26.M.Aoki,Toward a Comparative Institutional Analysis (MIT Chinese version of the triad task:M.Hunter for statistical Supplementary Materials Press,Cambridge,MA,2001). quidance;and 1.P.Seder,A Putnam,Y.Wang.T.Wilson,and www.sciencemag.org/content/344/6184/603/suppl/DC1 27.Food and Agricultural Organization (FAOMInternational E.Gilbert for comments on earlier versions of this paper.The data Materials and Methods Institute for Applied Systems Analysis (IIASA),Global are available at the Inter-University Consortium for Political and Figs.S1 and S2 Agro-ecological Zones (GAEZ v3.0)(2010). Social Research (ICPSR no.35027)or by request to the first Tables S1 to $12 author.This research was supported by a Fulbright Scholarship,a References (28-49) Acknowledgments:We thank Z.Xia,N.Qingyun,Y.Wu,Y.Wang, NSF Graduate Research Fellowship,and a NSF East Asian and Y.Ma,and A Jiao for collecting data;A.Leung and C.Wang for Pacific Summer Institute Fellowship.The Beijing Key Lab of Applied 4 October 2013:accepted 25 March 2014 making the loyalty/nepotism task available;L Jun Ji for the Experimental Psychology supplied laboratory space for the study. 10.1126/science.1246850 REPORTS vealed by QO or possibly created by their neces- Fermi Surface and Pseudogap sarily high magnetic fields. A zero-field altemative to QO,angle-resolved Evolution in a Cuprate Superconductor photoemission spectroscopy(ARPES),has a long history of mapping the FS in BiSr2CaCu2Os (Bi2212)(2,7-//).Here,the onset of the pseu- Yang He,1 Yi Yin,1*M.Zech,1 Anjan Soumyanarayanan,1 Michael M.Yee,1 Tess Williams,1 dogap (PG)is defined by the opening of an M.C.Boyer,Kamalesh Chatterjee,2 W.D.Wise,2 I.Zeljkovic,Takeshi Kondo,3s T.Takeuchi,3 H.lkuta,3 Peter Mistark,4 Robert S.Markiewicz,4 Arun Bansil,4 Subir Sachdev,1 antinodal gap and the reduction of the large FS to a"Fermi arc,"which may actually be one side of E.W.Hudson,2I].E.Hoffman2 a Fermi pocket,consistent with QO results (10). The PG onset may be associated with a QPT just The undlear relationship between cuprate superconductivity and the pseudogap state remains an above optimal doping at p=0.19(/D).A second impediment to understanding the high transition temperature (7)superconducting mechanism.Here, QPT to another competing phase is suggested to we used magnetic field-dependent scanning tunneling microscopy to provide phase-sensitive proof occur()at lower doping (p=0.076),similar that d-wave superconductivity coexists with the pseudogap on the antinodal Fermi surface of an perhaps to that found by QO(5,6).However,if overdoped cuprate.Furthermore,by tracking the hole-doping (p)dependence of the quasi-partice the transition near optimal doping is a FS recon- interference pattern within a single bismuth-based cuprate family,we observed a Fermi surface struction to pockets,as suggested in (10),why are reconstruction slightly below optimal doping,indicating a zero-field quantum phase transition in sharp antinodal quasiparticles seen below this notable proximity to the maximum superconducting T.Surprisingly,this major reorganization of the doping,all the way down to p=0.08(7,9.//) system's underlying electronic structure has no effect on the smoothly evolving pseudogap. Further,if the antinodal FS persists down to p 0.08.what impact does the OPT associated with uperconductivity is one of several phenome- insulator transition (5)or the formation of density- the onset of the PG at p=0.19 have on the FS? na,including the pseudogap,that arises wave order(6).However,the large-to-small FS To address these outstanding questions,we from interactions of electrons near the transition presumed to occur at higher doping used scanning tunneling microscopy (STM) Fermi surface(FS)in hole-doped cuprates.The has thus far not been observed by QO within a to study (Bi,Pb)2(Sr,La)2CuO6+8 (Bi2201).In FS topology is therefore crucial to understanding single hole-doped material system.Furthermore, this hole-doped cuprate,the absence of bilayer these phenomena and their relationships.High- it is unclear whether the small FS is merely re- splitting and the suppression of the supermodu- field quantum oscillation (QO)measurements (1-3)revealed an