arX

iv:c

ond-

mat

/000

7283

v4 [

cond

-mat

.str

-el]

24

Aug

200

0

Angle resolved photoemission spectroscopy of Sr2CuO2Cl2 – a revisit

C. Durr, S. Legner, R. Hayn, S. V. Borisenko, Z. Hu, A. Theresiak, M. Knupfer, M. S. Golden, and J. FinkInstitute for Solid State and Materials Research Dresden, P.O. Box 270016, D-01171 Dresden, Germany

F. Ronning and Z.-X. ShenDepartment of Physics and Stanford Synchrotron Radiation Laboratory, Stanford University, Stanford, CA 94305-4045, USA

H. Eisaki and S. UchidaDepartment of Superconductivity, The University of Tokyo, Bunkyo-ku, Tokyo 113, Japan

C. Janowitz and R. MullerInstitut fur Physik der Humboldt-Universitat Berlin, Invalidenstrasse 110, 10115 Berlin, Germany

R. L. JohnsonII. Institut fur Experimentalphysik der Universitat Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany

K. Rossnagel and L. KippInstitut fur Experimentelle und Angewandte Physik, Christian-Albrechts-Universitat zu Kiel, Leibnizstrasse 19, 24118 Kiel,

Germany

G. ReichardtBESSY GmbH, Albert-Einstein-Str. 15, 12489 Berlin, Germany

We have investigated the lowest binding-energy electronic structure of the model cuprateSr2CuO2Cl2 using angle resolved photoemission spectroscopy (ARPES). Our data from about 80cleavages of Sr2CuO2Cl2 single crystals give a comprehensive, self-consistent picture of the natureof the first electron-removal state in this model undoped CuO2-plane cuprate. Firstly, we show astrong dependence on the polarization of the excitation light which is understandable in the contextof the matrix element governing the photoemission process, which gives a state with the symme-try of a Zhang-Rice singlet. Secondly, the strong, oscillatory dependence of the intensity of theZhang-Rice singlet on the exciting photon-energy is shown to be consistent with interference effectsconnected with the periodicity of the crystal structure in the crystallographic c-direction. Thirdly,we measured the dispersion of the first electron-removal states along Γ →(π,π) and Γ →(π, 0), thelatter being controversial in the literature, and have shown that the data are best fitted using anextended t-J-model, and extract the relevant model parameters. An analysis of the spectral weightof the first ionization states for different excitation energies within the approach used by Leung et

al. (Phys. Rev. B 56, 6320 (1997)) results in a strongly photon-energy dependent ratio between thecoherent and incoherent spectral weight. The possible reasons for this observation and its physicalimplications are discussed.

I. INTRODUCTION

Extensive effort continues to be expended to under-stand the electronic properties of the cuprate high Tc su-perconducting compounds. Apart from many differences,the cuprate superconducting materials have importantproperties in common. Namely they are all layered com-pounds possessing CuO2-planes, where the origin of thesuperconducting behavior is to be found. The electronicstructure of the states with the lowest binding energy issatisfactorily understandable only in models which takeinto account correlation effects. ARPES has proven tobe a powerful tool to investigate the low binding-energyelectronic structure of the cuprates. Important examplesfor the success of this method are the mapping of the

Fermi surface1 and the determination of an anisotropy ofthe superconducting gap consistent with a d-wave orderparameter2.

In the undoped regime the cuprates are two-dimensional antiferromagnetic insulators with CuO2-planes resulting in a correlation-gapped half-filledCu3dx2−y2-O2px/O2py antibonding band of lowestbinding-energy. Upon doping with holes, the states withlowest binding energy evolve towards the chemical poten-tial, and the cuprate becomes metallic or superconduct-ing. To clarify the main principles of the evolution ofthe lowest binding-energy states with doping by apply-ing model Hamiltonians, one has to go step by step fromsimple situations or limiting cases to more complicatedscenarios. A natural starting point, then, is to investi-

1

gate the propagation of a single hole in a CuO2-planeby studying the undoped parent compounds of cupratesuperconductors by photoemission, where one electron isremoved from the CuO2-plane. The states thus investi-gated can be termed the first electron-removal states.

A special class of parent compounds are the oxy-halides such as Sr2CuO2Cl2, Ca2CuO2Cl2, Sr2CuO2F2

(one layer compounds), and Ca3Cu2O4Cl2 (double lay-ered compound)3,4, all of which contain an apical halo-gen atom, rather than an oxygen. It is now well es-tablished that the apical oxygen which is contained inmost of the cuprate superconductors is not necessary forhigh Tc superconductivity as Hiroi et al. 5 showed thatCa2−xNaxCuO2Cl2 is superconducting (Tc = 26K). Outof the class of cuprate parent compounds without apicaloxygen, the layer compound Sr2CuO2Cl2 is remarkabledue to its extremely stable stoichiometry. Despite consid-erable efforts so far it has not been possible to dope thissubstance chemically. Furthermore, the CuO2-planes areunbuckled and the crystal structure shows neither or-thorhombic distortion nor a superstructure at least downto 10 K (Ref. 6). Therefore, Sr2CuO2Cl2 can be seen asthe best realization of a two-dimensional antiferromagnetat half-filling and it is in this limit an ideal test case forany Hamiltonian in the low-doping regime.

In theoretical studies, the lowest binding-energy ion-ization states of the cuprates were predicted to be es-sentially described by a singlet antibonding combinationof a Cu3dx2−y2 orbital (containing the intrinsic Cu3d9

hole) and a coherent combination of the four neighboringO2px/O2py orbitals which can be thought of as contain-ing the hole created in the photoemission process7,8. Thistwo-hole state is generally referred to as the Zhang-Ricesinglet state9. The singlet character of the first electron-removal states, at least in CuO, has been experimentallyverified using spin-resolved resonant photoemission10.

There are various possibilities to theoretically modelthe dynamics of this lowest binding-energy excitation.For instance, in the framework of a three-band Hub-bard Hamiltonian (H3b), the Zhang-Rice singlet stateis a two-particle state and belongs to the A1g (totallysymmetric) irreducible representation of the eigenstatesof H3b. In the one-band Hubbard Hamiltonian (H1b),the t-J-model and its extensions, the Zhang-Rice singletstate is an one-particle state belonging to the B1g irre-ducible representation and has the same symmetry asa Cu3dx2−y2 orbital. Figure 1 shows a schematic rep-resentation of a Zhang-Rice singlet state, including thetwo mirror planes M1 and M2 which are perpendicular tothe CuO2-plane and which are relevant for photoemissionalong along Γ →(π, π) and Γ →(π, 0), respectively.

