A coherent three-dimensional Fermi surface in a high-transition-temperature superconductor

All conventional metals are known to possess a three-dimensional Fermi surface, which is the locus in reciprocal space of the long-lived electronic excitations that govern their electronic properties at low temperatures. These excitations should have well-defined momenta with components in all three dimensions. The high-transition-temperature (high-Tc) copper oxide superconductors have unusual, highly two-dimensional properties above the superconducting transition1. This, coupled with a lack of unambiguous evidence for a three-dimensional Fermi surface, has led to many new and exotic models for the underlying electronic ground state2. Here we report the observation of polar angular magnetoresistance oscillations3 in the overdoped superconductor Tl2Ba2CuO6+δ in high magnetic fields, which firmly establishes the existence of a coherent three-dimensional Fermi surface. Analysis of the oscillations reveals that at certain symmetry points, however, this surface is strictly two-dimensional. This striking form of the Fermi surface topography, long-predicted by electronic band structure calculations4, provides a natural explanation for a wide range of anisotropic properties both in the normal5,6 and superconducting states7,8,9. Our data reveal that, despite their extreme electrical anisotropy, the high-Tc materials at high doping levels can be understood within a framework of conventional three-dimensional metal physics.