d-wave duality and its reflections in high-temperature superconductors

The Bardeen-Cooper-Schrieffer theory describes the formation of electron pairs, or Cooper pairs, and their instant condensation into a superconducting state. Helium atoms are 'preformed' bosons and, in addition to their superfluid state, can also form a quantum solid that lacks phase coherence. Here I show that the fate of Cooper pairs can be more varied than the Bardeen-Cooper-Schrieffer or helium paradigms. In copper oxide d-wave superconductors, Cooper pairs are non-local objects, with both centre-of-mass and relative motions. As the level of doping of charge carriers decreases, the centre-of-mass fluctuations force a correlated d-wave superconductor into a state with enhanced diamagnetism and robust but short-ranged superconducting order. At extreme underdoping, the relative fluctuations take over and two pseudogaps - 'small' (charge) and 'large' (spin) - emerge naturally, as Cooper pairs 'disintegrate' and charge detaches from spin-singlet bonds. The ensuing ground state(s) are governed by antiferromagnetic rather than by superconducting correlations.