It is now generally accepted that the H3b is a goodstarting point to describe the low binding-energy elec-tronic structure in the strongly correlated cuprate sys-tems and consequently the H3b has been investigatedin detail11. Additionally, it has been shown that theH1b still carries enough information to describe the low-energy dynamics in the cuprates12. In the next level of

simplifying these models, the Hubbard Hamiltonian canbe expressed in terms of new Fermionic operators. Inthe large-U -limit, this new Hamiltonian can be writtenin a t2/U series and gives an effective one-band Hamil-tonian, the t-J-model. This has been shown to give thesame results for both the H3b (Ref. 7) and the H1b (Ref.13) approaches. Extensions of the t-J-model have beencarried out mainly in two different ways. Firstly, twofurther parameters - t′ describing the diagonal hoppingand t′′ for the next nearest neighbor hopping - can beintroduced in addition to the direct hopping t.

The fact that a t-mediated hopping creates stringsof spin defects leads to a predicted bandwidth for theZhang-Rice singlet state which is governed by t2/U ∼ J .Hopping events mediated by t′ and t′′, however, takeplace on the same spin sub-lattice and therefore eventaking small values of these parameters has a signifi-cant effect on the results the t-J-model gives for thek-dependent spectral function of the Zhang-Rice singletstate. Secondly, the t-J-model has also been extended totake three-site hopping terms (proportional to J/4) intoaccount14, which appear in a natural way if one employsa more detailed derivation of an effective Hamiltonian forthe low binding-energy excitations15.

A different ansatz to understand the dynamics of holesin CuO2-planes was proposed by Laughlin16. He arguedthat the hole created by photoemission decays into spinand charge degrees of freedom and that the photoemis-sion experiment measures the dispersion of the spinon16.However, in a gauge-field treatment of this model thisdecay of the quasiparticles is suppressed below the Neel-temperature, TN , due to confinement17. Another funda-mental approach to calculate the properties of the Hub-bard Hamiltonian and the t-J-models uses the fact thatthey share an approximate SO(5) symmetry18.

The preceding discussion highlights the intense the-oretical interest in the lowest binding-energy electron-removal states of the undoped cuprates. Although orig-inally trailing a few years behind the theoretical work,experimental investigations of the first electron-removalstate in undoped cuprates have been carried out usingARPES19–23. Before going on to mention the status inthe field to date, we first ask the question: what kind ofinformation does an ARPES experiment provide us with?

Neglecting “extrinsic” effects such as scattering of thephotoelectrons on their way to the surface and assum-ing the applicability of the sudden approximation, thephotoemission intensity I(k, E), reads

I(k, E) ∼∑

|i〉,|f〉

| Mi,f |2 S(k, E) f(E) (1)

where the sum runs over all final states and initialstates, f(E) denotes the Fermi function and S(k, E) thespectral function:

S(k, E) = −1

πIm 〈i | ck

1

E − H + Ei

c†k| i〉 . (2)

2

Mi,f = 〈f | A · p | i〉 is the matrix element to betaken between the initial state | i〉 with energy Ei andfinal states | f〉 with energy E, A ·p is the photoemissioninteraction operator and H the Hamiltonian of the sys-tem. From an ARPES experiment one can gain mainlytwo kinds of information. Firstly, the spectral functionS(k, E) gives direct information about the dispersion andthe quasiparticle character of the states and can be com-pared directly to predictions of model Hamiltonians. Allinformation carried by S(k, E) is expected to be inde-

pendent of the excitation energy and geometry of theexperiment. Secondly, the matrix element Mi,f includesall information concerning the photoemission interaction.As such it is sensitive to the experimental geometry viasymmetry selection rules as well as to the photon-energy.

The first ARPES experiments on Sr2CuO2Cl2 (Ref.19) were able to make the important observation thatthe Zhang-Rice singlet state bandwidth along Γ →(π, π)is of the order of 2J , and that the Zhang-Rice singletstate approaches closest to the chemical potential at the(π/2, π/2) point. These observations fit the predictions ofthe t-J-model. However, these early experiments foundvery little dispersion along Γ →(π, 0), which is in con-flict with the predictions of the same model. Subsequentstudies have confirmed the behavior along Γ →(π, π),but have also observed dispersion along the Γ →(π, 0)-direction in reciprocal space (k-space)20,21,23.

Nevertheless, the situation as regards the exact disper-sion relation along Γ →(π, 0), and in particular concern-ing the minimum energy difference between the statesalong Γ →(π, 0) and those at the (π/2, π/2) point is un-clear. This is more than a mere ARPES detail, as it isalong the Γ →(π, 0) direction that the predictions of thedifferent models vary the most - thus making this direc-tion in k-space important for the quantitative comparisonbetween theory and experiment.

Furthermore, the recent controversy surrounding thecorrect Fermi surface topology in the doped high tem-perature superconductor Bi2Sr2CaCu2O8+δ (Ref. 24) hasillustrated that data sets recorded from the same systemwith different experimental conditions can be remark-ably dissimilar. Consequently, both the photon-energyand exact polarization geometry used in an ARPES ex-periment are important parameters which, if they cannotbe treated at a quantitative, microscopic level, should atleast be thoroughly investigated on the experimental side.

In this paper, we address the electronic structureand dynamics of the lowest binding-energy electron-removal states in the “standard” undoped model cuprateSr2CuO2Cl2 using ARPES. Following the description ofthe experimental status given above, our “re-visit” of thissystem concentrates on the following points:

a) a thorough characterization of the photon-energydependence of the first electron-removal states at(π/2, π/2) and close to (π/2, 0) (the two points alongΓ →(π, π) and Γ →(π, 0) for which the first electron-removal states have maximum spectral weight); b) athorough characterization of the polarization dependence

of the first electron-removal states along these high-symmetry directions in k-space; c) the determination ofthe dispersion relation of the first electron-removal statesalong Γ →(π, π) and Γ →(π, 0), with subsequent compar-ison of the results with both existing ARPES data andthe predictions of an extended t-J-model and d) the de-termination of the k-dependent evolution of the coherentand incoherent parts of the spectral weight of the firstelectron-removal state along Γ →(π, π) and Γ →(π, 0),and comparison of these data with theoretical predic-tions.

II. EXPERIMENT

Experiments were performed at the beamlines F2.2and W3.2 at the Hamburg Synchrotron Laboratory (HA-SYLAB), at the undulator beamline U2-FSGM andthe 2m SEYA beamline at the Berliner Elektronen-speicherring Gesellschaft fur Synchrotronstrahlung mbH(BESSY). At the storage rings and monochromators usedin these studies, highly linearly polarized synchrotron ra-diation was available. In addition, the crossed undula-tor U2-FSGM beamline gave the possibility to use ver-tically oriented linearly polarized light. At this latterfacility, polarization-dependent measurements could beperformed without changing any other parameter in theexperiment. A total energy resolution (beamline and an-alyzer) of better than 70 meV and an angular acceptanceof the analyzer of ±1 degree was used. Fresh samples ofSr2CuO2Cl2 were cleaved in situ at a base pressure of1 × 10−10mbar, and spectra were taken within six hoursafter cleavage. Samples were either pre-oriented usingX-ray diffraction measurements or aligned in-situ withthe aid of low energy electron diffraction (LEED). In allcases, the fine angular adjustment was carried out usingthe k-space symmetry of the sharp ARPES features re-lated to non-bonding O2p states around (π, π) and (π, 0),as discussed in Refs. 25 and 26.

