  We report on the study of the Fermi surface of the electron-doped cuprate
superconductor Nd$_{2-x}$Ce$_x$CuO$_{4}$ by measuring the interlayer
magnetoresistance as a function of the strength and orientation of the applied
magnetic field. We performed experiments in both steady and pulsed magnetic
fields on high-quality single crystals with Ce concentrations of $x=0.13$ to
0.17. In the overdoped regime of $x > 0.15$ we found both semiclassical
angle-dependent magnetoresistance oscillations (AMRO) and Shubnikov-de Haas
(SdH) oscillations. The combined AMRO and SdH data clearly show that the
appearance of fast SdH oscillations in strongly overdoped samples is caused by
magnetic breakdown. This observation provides clear evidence for a
reconstructed multiply-connected Fermi surface up to the very end of the
overdoped regime at $x\simeq 0.17$. The strength of the superlattice potential
responsible for the reconstructed Fermi surface is found to decrease with
increasing doping level and likely vanishes at the same carrier concentration
as superconductivity, suggesting a close relation between translational
symmetry breaking and superconducting pairing. A detailed analysis of the
high-resolution SdH data allowed us to determine the effective cyclotron mass
and Dingle temperature, as well as to estimate the magnetic breakdown field in
the overdoped regime.
