We report the observation of a change in Fermi surface topology of
Bi2Sr2CaCu2O8 with doping. By collecting high statistics ARPES data from
moderately and highly overdoped samples and dividing the data by the Fermi
function, we answer a long standing question about the Fermi surface shape of
Bi2Sr2CaCu2O8 close to the (pi,0) point. For moderately overdoped samples
(Tc=80K) we find that both the bonding and antibonding sheets of the Fermi
surface are hole-like. However for a doping level corresponding to Tc=55K we
find that the antibonding sheet becomes electron-like. This change does not
directly affect the critical temperature and therefore the superconductivity.
However, since similar observations of the change of the topology of the Fermi
surface were observed in LSCO and Bi2Sr2Cu2O6, it appears to be a generic
feature of hole-doped superconductors. Because of bilayer splitting, though,
this doping value is considerably lower than that for the single layer
materials, which again argues that it is unrelated to Tc

A. Kaminski

H. M. Fretwell

H. Raffy

J-M. Park

J. C. Campuzano

M. R. Norman

M. Randeria

S. Rosenkranz

T. Kondo

Z. Konstantinovic

Z. Z. Li

Physical Review B

English

arXiv

We report the observation of a change in Fermi-surface topology of Bi_2Sr_2CaCu_2O_8+δ with doping. By collecting high-statistics angle-resolved photoemission spectroscopy data from moderately and highly overdoped samples and dividing the data by the Fermi function, we answer a long-standing question about the Fermi-surface shape of Bi_2Sr_2CaCu_2O_8+δ close to the (π,0) point. For moderately overdoped samples (T_c=80 K) we find that both the bonding and antibonding sheets of the Fermi surface are hole like, but for a doping level corresponding to T_c=55 K we find that the antibonding sheet becomes electron like. Similar observations of a topology change were observed in La_2−xSr_xCuO_4 and in Bi_2Sr_2CuO_6+δ. On the other hand, whereas this critical doping value in single-layer materials corresponds to a T_c near zero, it occurs at a smaller doping value in the double-layer case where T_c is still quite high (the difference in doping levels is due to the bilayer splitting). This argues against a van Hove singularity scenario for cuprate superconductivity

Kaminski, A.

Rosenkranz, S.

Fretwell, H. M.

Norman, M. R.

Randeria, M.

Campuzano, J. C.

Park, J-M.

Li, Z. Z.

Raffy, H.