The high-quality single crystalline Sr2CuO2Cl2 wasgrown according to the method described in Ref. 3,where pre-dried high-purity SrCO3, SrCl2 and CuO ina ratio 1:1:1 were melted at 1100 ◦C. Although TN forSr2CuO2Cl2 is 251 K (Ref. 6), all ARPES experimentswere carried out at room temperature. This decision wasbased on two arguments. Firstly, and most importantly,as these experiments involve electron ejection from per-fect single crystals of a compound with an energy gapof the order of 2 eV, we had to eliminate uncertaintiesdue to charging effects, which meant measuring at roomtemperature. Secondly, although we measure at a tem-perature some 50 K above the Neel temperature, it hasbeen shown that the antiferromagnetic spin correlationlength of Sr2CuO2Cl2 at 350 K is still 250 A (Ref. 27),meaning that the lowest binding-energy hole state cre-ated in the photoemission process is still embedded in anantiferromagnetic spin background.

3

To be absolutely sure that variations in the flux ofthe incident photons from the storage ring did not leadto charging-induced energy shifts, we also adjusted thebeamline such that the photon flux impinging on the sam-ple (monitored with a gold mesh upstream of the sam-ple) was constant. This means that measuring time isthe only parameter required for the normalization of thedata. Bearing in mind that the data presented here area selection of data from about 80 different cleavages, wemade the qualitative observation that best and sharpestenergy distribution curves (EDC) were observed for sam-ples which behaved most sensitively to charging effects.This relation, of course, is reasonable as it correlatescleavage quality with the intrinsically highly insulatingnature of perfect Sr2CuO2Cl2.

Essentially two different experimental geometries wereused. They can be characterized by the orientation of twoplanes: a) the plane of polarization and b) the emissionplane. The plane of polarization is the plane spanned bythe vector of the direction of the synchrotron light andthe vector of its electric field (vector of polarization). Theemission plane includes the vector of the direction of thephotoelectron and the surface normal. Throughout thispaper we call the experimental geometry parallel if thesetwo planes are parallel, perpendicular if these two planesare perpendicular to each other (see Fig. 2 for a sketchof the two geometries).

III. PHOTON-ENERGY AND POLARIZATION

DEPENDENCE OF THE FIRST

ELECTRON-REMOVAL STATES OF AN

UNDOPED CUO2-PLANE

As mentioned above, both the inconsistencies in theliterature regarding the dispersion relation of the firstelectron-removal states along the Γ →(π, 0) direction(Ref. 28) in Sr2CuO2Cl2, as well as the ongoing con-troversy regarding the photon-energy dependence of theARPES data from Bi2Sr2CaCu2O8+δ, mean that beforecomparison with theory is carried out, the photon-energydependence of the first electron-removal states should beexamined in detail.

In Fig. 3, photon-energy dependent ARPES data forthe first electron-removal state in Sr2CuO2Cl2 at twopoints in the Brillouin zone: a) (π/2, π/2) (perpendic-ular geometry); and b) (0.7π, 0) (parallel geometry) areshown. In these regions of k-space the spectral weight ofthe first electron-removal state is known to be at a localmaximum along the respective k-space directions19–21,23.The spectra, which are normalized as described in thelast section, illustrate clearly the strong variation of thefirst electron-removal state intensity with photon-energy.The data shown in Fig. 3 represent only a small por-tion of the photon-energy dependent data recorded, andare intended to give the reader a direct impression ofthe strength of the effects at play. Each of the shown

spectra is part of a short k‖-series of three or five spec-tra. This was done to ensure we always captured thespectrum with the highest spectral intensity for the firstelectron-removal states. Within the errors given by the fi-nite k-resolution of the experimental setup (0.054 A−1 for16 eV photon-energy up to 0.152 A−1 for 80 eV photon-energy) we found the highest intensities always at thesame k-positions, namely at (π/2, π/2) and at (0.7π, 0).

This is in contrast to the results reported in Ref. 23,where series of EDCs on Sr2CuO2Cl2 along Γ →(π, π)taken with two different photon-energies show differencesnot only in intensity, but also in the EDC-derived disper-sion relation of the first ionization states. This was dis-cussed in Ref. 23 as not being due to either a) the exper-imental setup; b) the excitation of different initial statesor c) in the variation of k⊥ of the photoelectron. Theeffect was rather attributed to the strong impact of thematrix element, not only on the strength of the photoe-mission signal but also on the position of the quasiparticlepeak in the photoemission spectra, leading to differencesin the EDC-derived dispersion relations. We are forcedto disagree with the last point, as in our extensive col-lection of ARPES data, there was never evidence for aphoton-energy dependent shift of the k-position for whichthe first electron-removal states have minimum bindingenergy along Γ →(π, π). The same, in fact, holds forother directions in the Brillouin zone as well as for thedispersion of other features with low binding energy. Ifmatrix element effects change the EDC-derived disper-sion relation, then this change is, at least for our data,smaller than the energy resolution and angular resolvingpower of our ARPES experiments, which is equal to ∆k

or better than ∆E the values used in Ref. 23).Figure 4 shows an analysis of the spectral weight of

the first electron-removal states at the same k-points asshown in Fig. 3. These data are derived from a largeset of photon-energy dependent ARPES data coveringmeasurements from 10 (6) cleaves for the upper (lower)panels. From Fig. 4 it is clear that the ARPES spectralweight of the first electron-removal states oscillates withthe final state kinetic energy, that is with k⊥. We used avalue of 8.0 eV for the inner potential E0 (E0 = V0 − Φ,where Φ is the work function) to calculate k⊥, a valuewhich in the range of 6.9−8.9 eV used by other groups29.We see clear maxima at k⊥=0.82, 1.63, 2.40 and 3.12A−1, corresponding to photon-energies of 16, 25, 35 and48 eV.

The oscillatory nature of the photon-energy depen-dence, coupled to the absence of a classical resonance be-havior at the Cu 3p threshold (around 74-76 eV photon-energy) indicates that the factor dominating the observedbehavior is something other than the atomic photoioniza-tion cross-sections, and could be related, for example, tothe extreme two-dimensionality of the electronic statesconcerned. This could lead to a matching of the finalstate k⊥ to the periodicity of the unit cell of Sr2CuO2Cl2in c-direction. Note that the differences between the fourk⊥ is 0.72 − 0.81 A−1 which represents in real space a

4

distance of 7.8−8.7 A which is comparable to c-axis sep-aration of two neighboring CuO2-planes (= 7.805 A) inSr2CuO2Cl2. The oscillation of the photoemission inten-sity with photon-energy can therefore be attributed tointerference effects of the photoelectron wave diffractedfrom the c-axis periodicity of the layered crystal struc-ture, similar to the explanation of the strong photon-energy dependence of the photoemission intensity fromthe molecular orbitals of C60 (Ref. 30).

