17

Highlights 2001

The nature of the low energy electronicexcitations near the (π,0) region of k-space is of vital relevance to a number ofkey physical properties of the cupratesuperconductors, as it is here that thesuperconducting order parameter has itsmaximal magnitude and where manybelieve that the coupling which causessuperconductivity makes itself moststrongly felt. Unfortunately, this region ofk-space does not willingly reveal itssecrets and the true situation is veiled bythe effects of, for example, the couplingbetween the different CuO2 planes in mul-tilayer HTSC. As ARPES is a very direct,k-resolved probe of the electronic

system, the low energy photoemissionspectra from the (π,0)-point of the Brillou-in zone (BZ) of the HTSC, and in particu-lar of Bi2Sr2CaCu2O8 in the superconduc-ting state have been the focus of uncea-sing experimental and theoretical interestover the last years. Of particular interesthas been the now famous peak-dip-hump(PDH) lineshape seen at (π,0) in thesuperconducting state [1]. This lineshapewas, up to the present, widely believed tobe the result of a single spectral function(see for instance Refs. 2-4), and is cau-sed by a strong coupling to bosons (e.g.phonons or spin fluctuations) [4,5]. Thedetails of the peak-dip-hump line-shape

Sergey Borisenko,Alexander Kordyuk,Timur Kim, Konstantin Nenkov,Martin Knupfer, Mark S. Golden,Jörg Fink

Fig.1.Left panel: inside theUHV chamber: theIFW cryo-manipula-tor (top left) and theSES-100 lenssystem (right).Right panel: theIFW-DresdenARPES endstationmounted on theU125/1 PGM beamli-ne at BESSY GmbH.

Origin of the peak-dip-hump structure in the photoemission spectra of Bi2Sr2CaCu2O8

The scientific and technological significance of high temperature superconduc-tivity (HTSC) has made cuprates perhaps the most studied objects in the historyof condensed matter physics. Unlike their conventional counterparts for whichthe theory is well developed, the cuprate superconductors still guard their secretdespite extensive efforts undertaken by the scientific community during the last15 years. The central question is: what helps the electrons to co-operate at lowtemperatures to carry the superconducting current? It is known that in the caseof simple metals formation of electron pairs is driven by the coupling betweenelectrons and phonons. In the high Tc cuprates, the nature of the force driving thepairing is of yet unknown or controversial origin. A wealth of information relatedto this issue has been provided by angle-resolved photoemission spectroscopy(ARPES), which has emerged as a leading technique as far as the experimentaldetermination of the single particle excitations in solids are concerned. The com-plex, peak-dip-hump-like lineshape observed in certain photoemission spectra ofthe two-layer BSCCO compounds was interpreted as being a result of the stronginteraction with bosons thus marking out those electrons (i.e. their momenta andenergies) which actively participate in such coupling. Here we show that thelineshape of these spectra can be easily understood in terms of superposition ofspectral features originating from the bi-layer split Cu-O band. This implies thatthe strength of coupling of electrons with momenta near to the (π,0) region of k-space to other degrees of freedom is significantly less than was previouslythought, thus meaning that models for superconductivity based on the previousinterpretation of the peak-dip-hump spectra at (π,0) should be reconsidered.

18

Highlights 2001

are expected to reveal, at a fundamentallevel, the identity of the interactions invol-ved in the generation and perpetuation ofthe superconducting state in thesesystems [5-7]. It is safe to say that theline-shape of the photoemission spec-trum at this point in k-space and its inter-pretation is undoubtedly one of the outs-tanding features in the high Tc canon.We report the results of a detailed, highresolution ARPES study of this importantBZ region in overdoped, modulation-freePb-Bi2212 crystals using a wide range ofexcitation energies. The central result isthat the strongly differing photon energydependence of the intensity of the ‘peak’and ‘hump’ in the (π,0) spectrum essenti-ally exclude a scenario in which the peak,dip and hump features originate from asingle-band spectral function. The datasupport a paradigm change in our inter-pretation of the PDH line-shape, andargue for a straightforward picture inwhich - at least for the overdoped compo-unds - the ‘superconducting’ peak is rela-ted to the antibonding CuO-bilayer bandand the hump is mainly formed by thebonding band.The ARPES experiments were carriedout using angle-multiplexing photoemissi-on spectrometers (SCIENTA SES200 andSES100) coupled to high precision cryo-manipulators which allow the rotation ofthe sample around three perpendicularaxes. Both manipulators are designedand constructed in the IFW, and areessential and unique components of ourARPES apparatus (see Fig.1, left panel).The momentum distribution maps andseries of energy distribution curves(MDMs and EDCs) were measured at300K or 39K using hν = 21.218 eV pho-tons from a He source (for details seeRefs. [8-10]). The (π,0) EDCs were recor-ded using radiation from the U125/1-PGM beamline [11] at BESSY (Fig.1,right panel). The total energy resolutionranged from 8 meV (FWHM) at hν = 17-25 eV to 22.5 meV at hν = 65 eV, asdetermined for each excitation energyfrom the Fermi edge of polycrystallinegold (which also gives the calibration ofthe energy scale in each case). Theangular resolution was less than 0.1°. Alldata were collected on overdoped (OD,Tc = 69K) and underdoped (UD, Tc = 71K)single crystals of Pb-Bi2212, except forthe Fermi surface map taken from pure

