Doping a Mott insulator: physics of high-temperature superconductivity. The local spectra remain qualitatively the same across the insulator-to-superconductor transition, and the quasiparticle interference becomes long-ranged. Each chequerboard plaquette contains approximately two holes and exhibits a stripy internal structure that has a strong influence on the superconducting spectroscopic features. We observe a smooth crossover from the Mott insulator to superconductor on small islands that have chequerboard order. We make these observations via scanning tunnelling microscopy on underdoped Bi 2La xSr 2 − xCuO 6 + δ. Here we examine the evolution of pairing and phase-ordering in underdoped cuprates, and find that a chequerboard plaquette pattern of charge order plays a crucial role, such that the global phase coherence is established once its spatial occupation exceeds a threshold. It has been proposed that pairing and phase coherence may occur separately in cuprates, and that the measured critical temperature corresponds to the phase-coherence temperature controlled by the superfluid density. The cuprate high-temperature superconductors belong to a different category because, being doped Mott insulators, they are known to have low superfluid density and are therefore susceptible to phase fluctuations. In conventional metallic superconductors such as aluminium, the large number of weakly bounded Cooper pairs become phase-coherent as soon as they start to form.
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