These strong variations in intensity as a function ofphoton-energy are also reminiscent of ARPES data ofYBa2Cu3O7−δ, in which an out-of-phase behavior re-garding intensity vs. k⊥ was observed for the CuO2-derived band which crosses the Fermi energy near the Xpoint and the so-called “1 eV peak”31. This fact was, atthat time, used to argue against the surface-state originof the 1 eV peak, a feature which is now believed to bedue to non-mixing O2p states of particular symmetry25.Nevertheless, the data presented here, taken togetherwith the theoretical and experimental investigations onBi2Sr2CaCu2O8+δ (Refs. 32 and 24), indicate clearly thatcare should be taken in the interpretation of absolutespectral weights observed in the ARPES data of the lay-ered cuprates, as matrix element and diffraction effectsdo play an important role in these systems.

A further experimental variable in an ARPES ex-periment is the polarization of the incoming radiation.Figure 5 shows two series of ARPES measurements onSr2CuO2Cl2 recorded along the high-symmetry direc-tions Γ →(π, 0) and Γ →(π, π). The photon-energy wasset to 22.4 eV, which is near a maximum of intensity asshown in Fig. 3 above. In each case, the series are pre-sented in pairs of data sets recorded with perpendicularand parallel polarization geometries as described in theexperimental section.

Along the Γ →(π, π) direction in k-space the firstelectron-removal state feature shows highest photoemis-sion intensity with perpendicular geometry (Fig. 5a),whereas along Γ →(π, 0) maximal intensities are observedin the parallel geometry (Fig. 5d), a result which tallieswith earlier measurements with 25 eV photon-energy20.This remarkable dependence of the photoemission inten-sity on the polarization was first explained in the contextof the strong polarization dependence in photoemissiondata from surface states33.

The physical picture behind the polarization depen-dence can be described as follows. The interaction op-erator A · p has even (+) parity in a parallel and odd(-) parity in a perpendicular experimental geometry. As-suming the applicability of the Zhang-Rice singlet stateconstruction to the first electron-removal final state, ina many-body picture this state belongs to the A1g rep-resentation, therefore being totally symmetric. Thus inthis representation the Zhang-Rice singlet has even par-ity with respect to a mirror plane along the Cu3dx2−y2 -O2px/O2py orbital bonds (M2) as well as at 45 degreesto the bonds (M1). In k-space M1 corresponds to theΓ →(π, π) direction and M2 to Γ →(π, 0). The initial

state (ground state) is a one-hole state with dx2−y2-symmetry, and therefore has even parity with respectto M2 and odd parity with respect to M1. The matrixelement thus formally vanishes for the two cases

parallel for Γ →(π, π) ⇒ M ∼ 〈+| + |−〉 = 0

perpendicular for Γ →(π, 0) ⇒ M ∼ 〈+| − |+〉 = 0

This argumentation also holds in the one band picture.Here the initial state (ground state) is totally symmetricand the final state has dx2−y2-symmetry (as shown inFig. 1), leading to the same result.

Thus, the observed polarization dependence of the firstelectron-removal states of an undoped CuO2-plane indi-cates that these states have a symmetry fully consistentwith that of the Zhang-Rice singlet. These results amendearlier reports (Ref. 26) regarding the polarization depen-dence of the first electron-removal states along Γ →(π, 0)in Sr2CuO2Cl2.

IV. THE DISPERSION RELATION AND

SPECTRAL FUNCTION OF THE FIRST

ELECTRON-REMOVAL STATES

The common picture given by the t-J-model and itsextensions34–37 is a strong dispersion of the Zhang-Ricesinglet state along the Γ →(π, π) direction with the min-imum binding energy at (π/2, π/2). At this k-point,the spectral weight of the first electron-removal statealso has its maximum and vanishes going away from(π/2, π/2). Recent ARPES experiments on Sr2CuO2Cl2confirm this19–21,23,25. Along the Γ →(π, 0) direction thet-J-model predicts a rather low binding energy near thehigh-symmetry point (π, 0) which is, in fact, almost ener-getically degenerate with that at (π/2, π/2). In the samemodel, the spectral weight of the quasiparticle increasesand is maximal at (π, 0). This is in contrast to the re-sult given in Ref. 19 where no dispersion was observedand in Refs. 20,21,23 where the binding energy of thefirst electron-removal state increases and the quasiparti-cle weight decreases after (π/2, 0). For the (π, 0)→(0, π)direction, the t-J-model predicts only little dispersion,whereas experiment has shown a strong isotropic dis-persion around the (π/2, π/2) point (Ref. 19). Exten-sions of the t-J-model and the spin and charge separa-tion ansatz exhibit new properties along Γ →(π, 0) and(π, 0)→(0, π). The Zhang-Rice singlet state around (π, 0)can now lower its energy by delocalization and is thuspushed to higher binding energies and the dispersion inthis direction is essentially parabolic. In these models,both a quasiparticle dispersion along (π, 0)→(0, π) whichis isotropic around (π/2, π/2) as well as a reduced spec-tral weight near (π, 0) can be achieved. In the spin andcharge separation model the isotropy along Γ →(π, π)and (π, 0)→(0, π) is intrinsic and near (π/2, π/2) the dis-persion relation is wedge-like rather than parabolic. Sur-prisingly, the data in Ref. 19 agree well with the extended

5

t-J-model along (π, 0)→(0, π), but not along Γ →(π, 0).In contradiction to that, other data along Γ →(π, 0) areconsistent with the extended t-J-model and the spin andcharge ansatz20, a view which appears to be supportedby further data sets21,23. Thus, the experimental dis-persion along the Γ →(π, 0) remains controversial, andyet it is the dispersion and the evolution of the spectralweight along Γ →(π, 0) that is of the deepest theoreticalinterest for the following reasons. Firstly, the states near(π, 0) evolve with increasing hole concentration to be-come the flat bands located near the chemical potentialin the metallic systems. These flat band regions are be-lieved by some to hold the key to high temperature super-conductivity. Secondly, the dispersion and quasiparticlespectral weight along Γ →(π, 0) are fingerprints for thedifferent models and parameters used in them. Thirdly,there are strong indications that the dispersion in theinsulator is closely connected with the pseudogap in theunderdoped region of the high Tc superconductor phasediagram and thus may also be related to the supercon-ducting gap in the doped superconducting systems17,22.

Consequently, the importance of experimental datawhich allow the determination of the dispersion andspectral weight of the first electron-removal states alongΓ →(π, 0) cannot be overestimated. Nevertheless, the ex-perimentalist is faced with a number of challenges whencollecting data along this direction: firstly, at severalpoints in the Brillouin zone, there is no or only weakphotointensity from the first electron-removal state. Forexample, near Γ the Zhang-Rice singlet has no spectralweight, because the Cu3dx2−y2 and O2px/O2py orbitalscannot hybridize there25, in addition the matrix elementsfor emission along the surface normal are formally zerofor a perfectly two-dimensional electronic state locatedin the CuO2-plane. Furthermore, near (π, 0) the photoe-mission intensity of the first electron-removal states be-comes weak as predicted by the extended t-J-models andthe spin and charge separation ansatz. Secondly, onlyperfectly aligned samples with fresh and clean surfacesexcited with UV-light in a well-adjusted measurementgeometry will show usable photoemission data from thefirst electron-removal state. Lastly, as the clean, defect-free surface of Sr2CuO2Cl2 is highly insulating, avoidingcharging effects can be difficult.

