  In the pseudogap state of the high-Tc copper-oxide (cuprate) superconductors,
angle-resolved photoemission (ARPES) measurements have seen an Fermi arc, i.e.,
an open-ended gapless section in the large Fermi surface, rather than a closed
loop expected of an ordinary metal. This is all the more puzzling because Fermi
pockets (small closed Fermi surface features) have been suggested from recent
quantum oscillation measurements. The Fermi arcs have worried the high-Tc
community for many years because they cannot be understood in terms of existing
theories. Theorists came up with a way out in the form of conventional Fermi
surface pockets associated with competing order, with a back side that is for
detailed reasons invisible by photoemission. Here we report ARPES measurements
of La-Bi2201 that give direct evidence of the Fermi pocket. The charge carriers
in the pocket are holes and the pockets show an unusual dependence upon doping,
namely, they exist in underdoped but not overdoped samples. A big surprise is
that these Fermi pockets appear to coexist with the Fermi arcs. This
coexistence has not been expected theoretically and the understanding of the
mysterious pseudogap state in the high-Tc cuprate superconductors will rely
critically on understanding such a new finding.