KnowledgeBank at OSU

PHYSICAL REVIEW B 73, 174511 2006Change of Fermi-surface topology in Bi2Sr2CaCu2O8+ with dopingA. Kaminski,1 S. Rosenkranz,2 H. M. Fretwell,1 M. R. Norman,2 M. Randeria,3 J. C. Campuzano,2,4 J-M. Park,1 Z. Z. Li,5and H. Raffy51Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA2Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA3Department of Physics, Ohio State University, Columbus, Ohio 43210, USA4Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, USA5Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, FranceReceived 1 December 2005; published 12 May 2006We report the observation of a change in Fermi-surface topology of Bi2Sr2CaCu2O8+ with doping. Bycollecting high-statistics angle-resolved photoemission spectroscopy data from moderately and highly over-doped samples and dividing the data by the Fermi function, we answer a long-standing question about theFermi-surface shape of Bi2Sr2CaCu2O8+ close to the  ,0 point. For moderately overdoped samples Tc=80 K we find that both the bonding and antibonding sheets of the Fermi surface are hole like, but for adoping level corresponding to Tc=55 K we find that the antibonding sheet becomes electron like. Similarobservations of a topology change were observed in La2−xSrxCuO4 and in Bi2Sr2CuO6+. On the other hand,whereas this critical doping value in single-layer materials corresponds to a Tc near zero, it occurs at a smallerdoping value in the double-layer case where Tc is still quite high the difference in doping levels is due to thebilayer splitting. This argues against a van Hove singularity scenario for cuprate superconductivity.DOI: 10.1103/PhysRevB.73.174511 PACS numbers: 74.25.Jb, 74.72.Hs, 79.60.BmThe Fermi surface is a fundamental property incondensed-matter physics. In recent years there has been alively debate about the shape of the Fermi surface of one ofthe most frequently studied high-temperature superconduct-ors: Bi2Sr2CaCu2O8+.1,2 Initially, the Fermi surface of thiscompound was determined by angle-resolved photoemissionspectroscopy ARPES to be hole like and consistent withLuttinger’s theorem.3 Later there were reports of an electronlike Fermi surface when measurements were performed athigher photon energies.4,5 High-momentum-resolution stud-ies utilizing new-generation electron analyzers reestablishedthe hole like shape of the Fermi surface for optimaldoping.6,7 The observation of bilayer splitting in the over-doped regime8 provided further evidence that at least thebonding sheet of the Fermi surface is hole like for a widerange of dopings. However, this study did not address thequestion of the shape of the antibonding sheet of the Fermisurface. For a long time, the answer to this question re-mained elusive, as the antibonding band near  ,0 is lo-cated very close to the chemical potential. It is important todetermine the exact shape of the whole Fermi surface, as itpotentially affects transport and collective properties.Knowledge of the band dispersion in this region of the Bril-louin zone is also of importance for theoretical studies ofself-energy effects in ARPES and tunneling, modeling of op-tical conductivity, and calculations of the dynamic magneticresponse. In a broader scope, it was previously shown that achange in the topology of the Fermi surface occurs in over-doped La2−xSrxCuO4 LSCO Refs. 9 and 10 and heavilyoverdoped single-layer Bi2Sr2CuO6+ Ref. 11; therefore,this phenomenon should be a generic property of hole-dopedcuprates. Here, we present high-resolution ARPES data mea-sured to a high degree of statistical accuracy in order todetermine the evolution of the Fermi surface with doping.We find that for moderately doped samples, both sheets ofthe Fermi surface are hole like, while at higher doping levelsthe antibonding band becomes electron like. This change is1098-0121/2006/7317/1745114 174511not accompanied by any abrupt change in the critical tem-perature at this particular value of doping. The lack of cor-relation of the topology change with Tc argues against a vanHove singularity scenario for cuprate superconductivity.The overdoped thin-film samples were grown using amagnetron sputtering technique on a SrTiO3 substrate.12They were mounted with -M parallel to the photon polar-ization and cleaved in situ at pressures of less than 210−11 Torr. Measurements were carried out at the Synchro-tron Radiation Center in Madison, Wisconsin, on the U1 un-dulator beamline supplying 1012 photons/sec, using a Sci-enta SES 50 electron analyzer with an energy resolution of20 meV and momentum resolution of 0.01 Å−1 for a photonenergy of 22 eV. The value of the chemical potential wasdetermined by measuring the Fermi edge of a gold filmevaporated onto silicon in electrical and thermal contact withthe sample. This value was stable to within 0.5 meV as veri-fied by periodic measurements of the gold reference through-out the experiment.One of the limitations of the ARPES technique