In Fig. 6 we present series of ARPES spectrarecorded along Γ →(π, 0) taken with parallel polarizationand Γ →(π, π) with perpendicular polarization and withphoton-energies of 16, 22 and 35 eV - thus measuring neara peak in the photoemission intensity oscillation in eachcase. The position of the low energy part of the disper-sive structure has been fitted using a Gaussian functionwhile the high binding-energy background was modelledsimply with the tail of another Gaussian. Although thisfit is physically somewhat simplistic, it proved to be suf-ficient to reliably find the positions of the peak as indi-cated by the triangles in each plot. The absolute valueon a binding-energy scale changes from one cleavage tothe next and is rather arbitrary due to the insulating na-

ture of the substance. However, the two series with 16eV were taken during one and the same cleavage, whichis the prerequisite to compare the binding-energy scalesof both series. The binding-energy scales of the 22 and35 eV data have been adjusted to that of the 16 eV data.We present a summary of the dispersion relations derivedfrom the fits to the data in Fig. 7.

We repeat here that we observe no evidence for aphoton-energy dependence of the dispersion relation ofthe first ionization states, as is consistent with the ar-guments regarding the spectral function given in the in-troduction. The dispersion of the first electron-removalstates along Γ →(π, π) agrees with the previous resultshaving a parabolic shape with its minimum binding en-ergy at (π/2, π/2). Along Γ →(π, 0) we also find aparabolic dispersion, in agreement with the dispersionreported in Refs. 20,21,23, but in contrast to the datagiven in Ref. 19. For 16 eV photon-energy, we measured72 meV difference in the lowest binding energies of thefirst electron-removal state along each of the two high-symmetry directions, which is half as small as in Ref. 20.In Ref. 21, a series of spectra representing a “maximumintensity cut” for a photon-energy 22.4 eV along a linefrom (π/2, π/2) to (0.67π, 0) was shown, which displayeda dispersion of about 300 meV. However, as we will show,the points of maximum intensity along Γ →(π, 0) do notcoincide with those possessing minimum binding energy.Thus such a maximum cut will not trace the line of min-imum binding energy. It turns out that this differencestrongly influences the parameters in model Hamiltoni-ans fitted to the dispersion curves.

We now go on to compare the experimental disper-sion with theoretical results obtained within the extendedt-J-model

H = −∑

iσ

3∑

l=1

tl Xσ0i X0σ

i+l + J∑

〈i,m〉

Si · Sm , (3)

with the additional hopping terms to second (t2) andthird (t3) neighbors now added besides the dominatingnearest neighbor hopping t = t1. The Hamiltonian is

written in terms of Hubbard operators Xσ0i = c†iσ(1 −

ni−σ) where σ = ±1 is the spin index. The values ofthe hopping terms are determined by mapping the morerealistic Emery model with parameters derived from aconstrained density-functional calculation39 to its lowbinding-energy part by means of the cell-perturbationmethod. This procedure gives t2/t1 = −0.08 and t3/t1 =−0.15. The theoretical dispersion relation shown in Fig.7 is calculated using a variational method involving a spinpolaron of small radius40. There are also related workswhich lead to similar dispersions41.

It has been shown in exact diagonalisation studies ofsmall clusters42 that the dispersive bandwidth scales withthe single parameter, J , whereas the form of the disper-sion curve is fixed by the ratios t2/t1 and t3/t1. Thereforewe use the variational ansatz for J = t1 and then we scalethe bandwidth in Fig. 7 with a factor J = 0.22 eV. For

6

reference, we also show the dispersion relation withoutadditional hopping terms (t2 = t3 = 0, scaling factorJ = 0.28 eV), which shows a much too small energy dif-ference between the lowest binding energies of the firstelectron-removal states along Γ →(π, 0) and Γ →(π, π) toobtain good agreement with the experimental spectra.

Another important prediction from model Hamiltoni-ans is the evolution of the spectral weight along certaindirections in the Brillouin zone. Here we map this evo-lution and distinguish between the coherent and inco-herent parts of the first electron-removal states followingthe procedure proposed in Ref. 43, in which the contribu-tion from the main valence band tail was first subtractedfrom the spectra. The photoemission intensity was thendefined as the coherent spectral weight and fitted using aGaussian. The ARPES intensity which is neither part ofthe valence band tail nor in the Gaussian is then taken tobe a measure of the incoherent part of the first electron-removal state spectral function [see Ref. 43]. In our case,we have used a Lorentzian broadened by the experimentalresolution (i.e. a Voigt profile) to fit the lowest bindingenergy intensity (the coherent part). Of course, this pro-cedure is not physically rigorous, but does offer a roughestimation of the possible split between the coherent andincoherent spectral weight.

In Fig. 8, the momentum distributions of the twoparts of the ARPES spectra are shown for 16 eV and22 eV excitation energy. Note that the overall shape ofthese distributions is independent of the photon-energy.Along Γ →(π, π) both the coherent and incoherent partsof the first electron-removal states are symmetric around(π/2, π/2) at which point they both reach their maxi-mum weight. In the Γ →(π, 0) direction, we observe asteady increase in spectral weight of both componentsup to (0.7π, 0) after which point it drops fast. One canfind signs of a qualitatively similar behavior in ARPESdata from other groups19–21,23,38 and for measurementson the related substance Ca2CuO2Cl2 (Ref. 22), althoughthe coherent and incoherent spectral weights were notanalysed in these studies. Note that along Γ →(π, 0) theminimum binding energy of the low binding-energy fea-ture and the maximum of the coherent intensity do notcoincide at the same k-point. In calculations using ex-tensions of the t-J-model this behavior was predicted14,44

and can now be considered as experimentally verified.Within the simple fit procedure we can give these quan-

tities some numbers: the ratio of the coherent to incoher-ent spectral weight for the two locations in k-space is 0.6((π/2, π/2)) and 0.5 ((0.7π, 0)) for 16 eV photon-energyand 2.4 ((π/2, π/2)) and 3.8 ((0.7π, 0)) for 22 eV photon-energy. It is important to realise that we observe here anextremely strong apparent dependence of the ratio be-tween the coherent and incoherent spectral weight uponthe photon-energy. To discuss the physical significanceof this, we re-write equation 2 as

S(k, E) = −1

πIm 〈i | ck (

1

E − E(k) − Σ+ Ginc) c†

k| i〉,

(4)

in order to separate the coherent from the incoherentspectral weight (Σ is the self-energy of the quasiparticle).Plugging this into equation 1, it is immediately clear thatin taking the ratio of the coherent and the incoherentintensity, the matrix element cancels out. Thus, this ratiois then determined by the spectral function S(k, E) aloneand should not depend on the excitation energy.

