  The Fermi surface calculated within the rotating antiferromagentism theory
undergoes a topological change when doping changes from p-type to n-type, in
qualitative agreement with experimental data for n-type cuprate
Nd$_{2-x}$Ce$_x$CuO$_4$ and p-type La$_{2-x}$Sr$_x$CuO$_4$. Also, the
reconstruction of the Fermi surface observed experimentally close to optimal
doing in p-type cuprates, and slightly higher than optimal doping in the
overdoped regime for this n-type high-$T_C$ cuprate is well accounted for in
this theory, and is a consequence of quantum criticality caused by the
disappearance of rotating antiferromagnetism. The present results are in
qualitative agreement with the recently observed quantum oscillations in some
high-$T_C$ cuprates regarding the change in the size of the Fermi surface as
doping evolves and the location of its reconstruction. This paper presents new
results about the application of the rotating antiferromagnetism theory to the
study of electronic structure for n-type materials.
