  In order to understand the origin of superconductivity, it is crucial to
ascertain the nature and origin of the primary carriers available to
participate in pairing. Recent quantum oscillation experiments on high Tc
cuprate superconductors have revealed the existence of a Fermi surface akin to
normal metals, comprising fermionic carriers that undergo orbital quantization.
However, the unexpectedly small size of the observed carrier pocket leaves open
a variety of possibilities as to the existence or form of any underlying
magnetic order, and its relation to d-wave superconductivity. Here we present
quantum oscillations in the magnetisation (the de Haas-van Alphen or dHvA
effect) observed in superconducting YBa2Cu3O6.51 that reveal more than one
carrier pocket. In particular, we find evidence for the existence of a much
larger pocket of heavier mass carriers playing a thermodynamically dominant
role in this hole-doped superconductor. Importantly, characteristics of the
multiple pockets within this more complete Fermi surface impose constraints on
the wavevector of any underlying order and the location of the carriers in
momentum space. These constraints enable us to construct a possible
density-wave scenario with spiral or related modulated magnetic order,
consistent with experimental observations.