Our observation that the ratio does appear to dependon hν leads then to the following possible conclusions: (i)the fit procedure used is too simple and therefore does notcorrectly quantify, however roughly, the coherent and in-coherent parts of the spectral function. (ii) there are sig-nificant extrinsic contributions to the photoemission sig-nal in this binding energy region. These could be the re-sult of an energetic shift of spectral weight due to inelas-tic losses45, which could be sensitively dependent on thephotoelectron kinetic energy, as are the data from elec-tron energy loss spectroscopy in reflection of Sr2CuO2Cl2(Ref. 46). (iii) the photoemission intensity between thethe main valence band edge and the chemical potentialis not derived from the spectral weight (coherent + inco-herent) resulting from a single electronic state - i.e. thereis spectral weight from an additional, different electronicstate in this energy region.

The fit procedure, as we have discussed above, is sim-plistic - however the coherent-incoherent intensity ratiosvary by a factor of more than four between the twophoton-energies. The third possible conclusion - thatthere has to be spectral weight from more than onestate in this energy region could have important impli-cations. We can rule out a significant contribution fromsecondary electrons for the relatively high kinetic ener-gies dealt with here. Intensity from surface states is un-likely, as XPD data47 shows that the cleavage surface ofSr2CuO2Cl2 is terminated within the SrCl units, whichare essentially ionic and therefore do not support elec-tronic states close to the chemical potential. In addi-tion, our LEED investigations also gave no evidence fora reconstruction of this termination layer. Spin-resolvedresonant photoemission of CuO (Ref. 10) has shown in-tensity due to triplet states within 1eV of the Zhang-Ricesinglet, although those states would be expected to havethe same photon-energy dependence as the singlet in ourexperiment.

If there was an additional, different state in this en-ergy region, this would lead to a complicated k- and hν-dependent overlap between the intensity of this state andthe higher binding energy components attributed up tillnow to incoherent weight from the Zhang-Rice singlet.While this would not be expected to have a large impacton the observed dispersion relation for the Zhang-Ricesinglet (which is, after all, a quantity derived from thespectral structure at lowest binding energies for each k-point), it could, however lead to the observed photon-

7

energy dependence of the ratio between the low binding-energy (“coherent”) and higher binding-energy (“inco-herent”) parts of the photoemission spectra.

V. SUMMARY

In conclusion, we have presented a detailed ARPESstudy of the low binding-energy occupied electronicstructure of Sr2CuO2Cl2, which corresponds to an inves-tigation of the first electron-removal states of an undopedCuO2-plane. Our experiments, and the comparison oftheir results with theoretical models, have revealed thefollowing main points:

1. The photoemission signal of the first electron-removal states at both (π/2, π/2) and (0.7π, 0) exhibitsa marked photon-energy dependence. The intensity pro-file shows strong oscillations with maxima near 16, 25,35 and 49 eV, corresponding to final state crystal mo-menta k⊥=0.82, 1.63, 2.40 and 3.12 A−1. This strongphoton-energy dependence has complicated comparisonsbetween data in the literature from different groups asregards both the spectral weight and spectral form ofthe first electron-removal states in these systems. We at-tribute the oscillation of photoemission intensity (whichhas a period in k⊥ of ca. 0.75 A−1) to the diffraction ofthe photoelectron wave on the periodic c-axis separationof the CuO2-planes of 8.2 A.

2. Along the high-symmetry directions Γ →(π, π) andΓ →(π, 0) the first electron-removal states shows a strongpolarization dependence. This can be linked to thestrongly polarization-dependent matrix element, whichin turn allows the determination of the symmetry ofthe first electron-removal state itself. For both high-symmetry directions we observe a polarization depen-dence in keeping with that expected for a Zhang-Ricesinglet state in the framework of either a three-band orone-band model Hamiltonian.

3. Our data show that the dispersion of the firstelectron-removal states along both high symmetry di-rections (Γ →(π, π) and Γ →(π, 0)) is parabolic-like andindependent of the excitation energy. This, and therather large difference in lowest binding energy of thefirst electron-removal state along these directions, showsthe validity of the extended t-J-model for describing thedisperion relation of a single hole in an antiferromag-netic CuO2 plane. Thus, the inclusion of second (t2) andthird (t3) neighbor hopping terms with realistic values oft2 = −0.08 and t3 = 0.15 in units of the next neighborhopping t = t1 are required.

4. Upon application of a simple fit procedure, we inferthe momentum distribution of the spectral weight of thecoherent and incoherent part of the first electron-removalstate to have its maximum along Γ →(π, π) at (π/2, π/2)being symmetrically suppressed away from this point.Along Γ →(π, 0) the spectral weights of both parts reachtheir maximum at (0.7π, 0) and then drop fast. The ratio

between the coherent and incoherent spectral weight isstrongly photon-energy dependent, which, at first sightwould appear to violate the physics of the spectral func-tion. There are different possible explanations for this in-cluding: (i) the necessity for a more sophisticated frame-work in which to analyse the weight of the coherent andincoherent contributions to the spectral weight; (ii) sig-nificant (hν-dependent) intensity due to extrinsic pro-cesses (iii) intensity in this energy region due to intrinsicelectronic states other than the Zhang-Rice singlet.

We gratefully acknowledge the stimulating conversa-tions with S. Haffner. This work was supported bythe BMB+F under contract number 05 SB8 BDA6and by the DFG under Fi439/7-1 and as part of theGraduiertenkolleg “Struktur und Korrelationseffekte imFestkorper” der TU Dresden.

1 P. Aebi, J. Osterwalder, P. Schwaller, L. Schlapbach, M.Shimoda, T. Mochiku, and K. Kadowaki, Phys. Rev. Lett.72, 2757 (1994)

2 Z.-X. Shen, W. E. Spicer, D. M. King, D.S. Dessau, andB.O. Wells, Science 267, 343 (1995).

3 L. L. Miller, X. L. Wang, S. X. Wang, C, Stassis, D. C.Johnston, J. Faber, Jr., and C.-K. Loong, Phys. Rev. B41, 1921 (1990).

4 T.Sowa, M. Haritani, and K. Miyauchi, J. Solid State.Chem. 84, 178 (1990).

5 Z. Hiroi, N. Kobayashi, and M. Takano, Nature, 371, 139(1994); M. Al-Mamouri, P.P. Edwards, C. Greaves, andM. Slaski, Nature, 369, 382 (1994); Y. Zenitani, K. Inari,S. Sahoda, M Uehara, J. Akimitsu, N. Kubota, and M.Ayabe, Physica C 248, 167 (1995).

6 D. Vaknin, S. K. Sinha, C. Stassis, L. L. Miller, and D. C.Johnston, Phys. Rev. B 41, 1926 (1990).

7 F. C. Zhang and T. M. Rice, Phys. Rev. B 37, 3759 (1988).8 H. Eskes, L. H. Tjeng, and G. A. Sawatzky, Phys. Rev. B41, 288 (1990).

