  We prove that the Mott insulating state is characterized by a divergence of
the electron self energy at well-defined values of momenta in the first
Brillouin zone. When particle-hole symmetry is present, the divergence obtains
at the momenta of the Fermi surface for the corresponding non-interacting
system. Such a divergence gives rise to a surface of zeros (the Luttinger
surface) of the single-particle Green function and offers a single unifying
principle of Mottness from which pseudogap phenomena, spectral weight transfer,
and broad spectral features emerge in doped Mott insulators. We also show that
only when particle-hole symmetry is present does the volume of the zero surface
equal the particle density. We identify that the general breakdown of
Luttinger's theorem in a Mott insulator arises from the breakdown of a
perturbative expansion for the self energy in the single-particle Green
function around the non-interacting limit. A modified version of Luttinger's
theorem is derived for special cases.
