© Reprinted by permission from Macmillan Publishers Ltd: *Nature* 450, 1177-1183 (18 December 2007).

Graphical representation of the static magnetic interaction potential in real space seen by a quasiparticle moving on a square crystal lattice given that the other quasiparticle is at the origin (denoted by a cross). The spins of the interacting quasiparticles are taken to be antiparallel, such that the total spin of the Cooper pair is zero. The dashed lines show the regions where the d-wave Cooper-pair state has vanishing amplitude. This is the state that best matches the oscillations of the potential, in that a quasiparticle has minimal probability of being on lattice sites when the potential induced by the quasiparticle at the origin is repulsive. The size of the circle in each lattice site is a representation of the absolute magnitude of the potential (on a logarithmic scale). This picture is appropriate for a system on the border of antiferromagnetism in which the period of the real space oscillations of the potential is precisely commensurate with the lattice. (Unit: 8)