9 Throughout this paper we strictly differentiate between theterm first electron-removal state, which is a real object, andthe Zhang-Rice singlet state, which is rather a theoreticalconstruct to describe the first electron-removal state.

10 L.H. Tjeng, B. Sinkovic, N.B. Brookes, J.B. Goedkoop, R.Hesper, E. Pellegrin, F.M.F. de Groot, S. Altieri, S.L. Hul-bert, E. Shekel, and G.A. Sawatzky, Phys. Rev. Lett. 78,1126 (1997)

11 A. Nazarenko, K. J. E. Vos, S. Haas, E. Dagotto, and R.J. Gooding, J. Supercond. 8, No. 5, 671, (1995); F. Mila,Phys. Rev. B 38, 11358 (1988); G. Dopf, A. Muramatsu,and W. Hanke, Phys. Rev. Lett. 68, 353 (1992).

12 M. S. Hybertsen, E. B. Stechel, M. Schluter, and D. R.Jennison Phys. Rev. B 41, 11068 (1990); L. F. Feiner, J. H.Jefferson and R. Raimondi, Phys. Rev. B 53, 8751 (1996);N. Bullut, D. J. Scalapino, and S. R. White, Phys. Rev. B50, 7215 (1994); E. Dagotto, F. Ortolani, and D. Scalapino,

8

Phys. Rev. B 46, 3183 (1992).13 H. Eskes, and A. M. Oles, Phys. Rev. Lett. 73, 1279 (1994);

H. Eskes, A. M. Oles, M. B. J. Meiinders, and W. Stephan,Phys. Rev. B 50, 17980 (1994).

14 H. Eskes, and R. Eder, Phys. Rev. B 54, 14226 (1996).15 V. Yu. Yushankhai, V. S. Oudovenko, and R. Hayn, Phys.

Rev. B 55, 15562 (1997).16 R. B. Laughlin, J. Phys. Chem. Solids 56, 1627 (1995).17 R. B. Laughlin, Phys. Rev. Lett. 79, 1726 (1997).18 S. Meixner, W. Hanke, E. Demler, and S.-C. Zhang, Phys.

Rev. Lett. 79, 4902 (1997); R. Eder, W. Hanke, and S.-C.Zhang, Phys. Rev. B 57, 13781 (1998)

19 B. O. Wells, Z.-X. Shen, A. Matsuura, D. M. King, M. A.Kastner, M. Greven, and R. J. Birgeneau, Phys. Rev. Lett.74, 964 (1995).

20 S. LaRosa, I. Vobornik, F. Zwick, H. Berger, M. Grioni, G.Margaritondo, R. J. Kelley, M. Onellion, and A. Chubukov,Phys. Rev. B 56, R525 (1997). In this reference, conflict-ing statements are made as regards the polarization ge-ometry for which the maximal intensity along Γ →(π, 0)is observed. The correct situation for maximal intensity isthat corresponding to “parallel” as used here (M. Grioni,private communication).

21 C. Kim, P. J. White, Z.-X- Shen, T. Tohyama, Y. Shibata,S. Maekawa, B. O. Wells, Y. J. Kim, R. J. Birgeneau, andM. A. Kastner, Phys. Rev. Lett. 80, 4245 (1998).

22 F. Ronning, C. Kim, D. L. Feng, D. S. Marshall, A. G.Loeser, L. L. Miller, J. N. Eckstein, I. Bozovic, and Z.-X.Shen, Science 282, 2067 (1998).

23 S. Haffner, C. G. Olson, L. L. Miller, and D. W. Lynch,Phys. Rev. B 61, 14378 (2000).

24 Y.-D. Chuang, A. D. Gromko, D. S. Dessau, Y. Aiura, Y.Yamaguchi, K. Oka, A. J. Arko, J. Joyce, H. Eisaki, S.E. Uchida, K. Nakamura, and Y. Ando, Phys. Rev. Lett83, 3717 (1999); H. M. Fretwell, A. Kaminski, J. Mesot, J.C. Campuzano, M. R. Norman, M. Randeria, T. Sato, R.Gatt, T. Takahashi, and K. Kadowaki, Phys. Rev. Lett 84,4449 (2000); S. V. Borisenko, M. S. Golden, S. Legner, T.Pichler, C. Durr, M. Knupfer, J. Fink, G. Yang, S. Abell,and H. Berger, Phys. Rev. Lett 84, 4453 (2000); D. L.Feng, W. J. Zheng, K. M. Shen, D. H. Lu, F. Ronning,J.-I. Shimoyama, K. Kishio, G. Gu, D. Van der Marel, andZ.-X. Shen, cond-mat/9908056; S. Legner, S. V. Borisenko,C. Durr, T. Pichler, M. Knupfer, M. S. Golden, J. Fink, G.Yang, S. Abell, H. Berger, R. Mueller, C. Janowitz, and G.Reichardt, Phys. Rev. B. 62, 154 (2000).

25 J. J. M. Pothuizen, R. Eder, N. T. Hien, M. Matoba, A. A.Menovsky, and G. A. Sawatzky, Phys. Rev. Lett. 78, 717(1997).

26 R. Hayn, H. Rosner, V. Y. Yushankhai, S. Haffner, C. Durr,M. Knupfer, G. Krabbes, M. S. Golden, J. Fink, H. Eschrig,D. J. Singh, N. T. Hien, A. A. Menovsky, C. Jung, and G.Reichardt, Phys. Rev. B 60, 645 (1999)

27 M. Greven, R. J. Birgeneau, Y. Endoh, M. A. Kastner,B. Keimer, M. Matsuda, G. Shirane, and T. R. Thurston,Phys. Rev. Lett. 72, 1096 (1994).

28 We refer to the notation in Ref. 19 where Γ = (0, 0)means the center and (±π,±π) means the corners of thetwo-dimensional Brillouin zone of the square-planar CuO2-plane given in units 1/a where a = 3.967 Ais the lattice

constant of Sr2CuO2Cl2 (Ref. 3).29 R. Courths and S. Hufner, Physics Reports 112, 53 (1984).30 Y. B. Xu, M. Q. Tan, and U. Becker, Phys. Rev. Lett. 76,

3538 (1996)31 J. G. Tobin, C. G. Olson, C. Gu, J. Z. Liu, F. R. Solal, M.

J. Fluss, R. H. Howell, J. C. O’Brian, H. B. Radousky, andP. A. Sterne, Phys. Rev. B 45, 5563 (1992).

32 A. Bansil and M. Lindroos, Phys. Rev. Lett. 83, 5154(1999).

33 G. W. Gobeli, F. G. Allen, and E. O. Kane, Phys. Rev.Lett. 12, 94 (1964); E. Dietz, H. Becker, and U. Ger-hardt, Phys. Rev. Lett. 36, 1397 (1976); J. Hermanson,Solid State Commun. 22, 9 (1997).

