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 absence of simple examples of superconductivity adjoining itinerant-electron ferromagnetism in the phase diagram has for many years cast doubt on the validity of conventional models of magnetically mediated superconductivity. On closer examination, however, very few systems have been studied in the extreme conditions of purity, proximity to the ferromagnetic state and very low temperatures required to test the theory definitively. Here we report the observation of superconductivity on the border of ferromagnetism in a pure system, UGe2, which is known to be qualitatively similar to the classic d-electron ferromagnets. The superconductivity that we observe below 1 K, in a limited pressure range on the border of ferromagnetism, seems to arise from the same electrons that produce band magnetism. In this case, superconductivity is most naturally understood in terms of magnetic as opposed to lattice interactions, and by a spin-triplet rather than the spin-singlet pairing normally associated with nearly antiferromagnetic metals.

Superconductivity on the border of itinerant-electron ferromagnetism in UGe2

IT is well known that BCS mean-field theory is remarkably successful in describing conventional superconductors. A central concept of BCS theory is the energy gap in the electronic excitation spectrum below the superconducting transition temperature, Tc. The gap also serves as the order parameter: quite generally, long-range phase coherence and a non-zero gap go hand-in-hand1. But in underdoped high-Tc superconductors there is considerable evidence that a pseudogap (a suppression of spectral weight) is already formed in the normal state above Tc—first, from studies of the spin excitation spectrum2–5,24, which measure a 'spin gap', and later from a variety of other probes6–10. Here we present a study of underdoped Bi2Sr2CaCu2O8+δ (Bi2212) using angle-resolved photoemission spectroscopy (ARPES), which directly measures the momentum-resolved electron excitation spectrum of the CuO2 planes. We find that a pseudogap with d-wave symmetry opens up in the normal state below a temperature T* > Tc, and develops into the d-wave superconducting gap once phase coherence is established below Tc.

Spectroscopic evidence for a pseudogap in the normal state of underdoped high- T c superconductors

The case for dx2 − y2 pairing in the cuprate superconductors

Angle-resolved photoemission experiments reveal evidence of an energy gap in the normal state excitation spectrum of the cuprate superconductor Bi2Sr2CaCu2O8+delta. This gap exists only in underdoped samples and closes around the doping level at which the superconducting transition temperature Tc is a maximum. The momentum dependence and magnitude of the gap closely resemble those of the dx2-y2 gap observed in the superconducting state. This observation is consistent with results from several other experimental techniques, which also indicate the presence of a gap in the normal state. Some possible theoretical explanations for this effect are reviewed.

https://science.sciencemag.org/content/sci/273/5273/325.full.pdf

Excitation Gap in the Normal State of Underdoped Bi2Sr2CaCu2O8+δ

An anomalous temperature dependence of Cu nuclear spin-lattice relaxation time T 1 has been observed for both the Cu1 chain and Cu2 plane sites of YBa 2 Cu 3 O 6.91 ( T c =90 K) and discussed in connection with spin fluctuations and an anisotropic energy gap which nucleates in the vicinity of Cu2 nuclei.

Anomalous temperature dependence of Cu nuclear spin-lattice relaxation in YBa2Cu3O6.91

The zero-field antiferromagnetic nuclear resonance (AFNR) of Cu in the high- T c related oxide YBa 2 Cu 3 O 6 has been observed at 89.89±0.05 MHz for 63 Cu and 96.29±0.05 MHz for 65 Cu with well articulated quadrupole splittings at 1.3 K. These frequencies correspond to a hyperfine field of 79.65±0.05 KOe. From the analysis of the AFNR spectrum and the observation of NQR at 30.11±0.2 MHz for 65 Cu and 27.88±0.02 MHz for 63 Cu, both of which have no Zeeman splitting, it is concluded that the antiferromagnetic mounents reside only on the CuO 2 plane sites and the direction of moments is perpendicular to the c -axis. This is consistent with the spin structure proposed by neutron diffraction studies. The nuclear relaxation behavior is also discussed briefly.

Observation of Antiferromagnetic Nuclear Resonance of Cu in YBa2Cu3O6

Anomalous high-field magnetization and negative forced volume magnetostriction in Yb1-xMxCu2 (M=In and Ag)-evidence for valence change in high magnetic fields.

The zero-field nuclear magnetic resonance (NMR) of Cu in the high- T c related oxide, La 2 CuO 4-δ , has been observed at 93.85±0.1 MHz for 63 Cu and 100.1±0.1 MHz for 65 Cu with well-articulated quadrupole splittings at 1.3 K. The resonance pattern is successfully analyzed as a result of the combined effect of a quadrupole coupling (coupling constant ν Q =31.9 MHz for 63 Cu and 29.5 MHz for 65 Cu with asymmetry parameter η=0.03) and a Zeeman term where the internal field ( H N =78.78 kOe) is nearly perpendicular to the direction of the maximum electric field gradient (EFG). The quadrupole split zero-field NMR signals have also been observed in CuO. The observed frequencies yield parameter values of 137.1±0.1 MHz, 146.9±0.1 MHz, 20.07 MHz, 18.57 MHz, 0.20, 121.5 kOe, and the direction of H N is found to be nearly parallel to the direction of the maximum EFG.

Observation of Nuclear Resonance of Cu in Antiferromagnetic La2CuO4-δ and CuO

Nuclear spin-lattice relaxation times T 1 of 63 Cu and 65 Cu in the Cu(2) sites of the high T c superconductor YBa 2 Cu 3 O 7-δ (δ≃0.1, T c =91 K) have been measured for the wide temperature range between 2.2 K and 300 K. The temperature dependence of 1/ T 1 in the normal state has been found to be the one unexpected for simple metals. The influences of antiferromagnetic spin fluctuations in the d–p bands in the Cu(2)–O layers are discussed. The temperature dependence of 1/ T 1 below T c has also been found to be the one which is not expected for isotropic BCS superconductors. The power-law like temperature dependence of 1/ T 1 without any enhancement just below T c has been observed between 40 K and 91 K.

Tadashi Shimizu

Papers

Anomalous temperature dependence of Cu nuclear spin-lattice relaxation in YBa2Cu3O6.91

Observation of Antiferromagnetic Nuclear Resonance of Cu in YBa2Cu3O6

Anomalous high-field magnetization and negative forced volume magnetostriction in Yb1-xMxCu2 (M=In and Ag)-evidence for valence change in high magnetic fields.

Observation of Nuclear Resonance of Cu in Antiferromagnetic La2CuO4-δ and CuO

Nuclear Spin-Lattice Relaxation of 63,65Cu at the Cu(2) Sites of the High Tc Superconductor YBa2Cu3O7-δ