  We investigate the electron momentum distribution function (EMD) in a weakly
doped two-dimensional quantum antiferromagnet (AFM) as described by the t-J
model. Our analytical results for a single hole in an AFM based on the
self-consistent Born approximation (SCBA) indicate an anomalous momentum
dependence of EMD showing 'hole pockets' coexisting with a signature of an
emerging large Fermi surface. The position of the incipient Fermi surface and
the structure of the EMD is determined by the momentum of the ground state. Our
analysis shows that this result remains robust in the presence of next-nearest
neighbor hopping terms in the model. Exact diagonalization results for small
clusters are with the SCBA reproduced quantitatively.