unexpectedly small FS in un- derdoped YBa2Cu3O6.s(YBCO),in contrast to B the conventional,large FS of overdoped cuprates 250 SC.PG ① 3.0 OD15K like Tl2Ba2CuO(4).Further high-field inves- tigations led to the discovery of a quantum phase 200 2.5 OPT35K transition (OPT)at the low doping edge of this small FS regime,perhaps associated with a metal- 150- 2.0 UD32K- PG 1.5 100 Department of Physics,Harvard University,Cambridge,MA 1.0 02138,USA.Department of Physics,Massachusetts Institute AFM Hall anomaly of Technology (MIT),Cambridge,MA02139,USA.Department 50 UD25K- of Crystalline Materials Science,Nagoya University,Nagoya 0.5 464-8603,Japan.Department of Physics,Northeastern Uni versity,Boston,MA 02115,USA. 0.10 0.15 0.20 -10050 0 50100 *Present address:Department of Physics,Zhejiang University. 0.05 Hangzhou,China Estimated p Sample Bias(mV) tPresent address:Department of Physics,Clark University, Fig.1.Phase diagram and spectra.(A)Schematic temperature-doping phase diagram of Bi2201, Worcester,MA 01610,USA. Present address:Department of Physics,Boston College, showing antiferromagnetic insulator (AFM),superconductor (SC),and PG phases.Four black points Chestnut Hill.MA 02467,USA. represent the sample batches of this study,namely underdoped UD25K and UD32K,optimal OPT35K,and SPresent address:Institute for Solid State Physics,Univer- overdoped OD15K.The PG transition line T*is plotted as measured by ARPES (12),resistivity (12)and sity of Tokyo,Tokyo,Japan. nuclear magnetic resonance (13).Anomaly in the Hall coefficient(28)is marked by a black arrow.(B) Present address:Department of Physics,Pennsylvania The spatially averaged differential conductance g(E)for each sample.The PG edge is marked with State University,University Park,PA 16802,USA. Corresponding author.E-mail:jhoffman@physics.harvard. black arrows,whereas the low-energy kink in each spectrum,considered to be related to the super- edu (J.E.H.);ehudson@psu.edu (E.W.H.) conducting gap (14,15),is marked with red arrows.a.u.,arbitrary units. 608 9 MAY 2014 VOL 344 SCIENCE www.sciencemag.org26. M. Aoki, Toward a Comparative Institutional Analysis (MIT Press, Cambridge, MA, 2001). 27. Food and Agricultural Organization (FAO)/International Institute for Applied Systems Analysis (IIASA), Global Agro-ecological Zones (GAEZ v3.0) (2010). Acknowledgments: We thank Z. Xia, N. Qingyun, Y. Wu, Y. Wang, Y. Ma, and A Jiao for collecting data; A. Leung and C. Wang for making the loyalty/nepotism task available; L. Jun Ji for the Chinese version of the triad task; M. Hunter for statistical guidance; and J. P. Seder, A. Putnam, Y. Wang, T. Wilson, and E. Gilbert for comments on earlier versions of this paper. The data are available at the Inter-University Consortium for Political and Social Research (ICPSR no. 35027) or by request to the first author. This research was supported by a Fulbright Scholarship, a NSF Graduate Research Fellowship, and a NSF East Asian and Pacific Summer Institute Fellowship. The Beijing Key Lab of Applied Experimental Psychology supplied laboratory space for the study. Supplementary Materials www.sciencemag.org/content/344/6184/603/suppl/DC1 Materials and Methods Figs. S1 and S2 Tables S1 to S12 References (28–49) 4 October 2013; accepted 25 March 2014 10.1126/science.1246850 REPORTS Fermi Surface and Pseudogap Evolution in a Cuprate Superconductor Yang He,1 Yi Yin,1 * M. Zech,1 Anjan Soumyanarayanan,1 Michael M. Yee,1 Tess Williams,1 M. C. Boyer,2 † Kamalesh Chatterjee,2 W. D. Wise,2 I. Zeljkovic,1 ‡ Takeshi Kondo,3 § T. Takeuchi,3 H. Ikuta,3 Peter Mistark,4 Robert S. Markiewicz,4 Arun Bansil,4 Subir Sachdev,1 E. W. Hudson,2 ‖¶ J. E. Hoffman1 ¶ The unclear relationship between cuprate superconductivity and the pseudogap state remains an impediment to understanding the high transition temperature (Tc) superconducting mechanism. Here, we used magnetic field–dependent scanning tunneling microscopy to provide phase-sensitive proof that d-wave superconductivity coexists with the pseudogap on the antinodal Fermi surface of an overdoped cuprate. Furthermore, by tracking the hole-doping (p) dependence of the quasi-particle interference pattern within a single bismuth-based