is the factthat it only measures the occupied part of the spectrum. TheFermi cutoff makes it difficult to directly analyze the dataclose to the chemical potential. To combat these limitations,we have exploited a method of gaining information about thestates close to and above the chemical potential, which relieson dividing the ARPES data by the resolution-broadenedFermi function.13–15 This function is easily obtained by fit-ting the gold reference spectra with a Fermi function. Werenormalize the fitted Fermi function, so that its maximumamplitude is equal to 1, and then divide by it the ARPESspectra for the sample. The result very well approximates thespectral function Ak , modulo matrix elements which arealmost constant within a small range of momenta. The ef-fectiveness of this method depends on two conditions: thesample temperature and the statistics of the data. Working athigh temperature increases the spectral weight above thechemical potential and thus allows us to extract the data©2006 The American Physical Society-1KAMINSKI et al. PHYSICAL REVIEW B 73, 174511 2006there with less noise. For low temperatures, data of highstatistics are required, as the noise at energies above thechemical potential is rapidly amplified since the data are di-vided by the small values of the Fermi function. Given thehigh statistics of our data, we can reliably extract the spectralfunction for samples at T=100 K up to energies of50 meV above the chemical potential. Stability of thechemical potential is essential for successful application ofthis method. This was monitored frequently during the ex-periment, and the typical variation of its value was verysmall, of the order of 0.5 meV. We note that this is the domi-nant contribution to the error in our results; the errors arisingfrom peak fitting procedures are smaller for peaks near thechemical potential. We also note that the accuracy of fittingthe peak position depends crucially on the statistics and itsfunctional form and much less on the width of the peak.Another experimental consideration is the contribution to themeasured electron intensity from the second-order light,which is always present in synchrotron beamlines. In thecase of our beamline this contribution is very small 2% .We determine this contribution by looking at the averageintensity far above the chemical potential and then subtract-ing it from the data before performing the division operation.We illustrate the division by the Fermi function in Fig. 1.In panel a the raw ARPES data measured in the form ofenergy distribution curves EDC’s for a cut parallel to the ,−- , direction are shown, and in panel b the re-sult of the division of the Fermi function is plotted. In theraw data there are two clearly visible features: i dispersingpeaks corresponding to the bonding band and ii “nondis-persive” peaks near the chemical potential corresponding tothe antibonding band. As stated above, it is difficult to deter-mine the band position and dispersion of the antibondingband from such data. In contrast, it is quite easy to do sowhen the data are divided by the Fermi function, as shown inpanel b. Here the dispersion of both the bonding and anti-bonding bands is clearly visible at, and even above, thechemical potential. Such an approach allows us to determinethe precise location of the bottom of both bands even in closeproximity to the chemical potential. We next examine theaccuracy of the above method. To do this we present asample spectral function shown as a blue solid line in panelc of Fig. 1. We then multiply it by the Fermi function,convolve with a Gaussian to emulate the energy resolution-broadening, and then divide the result by the resolution-broadened Fermi function. The reconstructed spectral func-tion dashed red curve compares quite well to the originalspectral function. We then extract the peak dispersion fromboth curves and compare the results in panel d of Fig. 1.Both dispersions are in very good agreement—in the regionof the chemical potential, the differences are within experi-mental error bars of 0.5 meV.First, we examine the case of a moderately overdopedsample Tc=80 K. In Fig. 2 we plot the ARPES data dividedby the Fermi function for a cut parallel to the  ,−- ,direction. The first panel shows the divided EDC curves inthe proximity of the  ,0 point, while in panel b, we showthe peak dispersions for both bonding and antibonding bandsextracted from the EDC data by fitting them with a sum of174511two Lorentzians. The deviations from the parabolic disper-sion originate from the fact that the Lorentzian fitting proce-dure is less accurate for the bonding peak once it is far belowthe chemical potential and thus very broad. This does notaffect our conclusions, since we are interested in the energyposition of the bottom of the antibonding band, where thisfitting procedure works very well. We note that the bottomsof both bands along this direction lie below the