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.