LETTERS

Coexistence of Fermi arcs and Fermi pockets in ahigh-Tc copper oxide superconductorJianqiao Meng1, Guodong Liu1, Wentao Zhang1, Lin Zhao1, Haiyun Liu1, Xiaowen Jia1, Daixiang Mu1, Shanyu Liu1,Xiaoli Dong1, Jun Zhang1, Wei Lu1, Guiling Wang2, Yong Zhou2, Yong Zhu2, Xiaoyang Wang2, Zuyan Xu2,Chuangtian Chen2 & X. J. Zhou1

In the pseudogap state of the high-transition-temperature (high-Tc) copper oxide superconductors1, angle-resolved photoemission(ARPES) measurements have seen Fermi arcs—that is, open-endedgapless sections in the large Fermi surface2–8—rather than a closedloop expected of an ordinary metal. This is all the more puzzlingbecause Fermi pockets (small closed Fermi surface features) havebeen suggested by recent quantum oscillation measurements9–14.The Fermi arcs cannot be understood in terms of existing theories,although there is a solution in the form of conventional Fermi surfacepockets associated with competing order, but with a back side that isfor detailed reasons invisible to photoemission probes15. Here wereport ARPES measurements of Bi2Sr22xLaxCuO61d (La-Bi2201) thatreveal Fermi pockets. The charge carriers in the pockets are holes, andthe pockets show an unusual dependence on doping: they exist inunderdoped but not overdoped samples. A surprise is that theseFermi pockets appear to coexist with the Fermi arcs. This coexistencehas not been expected theoretically.

The high-resolution Fermi surface mapping (Fig. 1a) of the under-doped La-Bi2201 sample (with Tc518 K: UD18K) using a vacuumultraviolet (VUV) laser reveals three Fermi surface sheets with low

spectral weight (labelled LP, LS and LPS in Fig. 1a) in the momentumspace covered, in addition to the prominent main Fermi surface (LM).One particular Fermi surface sheet LP crosses the main band LM,forming an enclosed loop—a Fermi pocket—near the nodal region.Quantitative Fermi surface data measured using both a VUV laser(Fig. 2a) and a helium discharge lamp (Fig. 2b) are summarized inFig. 2c. All the possible umklapp bands16,17, shadow bands18,19 andumklapp bands of the shadow bands that may be present in thebismuth-based compounds are shown for comparison (see Sup-plementary Information and Supplementary Fig. 2 for more details).It is clear that the LP and LPS bands observed in VUV laser measure-ments (Fig. 2a) and the HP band observed in helium lamp measure-ments (Fig. 2b) are intrinsic; they cannot be attributed to any of theumklapp bands or shadow bands (Fig. 2c). The location of the threebands can be well connected by the same superlattice vector,indicating that the HP and LPS bands correspond to the first-orderumklapp bands of the main Fermi pocket, LP. The shape and area ofthe Fermi pockets are also consistent in these two independent mea-surements, making a convincing case for the presence of the Fermipocket. We note that in both the laser (Fig. 2a) and helium lamp

1National Laboratory for Superconductivity, Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.2Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China.

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Figure 1 | Fermi surface and band structure of a La-Bi2201 sample. In thepresent paper, we use the phrase ‘Fermi surface’ loosely to denote themomentum space locus of high-intensity low-energy spectral weight. Incopper oxide superconductors, the Fermi surface is usually measured in thesuperconducting state in spite of the gap opening because the sharpness ofthe features at low temperature facilitates the precise determination of theunderlying Fermi surface as compared to the normal state. It has been shownthat the ‘underlying Fermi surface’ determined from the minimum gap locusin the superconducting state is identical to that in the normal state31.a, Photoemission intensity at the Fermi energy (EF) as a function ofmomenta kx and ky for the La-Bi2201 UD18K sample (underdoped,

Tc 5 18 K) measured at a temperature of 14 K. It is obtained bysymmetrizing the original data with respect to the (0,0)–(p,p) line. FourFermi surface sheets are resolved in the covered momentum space, markedas LM for the main sheet, LP for the Fermi pocket, and LS and LPS for theothers. b–f, Band structure (bottom panels) and corresponding momentumdistribution curves (MDCs) at the Fermi level (upper panels) along fivetypical momentum cuts (cuts 1 to 5) as labelled in Fig. 1a. To see the weakfeatures more clearly, the original MDCs (thin grey lines) in the upper panelare expanded 10 times and plotted in the same figures (thick black lines).Note that the signal of the Fermi pocket LP is very weak; its intensity is overone order of magnitude weaker than that of the main band LM.