chemicalpotential, which means that for this doping value both sheetsof the Fermi surface remain hole like. To quantify this weplot in panel c the EDC’s at the  ,0 and 0.9 ,0 pointsand fit them using a combination of two Lorentzian func-tions, corresponding to the bonding and antibonding peaks.The  ,0 point is at −7 meV and −102 meV for the anti-bonding and bonding bands respectively.Next, we turn to the most heavily overdoped sample Tc=55 K that we could obtain. The data for this sample areshown in Fig. 3. In panels a and b we show the EDC’sand extracted peak dispersion along the 0.9 ,−0.3-FIG. 1. Color online Illustration of the division by the Fermifunction method at T=100 K for an overdoped sample Tc=55 Kalong the cut 0.8 ,−0.3-0.8 ,0.3. a Raw ARPES data. bData from a divided by the resolution-broadened Fermi function.c Effect of resolution broadening on extraction of the spectralfunction peaks: solid blue line is a model spectral function, reddashed line is the same spectral function after multiplying by theFermi function, convolution with the experimental energy resolu-tion function, and division by the resolution-broadened Fermi func-tion. d Dispersion obtained from the peak positions of panel c.0.9 ,0.3 cut. As in the previous case, these data show-2CHANGE OF FERMI-SURFACE TOPOLOGY IN¼ PHYSICAL REVIEW B 73, 174511 2006that the bottoms of both bands lie below the chemical poten-tial. However, the data obtained along the Brillouin zoneboundary i.e., along the  ,−0.3- ,0.3 cut, shown inpanels c and d, are different. Here, the bottom of theantibonding band is located slightly above the chemical po-tential. To check the exact location of the antibonding bandwe plot the EDC curves at  ,0 and 0.9 ,0 in panel e.Each EDC is fit with the sum of two Lorentzian functions toprecisely determine the energy locations of the peaks. Whilethe antibonding peak at 0.9 ,0 is located at 2.5 meV be-low the chemical potential consistent with the conclusionsfrom data in panels a and b, the same peak at  ,0 liesat 2 meV above the chemical potential. This is clear evi-dence that the antibonding Fermi surface closes before reach-ing the zone boundary and therefore becomes electron like.The Fermi crossing along 0,0- ,0 occurs close to0.95 ,0based on linear interpolation.The extraction of the Fermi-surface contours from thedata using the standard method of plotting the intensitywithin a small energy range about the chemical potentialover the whole Brillouin zone is quite difficult in this case.The main reasons for this are the presence of a background16and the relatively wide EDC peaks in the normal state com-bined with the close proximity to the chemical potential ofthe antibonding band at  ,0. To better illustrate the topolo-FIG. 2. Color online Data along the  ,− to  , directionfor a moderately overdoped sample of Tc=80 K at T=100 K. aEDC data divided by the Fermi function. b Dispersion extractedfrom a two-Lorentzian fit to the EDC’s. c EDC at  ,0 and0.9 ,0 divided by the Fermi function red circles and trianglesand a two-Lorentzian fit blue lines. EAB and EBB are the positionsof the antibonding and bonding peaks. Inset: magnified region closeto the chemical potential.gies, in Fig. 4 we plot Fermi surfaces resulting from tight-174511binding fits to the band dispersion extracted from the data.Panel a shows the Fermi surface contour for the moderatelyoverdoped sample of Tc=80 K. For this and lower dopinglevels, both sheets of the Fermi surface are hole like, asshown by previous studies. In the case of the heavily over-doped sample Tc=55 K, the bonding sheet of the Fermisurface remains hole like, but the antibonding Fermi surfacebecomes electron like and closes before it reaches the edgeof the Brillouin zone, as illustrated in panel b.The finding that the Fermi-surface topology changes be-low the level of doping corresponding to Tc=55 K has sev-eral important consequences. As the change of topology oc-curs in samples where Tc is still significantly high and is notassociated with a rapid change of Tc, our results are not insupport of those models of superconductivity which dependon the presence of a van Hove singularity. The relation of ourfinding to the question of quantum critical points in the phasediagram is a more subtle one. Anomalies in specific-heatFIG. 