+δ ( T c =50, 72 and 80 K) using the Cu NMR spin-echo technique. The results indicate that lightly doped high- T c Cu oxide inherently possesses the pseudo spin-gap.

Pseudo Spin-Gap in Single-Layer High-Tc Cu Oxide HgBa2CuO4+δ

We report the doping dependence of the planar 63 Cu Knight shift ( 63 K ), the nuclear spin-lattice relaxation rate 63 (1/ T 1 T ) and the Gaussian spin-echo decay rate 63 (1/ T G ) for the high- T c monolayer HgBa 2 CuO 4+δ over a wide doping range [ T c =50, 72, 82 K (underdoping), 96 K (optimal doping) and 30 K (overdoping)], measured by the Cu NMR spin-echo technique. We found the following new facts; (1) both the static and the dynamical spin susceptibilities exhibit the pseudo spin-gap behavior over a wide q region around the staggered mode Q , (2) the dynamical pseudo spin-gap in 1/ T 1 T can mainly be ascribed to the static one in 1/ T G , and (3) a spin fluctuation amplitude probed by the empirical ratio T 1 T /( T G ) 2 is a monotonic decreasing function of the doping level but not proportional to T c . From comparison with La 2- x Sr x CuO 4 , we discussed the role of the pseudo spin-gap in the high- T c superconductivity.

Pseudo spin-gap spectrum in the monolayer HgBa2CuO4+δ

We studied local electronic states near Zn in optimally doped ${\mathrm{YBa}}_{2}({\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Zn}}_{x}{)}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ and underdoped ${\mathrm{YBa}}_{2}({\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Zn}}_{x}{)}_{4}{\mathrm{O}}_{8}$ via satellite signals of plane-site Cu(2) nuclear quadrupole resonance (NQR) spectra. From the relative intensity of Cu NQR spectra, the satellite signals are assigned to Zn-neighbor Cu NQR lines. The Cu nuclear spin-lattice relaxation time of the satellite signal is shorter than that of the main signal, which indicates that the magnetic correlation is locally enhanced near Zn both for the underdoped and the optimally doped systems. The pure ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{4}{\mathrm{O}}_{8}$ is a stoichiometric, homogenous, underdoped electronic system; nevertheless, the Zn-induced inhomogeneous magnetic response in the ${\mathrm{CuO}}_{2}$ plane is more marked than that of the optimally doped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}.$

Zn-neighbor Cu NQR in Zn-substituted YBa 2 Cu 3 O 7 − δ and YBa 2 Cu 4 O 8

We report 59Co nuclear quadrupole resonance (NQR) studies of bilayer water intercalated sodium cobalt oxides NaxCoO2.yH2O (BLH) with the superconducting transition temperatures, 2 K +-7/2 and found a dome shape superconducting phase. The 59Co NQR spectrum of the non-superconducting BLH shows a broadening below T_M without the critical divergence of 1/T_1 and 1/T_2, suggesting an unconventional magnetic ordering. The degree of the enhancement of 1/T_1T at low temperatures increases with the increase of nu_3 though the optimal nu_3~12.30 MHz. In the NaxCoO2.yH2O system, the optimal-T_c superconductivity emerges close to the magnetic instability. T_c is suppressed near the phase boundary at nu_3~12.50 MHz, which is not a conventional magnetic quantum critical point.

Yutaka Itoh

Papers

63Cu(2) Nuclear Spin-Spin Relaxation in YBa2Cu3O6.98, YBa2(63Cu)3O7-δ, and YBa2Cu4O8

Pseudo Spin-Gap in Single-Layer High-Tc Cu Oxide HgBa2CuO4+δ

Pseudo spin-gap spectrum in the monolayer HgBa2CuO4+δ

Zn-neighbor Cu NQR in Zn-substituted YBa 2 Cu 3 O 7 − δ and YBa 2 Cu 4 O 8

59Co Nuclear Quadrupole Resonance Studies of Superconducting and Non-superconducting Bilayer Water Intercalated Sodium Cobalt Oxides NaxCoO2.yH2O