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(Fig. 2b and Supplementary Fig. 2) measurements, all the observedbands except for the ‘Fermi pocket bands’ can be explained by onlyone 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 additionalbands observed in our measurements.

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Figure 2 | Identification of the Fermi pocket in the photoemission data.a, Fermi surface measured in the La-Bi2201 UD18K sample using the VUVlaser. The four observed Fermi surface sheets in the covered momentumspace are quantitatively represented by red circles. b, Fermi surfacemeasured in the La-Bi2201 UD18K sample by a helium discharge lamp at aphoton energy of 21.218 eV. It is obtained by symmetrizing the original datawith respect to the (0,0)–(p,p) line. Black circles represent quantitativepositions of the observed Fermi surface sheets. c, Summary of the measuredFermi surface from VUV laser (open red circles, as in a) and heliumdischarge lamp (open black circles, as in b) observations. Red lines representthe main Fermi surface (central thickest line) and its correspondingumklapp bands (thinner lines on either side of the main Fermi surface). Thethickest green line represents the shadow band of the main Fermi surface,

and thinner green lines the umklapp bands of the shadow band. The pinkdashed lines represent possible high-order umklapp bands from the mainband in the third quadrant (see Supplementary Information andSupplementary Fig. 2 for more details). It is clear that the main Fermi surfacemeasured from the VUV laser (LM) shows a good agreement with that fromthe helium discharge lamp (HM). The LS band observed using the VUV laseragrees well with the first-order umklapp band of the shadow band. TheHMSP and HMSN bands observed in helium discharge lamp measurementscorrespond to the first-order umklapp bands of the main band. The threeellipses represent the position of the observed Fermi pockets. The matrixelement effect (associated with the photoemission process) on the relativespectral intensity between the main band and the Fermi pocket is aninteresting issue to be further explored.

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Figure 3 | Temperature dependence of the Fermi pocket. Top panels, Fermisurface and photoemission spectra for the La-Bi2201 UD18K sample belowTc; bottom panels, as in top panels but above Tc. a, Fermi surface mapping at14 K. b, Photoemission spectra (energy distribution curves, EDCs) along themain Fermi surface. Sharp peaks are observed near the nodal region and getweaker when moving to the antinodal region. c, The correspondingsymmetrized EDCs. The symmetrization procedure32 provides an intuitiveway to identify an energy gap opening which is characterized by theappearance of a dip near the Fermi level; zero gap corresponds to a peak atthe Fermi level. The gap size is determined by the EDC peak position with

respect to the Fermi level. It is clearly seen that the gap size increases from thenodal to antinodal regions. d, EDCs along the back side of the Fermi pocket.e, The corresponding symmetrized EDCs. The gap size increase is also cleargoing from the nodal to antinodal regions along the pocket. f, Fermi surfacemapping at 50 K. g, EDCs along the main Fermi surface. h, Thecorresponding symmetrized EDCs. At 50 K, there is a gapless region formednear the nodal region with its location denoted in f by pink filled circles; themain Fermi surface beyond this region remains gapped. i, EDCs along theFermi pocket. j, The corresponding symmetrized EDCs. At 50 K, the weakpeak near the Fermi level indicates gap closing along the Fermi pocket.

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The Fermi pocket is observed both in the normal state and thesuperconducting state, as shown in Fig. 3 for the La-Bi2201 UD18Ksample. Moreover, its location, shape and area show little changewith temperature (Fig. 3a and f). Below Tc, the opening of a super-conducting gap is clearly observed on both the main band (Fig. 3c)and the back side of the Fermi pocket (Fig. 3e). Above Tc, a portion ofthe main Fermi surface near the nodal region becomes gapless, asindicated by the pink filled circles on the main Fermi surface (Fig. 3f).This is reminiscent of the Fermi arc formation in previous ARPESresults, which show an increase in arc length with increasing temper-ature3,5. The back side of the Fermi pocket also becomes gapless aboveTc (Fig. 3j), forming a gapless Fermi pocket loop with part of the mainband. We note that the Fermi arc on the main band appears to extendfarther than the Fermi pocket section (Fig. 3f), giving rise to aninteresting coexistence of Fermi arc and Fermi pocket.