3. Color online Data parallel to the  ,− to  ,direction for a heavily overdoped sample of Tc=55 K at T=100 K.a EDC data divided by the Fermi function along the 0.9 ,−0.3-0.9 ,0.3 cut. b Dispersion extracted from a two-Lorenzian fit to the EDC data shown in a. c EDC data divided bythe Fermi function for a  ,−0.3- ,0.3 cut. d Dispersionextracted from a two-Lorentzian fit to the EDC data shown in c.e EDC’s at  ,0 and 0.9 ,0 divided by the Fermi function redcircles and a two-Lorentzian fit blue lines. Inset: magnified re-gion close to the chemical potential.data, which have been interpreted as due to the pseudogap-3KAMINSKI et al. PHYSICAL REVIEW B 73, 174511 2006closing, occur at a doping value of 0.19 in this material,17considerably lower than the doping of approximately 0.225we find our topology change to occur at.18 On the other hand,our doping value does correspond to the one where collectiveeffects were found to disappear or at least significantlyweaken in the in-plane infrared conductivity.19 And it isclose to the value where c-axis transport indicates that Tc andthe pseudogap temperature T* merge.20 It is interesting tonote that in single-layer Bi2Sr2CuO6+, the topology change11FIG. 4. Color online Fermi surface resulting from a tight-binding fit to data through the Brillouin zone. a For moderatelyoverdoped samples with Tc=80 K. b For heavily overdopedsamples with Tc=55 K. c Phase diagram with marked topology ofthe antibonding band. Dashed lines indicate uncertainty in the de-termination of the carrier concentration for the crossover intopology.is near where Tc=0, and there is evidence from NMR that174511the pseudogap temperature merges with Tc at this doping aswell.21 As this is similar to our observation concerning thebilayer case, it implies that there may well be some connec-tion between the pseudogap and the topologychange of theFermi surface.One might also naively expect that a change of topologywould affect transport properties, especially the Hall effect.However, the dependence of the Hall effect on doping issmooth in this range of doping.12 This is not a surprise,though, since the Fermi velocity of the antibonding sheet isquite low in the  ,0 region of the Brillouin zone. In sup-port of this, tight-binding simulations we have made of theHall effect find a hole like behavior for dopings far in excessof where the topology change occurs. Nevertheless, the pres-ence of the van Hove singularity in the antibonding sheetvery close to the chemical potential could have consequencesfor those properties which are sensitive to the breaking ofparticle-hole symmetry.In summary, we report the observation of a change in theFermi-surface topology in the heavily overdoped regime ofBi2Sr2CaCu2O8+. In overdoped samples, at dopings slightlybelow those corresponding to Tc=55 K, the antibondingband changes from hole like to electron like. The bondingband remains hole like over the whole doping range. Thisfinding has potential consequences for theories of high-temperature superconductivity as well as the interpretation oftransport measurements in this doping range.ACKNOWLEDGMENTSWe acknowledge useful remarks by Joe Orenstein and An-drey Chubukov and the hospitality of the Aspen Center forPhysics, where parts of this work were discussed and writtenup. This work was supported by NSF Grant No. DMR9974401 and the U.S. DOE, Office of Science, under Con-tract No. W-31-109-ENG-38. The Ames Laboratory is oper-ated for the U.S. DOE by Iowa State University under Con-tract No. W-7405-ENG-82. The Synchrotron RadiationCenter is supported by NSF Grant No. DMR 9212658.1 A. Damascelli et al., Rev. Mod. Phys. 75, 473 2003.2 J. C. Campuzano et al., in The Physics of Superconductors, editedby K. H. Bennemann and J. B. Ketterson Springer, Berlin,2004, Vol. 2, p. 167.3 H. Ding et al., Phys. Rev. Lett. 76, 1533 1996.4 D. L. Feng et al., cond-mat/9908056 unpublished.5 Y.-D. Chuang et al., Phys. Rev. Lett. 83, 3717 1999.6 H. M. Fretwell et al., Phys. Rev. Lett. 84, 4449 2000.7 S. V. Borisenko et al., Phys. Rev. Lett. 84, 4453 2000.8 D. L. Feng et al., Phys. Rev. Lett. 86, 5550 2001.9 A. Fujimori et al., J. Phys. Chem. Solids 59, 1892 1998.10 A. Ino et al., J. Phys. Soc. Jpn. 68, 1496 1999; A. Ino et al.,Phys. Rev. B 65, 094504 2002.11 T. Kondo et al., J. Electron Spectrosc. Relat. Phenom. 137-140,663 2004.12 Z. Konstantinovic et al., Phys. Rev. B 62, R11989 2002.13 T. Greber et al., Phys. Rev. Lett. 79, 4465 1997.14 T. Sato et al., Phys. Rev. B 64, 054502 2001.15 A. Kaminski et al., Phys. Rev. Lett. 90, 207003 2003.16 A. Kaminski et al., Phys. Rev. B 69, 212509 2004.17 J. L. Tallon and J. W. Loram, Physica C 349, 53 2001.18 We estimated the doping level for our two samples from the “uni-versal” Tc curve. See M. R. Presland et al., Physica C 176, 951991. We then used the position of the bottom of the antibond-ing band for these two samples to interpolate to the doping levelwhere the topology change occurs.19 J. Hwang et al., Nature London 427, 714 2004.20 T. Shibauchi et al., Phys. Rev. Lett. 86, 5763 2001.21 G.-q. Zheng et al., Phys. Rev. Lett. 94, 047006 2005.-4

Change of Fermi-surface topology in Bi_2Sr_2CaCu_2O_8+δ with doping

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Change of Fermi-surface topology in
                    
                      
                        
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The change of Fermi surface topology in Bi2Sr2CaCu2O8 with doping

The change of Fermi surface topology in Bi2Sr2CaCu2O8 with doping

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