Bi2212 (Tc = 89K). All (π,0)-EDCs weremeasured at a temperature of 27K –deep in the superconducting state.We start by presenting what are com-monly referred to as Fermi surface mapsof pristine and Pb-doped Bi2212 in Fig. 2.It is well known that in the case of pureBi2212 these intensity maps contain anadditional set of features originating fromthe scattering of the outgoing photoelec-

trons on the incommensurably modulatedBiO-layers [8,12]. Such diffraction repli-cas are extrinsic in nature and can beeasily identified given MDMs which covera sufficiently large portion of the k-space.With the aid of Fig. 2, it is also easy toestimate to what extent the line-shape ofa given EDC may be contaminated bythese extrinsic replicas (see, for example,the white dashed lines in Fig. 2).Obviously, the most perilous region forexamination would be one in which a highdensity of different features overlap or areclosely separated, such as the (π,0)-pointof Bi2212.The use of the modulation-free sampleshad allowed us to clarify the FS topology[8] and show that contradictions in thispoint could be explained by the presenceof the diffraction replicas and by thestrong influence of excitation energydependent matrix elements on the pho-toemission spectra from around the (π,0)region [9,13]. On the other hand, by ana-lyzing changes in the line-shape upon aconscious variation of experimental para-meters which are linked to the matrix ele-ments, one can gain insight into the natu-re of a given feature. For instance, theobservation that the (π,0) PDH lineshapeturned out to be insensitive to an alterati-on of the polarization conditions at a fixedphoton energy [2], has been one of thecornerstones of many of the single-bandtheories developed to explain the PDH

Fig.2. Fermi surface mapsof pure Bi2212 (leftpanel) and OD Pb-Bi2212 (rightpanel) measured atroom temperature.

19

Highlights 2001

lineshape in the superconducting state. Inthe last year [10], we utilize a possibilityto significantly alter the photoemissionmatrix elements by variation of the exci-tation energy. In this context it is inte-resting to note that the PDH spectrareported in all intensively referencedpublications over the last ten years havebeen recorded from pristine Bi2212 usingonly a very narrow range of photon ener-gies (19-22.4 eV) [1-4,6,14].Fig. 3 shows a collection of superconduc-ting state (π,0) photoemission spectra foroverdoped (left panel) and underdoped(right panel) Pb-Bi2212 recorded usingdifferent excitation energies hν (18-65eV). Upon a visual inspection of these rawexperimental data, it is evident that thePDH lineshape can no longer be conside-red to be the result of single band spectralfunction with a sophisticated self-energy.Let us examine the left panel, for exam-ple: at some excitation energies (e.g. 20eV) all three components (peak, dip andhump) are present; there are also photonenergies at which there is virtually no dip(25 or 42 eV), no hump (50 eV) or even nopeak (39 eV). A further firm conclusionwhich can be made from inspection ofthese data is that the hump and the dipthemselves cannot be considered as fea-tures appearing with fixed binding ener-gies for all hν (e.g., compare the EDCs for20 and 37 eV in the left panel). For further analysis of the data we carriedout a fitting procedure. We were able toshow that whilst there is no chance todescribe the PDH spectra at different pho-ton energies with a sophisticated single-band spectral function, they can be fitted

well - at least in the overdoped case - bya superposition of two one-particle spec-tral functions A ∝ Σ “/((ω -ε)2 + Σ“2) origina-ting from two bands at different bindingenergies, ε = ε a and ε b, but with the sameself-energy, the imaginary part of which,Σ“(ω,T) = √((αω)2 + (βT)2) , appeared to belinear in ω at higher binding energies (see[15] for details). The values that havebeen obtained from such a fitting proce-dure are the following: ε a = 11(1) meV, ε b

