1In the pseudogap state of the high−T c copper-oxide (cuprate) superconductors [1], angle-resolved photoemission (ARPES) measurements have seen an Fermi arc, i.e., an open-ended gapless section in the large Fermi surface [2,3,4,5,6,7,8], 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 [9,10,11,12,13,14]. The Fermi arcs have worried the high−T c 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 [15]. 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-T c cuprate superconductors will rely critically on understanding such a new finding.The high resolution Fermi surface mapping (Fig. 1a) on the underdoped La-Bi2201 UD18K sample using VUV laser reveals three Fermi surface sheets with low spectral weight (labeled as LP, LS and LPS in Fig. 1a) in the covered momentum space, in addition to the prominent main Fermi surface (LM). One particular Fermi surface sheet LP crosses the main band LM, forming an enclosed loop, an Fermi pocket, near the nodal region. Quantitative Fermi surface data measured from both VUV laser (Fig. 2a) and Helium discharge lamp ( (Fig. 2a) and HP band observed in Helium lamp measurement (Fig. 2b) are intrinsic; they can not be attributed to any of the umklapp bands or shadow bands (Fig. 2c). The location of the three bands can be well connected by the same superlattice vector, indicating that the HP and LPS bands correspond to the first order umklapp bands of the main Fermi pocket LP. The shape 2 and area of the Fermi pockets are also consistent in these two independent measurements, making a convincing case on the presence of the Fermi pocket. We note that in both the laser (Fig. 2a) and Helium lamp (Fig. 2b and SFig. 2 in the Supplementary) measurements, all the observed bands except for the "Fermi pocket bands" can be assigned by only one regular superstructure wavevector (0.24,0.24). The presence of additional superstructure, which would give rise to new bands, appears to be unlikely because there is no indication of such additional bands observed in our measurements.The Fermi pocket is observed both in the normal state and superconducting state, as shown in Fig. 3 for the La-Bi2201 UD18K sample. Moreover, its location, shape and area show little change with temperature (Figs. 3a and 3f). Below T c , the openi...

The design and performance of the first vacuum ultra-violet (VUV) laser-based angle-resolved photoemission (ARPES) system are described. The VUV laser with a photon energy of 6.994 eV and bandwidth of 0.26 meV is achieved from the second harmonic generation using a novel nonlinear optical crystal KBe 2 BO 3 F 2 (KBBF). The new VUV laser-based ARPES system exhibits superior performance, including super-high energy resolution better than 1 meV, high momentum resolution, super-high photon flux and much enhanced bulk sensitivity, which are demonstrated from measurements on a typical Bi 2 Sr 2 CaCu 2 O 8 high temperature superconductor. Issues and further development related to the VUV laser-based photoemission technique are discussed.

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