The Fermi pocket exhibits an unusual doping dependence, as seenin Fig. 4. It is observed not only in the UD18K sample (Fig. 4b), butalso in the UD26K sample (Fig. 4c). But it is not seen in the UD3Ksample (Fig. 4a) or the OP32K optimally doped sample (Fig. 4d)20.This peculiar doping dependence of the Fermi pocket—it can only beobserved in a limited doping range in the underdoped region—lendsfurther support to its intrinsic nature. The quantitative main Fermisurface and Fermi pocket at various dopings are summarized inFig. 4i. The areas enclosed by the Fermi pockets in the UD18K (blueellipse in Fig. 4i) and UD26K (grey ellipse in Fig. 4i) samples corre-spond to doping levels of 0.11 and 0.12 holes per copper site, respec-tively, which is in good agreement with the estimated holeconcentration of each sample21,22.

The Fermi pocket we have observed is hole-like, so it cannot corre-spond to the electron-like Fermi pocket suggested from quantumoscillation experiments11,23. Moreover, the observed Fermi pocketis not symmetrically located in the Brillouin zone: specifically, it isnot centred around (p/2,p/2) (Fig. 4i). This is distinct from theobservation reported in the Nd-LSCO system24 which is symmetricalwith respect to the (p,0)–(0,p) line, similar to the ‘shadow band’commonly observed in Bi2201 and Bi221218,19. This particular loca-tion makes it impossible that the Fermi pocket we have observedoriginates from the d-density-wave ‘hidden order’ that gives ahole-like Fermi pocket centred around the (p/2,p/2) point23,25.Among other possible origins of Fermi pocket formation26–29, the

phenomenological resonant valence bond picture27,28 shows a fairlygood agreement with our observations, in terms of the location,shape and area of the hole-like Fermi pocket and its doping depend-ence. In particular, the predicted Fermi pockets are pinned at the(p/2,p/2) point27,28, which is consistent with our experiment (Fig. 4i).One obvious discrepancy is that the spectral weight on the back sideof the Fermi pocket near (p/2,p/2) is expected to be zero from thesetheories26–28, which is at odds with our measurements (Figs 3d and i).We note that the existence of incommensurate density waves couldalso potentially explain the observed pockets. One possible wavevec-tor needed is (1 6 0.092,1 6 0.092), which is diagonal and can beexamined by neutron or X-ray scattering measurements. There areindications of the charge-density-wave (CDW) formation reportedin the Bi2201 system30; whether the Fermi surface reconstructioncaused by such a CDW order or its related spin-density-wave ordercan account for our observation needs to be further explored.

One peculiar characteristic of the Fermi pocket is its coexistencewith the large underlying Fermi surface (Figs 3 and 4). One maywonder whether this could originate from sample inhomogeneity: thatis, the large Fermi surface is caused by a phase at high doping, whereasthe Fermi pocket is from a phase at low doping. We believe this isunlikely, because there is no indication of two distinct superconduct-ing phases being detected in the magnetization measurement (Sup-plementary Fig. 1). In addition, no Fermi pocket is identified for theunderdoped UD3K sample (Fig. 4a). A more surprising observation isthe coexistence of Fermi arcs and Fermi pockets in the normal state,because this has not been expected theoretically. We believe these newfindings will provide key insights for understanding the anomalouspseudogap state in high-Tc copper oxide superconductors.

Received 14 May; accepted 10 September 2009.

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Supplementary Information is linked to the online version of the paper atwww.nature.com/nature.

Acknowledgements We thank D.-H. Lee, P. A. Lee, S. Sachdev, Z.-X. Shen,X. G. Wen, Z. Y. Weng, T. Xiang, G. M. Zhang and F. C. Zhang for discussions. Thiswork was supported by the NSFC, the MOST of China and the Chinese Academy ofSciences.

Author Contributions J.M. contributed to La-Bi2201 sample growth with theassistance of G.L.; X.D. and W.L. contributed to the magnetic measurement ofsamples; G.L., W.Z., L.Z., H.L., J.M., X.D., X.J., D.M., S.L., J.Z., G.W., Y. Zhou, Y. Zhu,X.W., Z.X. and C.C. contributed to the development and maintenance of thelaser-ARPES system; J.M. carried out the experiment with assistance from G.L.,W.Z., L.Z., H.L., X.J., D.M. and S.L.; X.J.Z. and J.M. analysed the data and wrote thepaper; X.J.Z. was responsible for overall project direction, planning, managementand infrastructure.

Author Information Reprints and permissions information is available atwww.nature.com/reprints. Correspondence and requests for materials should beaddressed to X.J.Z. (XJZhou@aphy.iphy.ac.cn).

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