= 154(4) meV, α = 1.1(1), β = 3(1) [16].The presence of a contribution from twobands in (π,0) spectra is quite understan-dable, bearing in mind the recently obser-ved bilayer splitting [17-19] in low tempe-rature, normal state ARPES data ofBi2212 (ε a and ε b then simply correspondto the antibonding and bonding Cu-Obands, respectively).To bring an additional point to the rea-der’s attention, we show in Fig. 4 a seriesof EDCs along the (0,0)-(π,0) direction.The fact that the ‘superconducting’ peakwas dispersionless along this directionrepresented the second cornerstone inthe PDH picture up to now [3]. Here thedata are recorded with hν = 21.2 eVabove and below Tc and clearly demon-strate the conventional dispersion of thebands forming the two features. It turnsout that the temperature, like the pola-rization or energy of the exciting radiationcan also be used to control the relativeintensities of the ‘b’ and ‘a’ components.At 300 K and hν = 21.2 eV the observedintensity from the antibonding, ‘a’ featureis extremely small. This is a consequenceof the relative values of spectral weight of‘a’ and ‘b’ features for this photon energyand the fact that the antibonding compo-nent lies very close to the Fermi level andis thus both much strongly influenced bytemperature through the self-energy andis drastically cut by the broad room tem-perature Fermi cut-off. In fact, the substi-tution of the relevant temperatures in ourmodel described above yields good agre-ement with the experimental spectra.Thus the amplitude of the bonding peakmainly determines the position of theroom temperature EDC maxima (which isfully consistent with the absence of aclearly resolved splitting in room tempe-rature MDMs shown in Fig. 2). In con-trast, the maxima of the low temperaturespectra probe the position of the antibon-ding band. It is clear from Fig. 4 that both

Fig. 3. The (π,0) photoemis-sion spectra from thesuperconductingstate of overdoped(left panel) andunderdoped (rightpanel) Pb-Bi2212samples for differentexcitation energies

20

Highlights 2001

the bonding and antibonding bilayerbands disperse in a similar manner aro-und the (π,0) point, re-enforcing the attri-bution of the spectral peak and hump toseparate electronic bands. Finally, we note that the strong photonenergy dependence of the (π,0)-photoe-mission lineshape is not restricted to theOD case: we have also observed a simi-lar pattern for the underdoped sample(see right panel of Fig. 3), but, due to thestrong influence of the gap on the UDspectra, it is not yet clear whether the‘peak’ and ‘hump’ in UD are of the sameorigin as for the OD case.

To sum up, in 2001 we have continuedour programme of highly resolvedARPES investigations of the high Tccuprate superconductors, carrying out adetailed investigation of the supercon-ducting state (π,0)-photoemission spectraof overdoped, modulation-free Pb-Bi2212single crystals. We demonstrate that thePDH lineshape is strongly dependent onthe excitation energy, which is practicallyirreconcilable with models in which thepeak, dip and hump are considered tostem from a single band spectral function.The lineshape of the spectra can bequantitatively reproduced by the superpo-sition of spectral features described byessentially identical single-particle spec-tral functions residing at different bindingenergies: the hump is mainly formed bythe bonding and the peak originates fromthe antibonding component of the bilayersplit Cu-O-derived bands. Models forsuperconductivity in cuprates based on a

single band PDH structure should bereconsidered.

CooperationInstitut de Physique Appliqu’ee, EPFL,Lausanne, Switzerland;BESSY GmbH

Funded byBMBF, DFG

References[1] D. S. Dessau et al., Phys. Rev. Lett.

66 2160 (1991)[2] H. Ding et al., Phys. Rev. Lett. 76

1533 (1996)[3] M. R. Norman et al., Phys. Rev. Lett.

79 3506 (1997)[4] J. C. Campuzano et al., Phys. Rev.

Lett. 83 3709 (1999)[5] A. Lanzara et al., Nature 412 510

(2001)[6] D. L. Feng et al., Science 289 277

(2000)[7] J. Orenstein and A. J. Millis, Science

288 468 (2000)[8] S. V. Borisenko et al., Phys. Rev. Lett.

84 4453 (2000)[9] S. V. Borisenko et al., Phys. Rev. B 64

094513 (2001)[10] A. A. Kordyuk et al., cond-

mat/0110379[11] R. Follath, Nucl. Instr. and Meth. A

467-468 418 (2001)[12] H. Fretwell et al., Phys. Rev. Lett. 84

4449 (2000)[13] S. Legner et al., Phys. Rev. B 62 154

(2000)[14] e.g. H. Ding et al., Phys. Rev. Lett.

78 2628 (1997); A. G. Loeser et al.,Phys. Rev. B 56 14185 (1997); A. V.Fedorov et al., Phys. Rev. Lett. 822179 (1999)

[15] A. A. Kordyuk et al., cond-mat/0104294

[16] The parameters α and β are similarto the value derived from a similaranalysis of the EDCs recorded alongthe nodal direction [9].

[17] D. L. Feng et al., Phys. Rev. Lett. 865550 (2001)

[18] Y.-D. Chuang et al., Phys. Rev. Lett.87 117002 (2001)

[19] P. V. Bogdanov et al., Phys. Rev. B64 180505 (2001)

Fig. 4. The series of EDCs,self-normalized totheir maxima, for kalong the (0,0)-(π,0)direction for T=300K(left panel) and 39K(right panel).