Evolution of the pseudogap from Fermi arcs to the nodal liquid

The response of a material to external stimuli depends on its low-energy excitations. In conventional metals, these excitations are electrons on the Fermi surface - a contour in momentum (k) space that encloses all of the occupied states for non-interacting electrons. The pseudogap phase in the copper oxide superconductors, however, is a most unusual state of matter(1). It is metallic, but part of its Fermi surface is 'gapped out' (refs 2,3); low-energy electronic excitations occupy disconnected segments known as Fermi arcs(4). Two main interpretations of its origin have been proposed: either the pseudogap is a precursor to superconductivity(5), or it arises from another order competing with superconductivity(6). Using angle-resolved photoemission spectroscopy, we show that the anisotropy of the pseudogap in k-space and the resulting arcs depend only on the ratio T/T*(x), where T*( x) is the temperature below which the pseudogap first develops at a given hole doping x. The arcs collapse linearly with T/T*( x) and extrapolate to zero extent as T --> 0. This suggests that the T = 0 pseudogap state is a nodal liquid - a strange metallic state whose gapless excitations exist only at points in k-space, just as in a d-wave superconducting state.