Superconductivity in a strong spin-exchange field. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in Bi 2Sr 2CaCu 2O 8+ δ.įulde, P. Finally, by visualizing the topological defects in these N( r, E) density waves at 2 Q, we find them to be concentrated in areas where the PDW spatial phase changes by π, as predicted by the theory of half-vortices in a PDW state 6, 7. Simultaneous imaging of the local density of states N( r, E) (where E is the energy) reveals electronic modulations with wavevectors Q and 2 Q, as anticipated when the PDW coexists with superconductivity.

Here, using a spectroscopic technique based on scanning tunnelling microscopy, we find strong Δ( r) modulations in the canonical cuprate Bi 2Sr 2CaCu 2O 8+ δ that have eight-unit-cell periodicity or wavevectors Q ≈ (2π/ a 0)(1/8, 0) and Q ≈ (2π/ a 0)(0, 1/8) (where a 0 is the distance between neighbouring Cu atoms). Although the signature of a cuprate PDW has been detected in Cooper-pair tunnelling 5, the distinctive signature in single-electron tunnelling of a periodic Δ( r) modulation has not been observed.

Recently, this concept has been generalized to the pair-density-wave (PDW) state predicted to exist in copper oxides (cuprates) 3, 4. The defining characteristic 1, 2 of Cooper pairs with finite centre-of-mass momentum is a spatially modulating superconducting energy gap Δ( r), where r is a position.

Wave imaging