Fermi-surface-free superconductivity in underdoped (Bi,Pb)₂(Sr,La)₂CuO_(6+δ) (Bi2201)

We show that hole-doped cuprates can harbor {\it Fermi-surface-free superconductivity} similar to the case of the pnictides. This occurs near the doping at which a new Fermi surface pocket appears in the antinodal region. The change in Fermi surface topology is accompanied by a characteristic rise in spectral weight. Our results support the presence of a trisected superconducting dome, and suggest that superconductivity is responsible for stabilizing the $(\pi,\pi)$ magnetic order.