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We use the Nernst effect to delineate the boundary of the pseudogap phase in the temperaturedoping phase diagram of hole-doped cuprate superconductors. New data for the Nernst coefficient ν(T ) of YBa2Cu3Oy (YBCO), La1.8−xEu0.2SrxCuO4 (Eu-LSCO) and La1.6−xNd0.4SrxCuO4 (Nd-LSCO) are presented and compared with previously published data on YBCO, Eu-LSCO, Nd-LSCO, and La2−xSrxCuO4 (LSCO). The temperature Tν at which ν / T deviates from its hightemperature linear behaviour is found to coincide with the temperature at which the resistivity ρ(T ) deviates from its linear-T dependence, which we take as the definition of the pseudogap temperature T -in agreement with the temperature at which the antinodal spectral gap detected in angleresolved photoemission spectroscopy (ARPES) opens. We track T as a function of doping and find that it decreases linearly vs p in all four materials, having the same value in the three LSCObased cuprates, irrespective of their different crystal structures. At low p, T is higher than the onset temperature of the various orders observed in underdoped cuprates, suggesting that these orders are secondary instabilities of the pseudogap phase. A linear extrapolation of T (p) to p = 0 yields T (p → 0) TN(0), the Néel temperature for the onset of antiferromagnetic order at p = 0, suggesting that there is a link between pseudogap and antiferromagnetism. With increasing p, T (p) extrapolates linearly to zero at p pc2, the critical doping below which superconductivity emerges at high doping, suggesting that the conditions which favour pseudogap formation also favour pairing. We also use the Nernst effect to investigate how far superconducting fluctuations extend above the critical temperature Tc, as a function of doping, and find that a narrow fluctuation regime tracks Tc, and not T . This confirms that the pseudogap phase is not a form of precursor superconductivity, and fluctuations in the phase of the superconducting order parameter are not what causes Tc to fall on the underdoped side of the Tc dome.

Strontium titanate is a wide-gap semiconductor avoiding a ferroelectric instability thanks to quantum fluctuations. This proximity leads to strong screening of static Coulomb interaction and paves the way for the emergence of a very dilute metal with extremely mobile carriers at liquid-helium temperature. Upon warming, mobility decreases by several orders of magnitude. Yet, metallicity persists above room temperature even when the apparent mean free path falls below the electron wavelength. The superconducting instability survives at exceptionally low concentrations and beyond the boundaries of MigdalEliashberg approximation. An intimate connection between dilute superconductivity and aborted ferroelectricity is widely suspected. In this review, we give a brief account of ongoing research on bulk strontium titanate as an insulator, a metal, and a superconductor. CONTENTS