cuprate family, we observed a Fermi surface reconstruction slightly below optimal doping, indicating a zero-field quantum phase transition in notable proximity to the maximum superconducting Tc. Surprisingly, this major reorganization of the system’s underlying electronic structure has no effect on the smoothly evolving pseudogap. Superconductivity is one of several phenome￾na, including the pseudogap, that arises from interactions of electrons near the Fermi surface (FS) in hole-doped cuprates. The FS topology is therefore crucial to understanding these phenomena and their relationships. High￾field quantum oscillation (QO) measurements (1–3) revealed an unexpectedly small FS in un￾derdoped YBa2Cu3O6.5 (YBCO), in contrast to the conventional, large FS of overdoped cuprates like Tl2Ba2CuO6+x (4). Further high-field inves￾tigations led to the discovery of a quantum phase transition (QPT) at the low doping edge of this small FS regime, perhaps associated with a metal￾insulator transition (5) or the formation of density￾wave order (6). However, the large-to-small FS transition presumed to occur at higher doping has thus far not been observed by QO within a single hole-doped material system. Furthermore, it is unclear whether the small FS is merely re￾vealed by QO or possibly created by their neces￾sarily high magnetic fields. A zero-field alternative to QO, angle-resolved photoemission spectroscopy (ARPES), has a long history of mapping the FS in Bi2Sr2CaCu2O8+x (Bi2212) (2, 7–11). Here, the onset of the pseu￾dogap (PG) is defined by the opening of an antinodal gap and the reduction of the large FS to a “Fermi arc,” which may actually be one side of a Fermi pocket, consistent with QO results (10). The PG onset may be associated with a QPT just above optimal doping at p = 0.19 (11). A second QPT to another competing phase is suggested to occur (11) at lower doping ( p = 0.076), similar perhaps to that found by QO (5, 6). However, if the transition near optimal doping is a FS recon￾struction to pockets, as suggested in (10), why are sharp antinodal quasiparticles seen below this doping, all the way down to p = 0.08 (7, 9, 11)? Further, if the antinodal FS persists down to p = 0.08, what impact does the QPT associated with the onset of the PG at p = 0.19 have on the FS? To address these outstanding questions, we used scanning tunneling microscopy (STM) to study (Bi,Pb)2(Sr,La)2CuO6+d (Bi2201). In this hole-doped cuprate, the absence of bilayer splitting and the suppression of the supermodu- 1 Department of Physics, Harvard University, Cambridge, MA 02138, USA. 2 Department of Physics, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA. 3 Department of Crystalline Materials Science, Nagoya University, Nagoya 464-8603, Japan. 4 Department of Physics, Northeastern Uni￾versity, Boston, MA 02115, USA. *Present address: Department of Physics, Zhejiang University, Hangzhou, China. †Present address: Department of Physics, Clark University, Worcester, MA 01610, USA. ‡Present address: Department of Physics, Boston College, Chestnut Hill, MA 02467, USA. §Present address: Institute for Solid State Physics, Univer￾sity of Tokyo, Tokyo, Japan. ‖Present address: Department of Physics, Pennsylvania State University, University Park, PA 16802, USA. ¶Corresponding author. E-mail: jhoffman@physics.harvard. edu (J.E.H.); ehudson@psu.edu (E.W.H.) Fig. 1. Phase diagram and spectra. (A) Schematic temperature-doping phase diagram of Bi2201, showing antiferromagnetic insulator (AFM), superconductor (SC), and PG phases. Four black points represent the sample batches of this study, namely underdoped UD25K and UD32K, optimal OPT35K, and overdoped OD15K. The PG transition line T* is plotted as measured by ARPES (12), resistivity (12) and nuclear magnetic resonance (13). Anomaly in the Hall coefficient (28) is marked by a black arrow. (B) The spatially averaged differential conductance g(E) for each sample. The PG edge is marked with black arrows, whereas the low-energy kink in each spectrum, considered to be related to the super￾conducting gap (14, 15), is marked with red arrows. a.u., arbitrary units. 608 9 MAY 2014 VOL 344 SCIENCE www.sciencemag.org