The properties of cuprate high-temperature superconductors are largely shaped
by competing phases whose nature is often a mystery. Chiefly among them is the
pseudogap phase, which sets in at a doping p∗ that is material-dependent.
What determines p∗ is currently an open question. Here we show that the
pseudogap cannot open on an electron-like Fermi surface, and can only exist
below the doping pFS at which the large Fermi surface goes from hole-like
to electron-like, so that p∗≤pFS. We derive this result from
high-magnetic-field transport measurements in
La1.6−xNd0.4SrxCuO4 under pressure, which reveal a large and
unexpected shift of p∗ with pressure, driven by a corresponding shift in
pFS. This necessary condition for pseudogap formation, imposed by details
of the Fermi surface, is a strong constraint for theories of the pseudogap
phase. Our finding that p∗ can be tuned with a modest pressure opens a new
route for experimental studies of the pseudogap.Comment: 15 pages, 5 figures, 7 supplemental figure