Quantum oscillations and Fermi surface in underdoped YBa$_2$Cu$_3$O$_{6.5}$

We report quantum oscillations in the transport properties of YBa$_2$Cu$_3$O$_{6.5}$ at 10\% doping, showing that a well-defined Fermi surface with closed orbits is a fundamental property of underdoped cuprates. In contrast with the large Fermi surface seen on the overdoped side, we observe a very small orbit whose area is only 1.9\% of the Brillouin zone. Such a small Fermi surface does not come from the band structure of YBa$_2$Cu$_3$O$_{6.5}$ and is most likely the result of a reconstruction.