34 S. A. Trugman, Phys. Rev. Lett. 65, 500 (1990).35 Z. Liu and E. Manousakis, Phys. Rev. B 45, 2425 (1992).36 E. Dagotto and A. Nazarenko, Phys. Rev. Lett. 73, 728

(1994).37 A. Moreo, S. Haas, A. W. Sandvik, and E. Dagotto, Phys.

Rev. B 51, 12045 (1995).38 S. Haffner, D. M. Brammeier, C. G. Olson, L. L. Miller,

and D. W. Lynch, preprint, cond-mat/0006366.39 M. S. Hybertsen, E. B. Stechel, M. Schluter, and D. R.

Jennison, Phys. Rev. B 41, 11068 (1990).40 R. Hayn, A. F. Barabanov, and J. Schulenburg, Z. Phys. B

102 359 (1997).41 A. Nazarenko, K. J. E. Vos, S. Haas, E. Dagotto, and R. J.

Gooding, Phys. Rev. B 95, 8676 (1995); V. I. Belinicher,A. L. Chernyshev, and V. A. Shubin, Phys. Rev. B 54,14914 (1996); T. Xiang and J. M. Wheatley, Phys. Rev. B54, R12656 (1996); F. Lema and A. A. Aligia, Phys. Rev.B 55, 14092 (1997); J. Eroles, C. D. Batista, and A. A.Aligia, Phys. Rev. B 59, 14092 (1999).

42 E. Dagotto, R. Joynt, A. Moreo, S. Bacci, and E. Gagliano,Phys. Rev. B 41, 9049 (1990).

43 P. W. Leung, B. O. Wells, and R. J. Gooding, Phys. Rev.B 56, 6320 (1997).

44 B. Kyung and R. A. Ferrell, Phys. Rev. B 54, 10125 (1996).45 R. Joynt, Science 284, 777 (1999).46 J. J. M. Pothuizen, Electrons in and close to Correlated

Systems, Ph.D. thesis, University of Groningen, 1998, PrintPartners Ipskamp (Enschede).

47 T. Boske, O. Knauff, R. Neudert, M. Kielwein, M. Knupfer,M. S. Golden, and J. Fink, Phys. Rev. B 56, 3438 (1997).

FIG. 1. Schematic representation of the Zhang-Rice sin-glet state in the one-particle representation. The Zhang-Ricesinglet has the same symmetry as a dx2−y2 -orbital, imply-ing the existence of two mirror planes perpendicular to theCuO2-plane, labelled M1 and M2.

FIG. 2. The experimental geometry for the photoemis-sion experiments: a) emission-plane and polarization-planeare parallel to each other, b) emission-plane and polariza-tion-plane are perpendicular to each other. Throughout thispaper we call the first case a) parallel and the second case b)perpendicular polarization.

9

FIG. 3. A typical example of ARPES data of the firstelectron-removal states of Sr2CuO2Cl2 as a function of pho-ton-energy. In panel a) the ARPES EDCs are recorded at(π/2, π/2) and in panel b) at (0.7π, 0). The photon-energiesare as shown.

FIG. 4. The photon-energy dependence of the photoe-mission intensity of the first electron-removal states a) at(π/2, π/2) and b) at (0.7π, 0), arrived at from the analysisof a large body of ARPES data such as that shown in Fig. 3.The solid black line represents a guide to the eye and the errorbars (located in the upper left corner of each panel) indicatethe error of the fit to the experimental intensity (95% con-fidence interval). The top axis shows the corresponding k⊥

scale calculated using an inner potential of 8.0 eV (for detailssee text).

FIG. 5. Series of energy-distribution curves for differ-ent polarization geometries. The photon-energy was set to22.4 eV and all spectra were taken at 300K. Panels a) andb) show measurements along Γ →(π,π) where the first elec-tron-removal state peak appears near 21.0 eV kinetic energyfor perpendicular polarization in a). The corresponding se-ries along Γ →(π, 0) are shown in panels c) and d). There,the first electron-removal states gives significant photocurrentnear 20.9 eV kinetic energy only for parallel polarization ind).

FIG. 6. ARPES series showing the dispersion of theZhang-Rice singlet state along the high-symmetry directions.The upper three panels show series along Γ →(π,π) the lowerthree panels along Γ →(π, 0). The excitation energy is thesame for each column, 16 eV (left), 22 eV (center) and 35eV (right). Black triangles are included as a guide indicatingthe kinetic energy of the first ionization state determined bya fitting procedure described in the text.

FIG. 7. The dispersion of a single hole in an antiferromag-netic CuO2-plane measured along two directions in k-space.The symbols represent data from the ARPES spectra fromSr2CuO2Cl2, recorded with the indicated photon-energies.The vertical error bars in the right panel indicate the errors ofthe fit (95% confidence interval) in determining the bindingenergy of the first ionization states. The k-resolution is 0.054,0.075 and 0.094 A−1 for 16, 22 and 35 eV photon-energy re-spectively, which corresponds to 4.5%[6.8%], 6.3%[9.6%] and7.8%[11.9%] of the direction Γ →(π,π)[Γ →(π, 0)]. The linesindicate the results of the calculations employing a variationalansatz using a spin polaron with small radius (for details seetext). The dashed line corresponds to a calculation where theadditional transfer terms t2 and t3 are chosen to be zero (i.e.the t-J-model), while for the solid line these terms are set tot2/t1 = −0.1 and t3/t1 = 0.2 (i.e. an extended t-J-model).The improved agreement to the experimental data providedby the extended t-J-model, particularly along Γ →(π, 0) isapparent.

FIG. 8. The coherent and incoherent part of the spectralweight of the first electron-removal states determined from thedata shown in Fig. 6 for a) 22 eV and b) 16 eV photon-energyfollowing the procedure used by Leung et al., Phys. Rev.B 56, 6320 (1997). The upper part in each case shows arepresentative result of the fit. In the lower part of the figure,the weight of the coherent (filled circles) and the incoherent(open circles) intensity, normalized to the coherent spectralweight at (π/2, π/2), is shown. The vertical bars indicate theerror of the least squares fit to the ARPES intensity (95%confidence interval).

10

This figure "fig1.gif" is available in "gif" format from:

http://arxiv.org/ps/cond-mat/0007283v4

This figure "fig2.gif" is available in "gif" format from:

http://arxiv.org/ps/cond-mat/0007283v4

This figure "fig3.gif" is available in "gif" format from:

http://arxiv.org/ps/cond-mat/0007283v4

This figure "fig4.gif" is available in "gif" format from:

http://arxiv.org/ps/cond-mat/0007283v4

This figure "fig5.gif" is available in "gif" format from:

http://arxiv.org/ps/cond-mat/0007283v4

This figure "fig6.gif" is available in "gif" format from:

http://arxiv.org/ps/cond-mat/0007283v4

This figure "fig7.gif" is available in "gif" format from:

http://arxiv.org/ps/cond-mat/0007283v4

This figure "fig8.gif" is available in "gif" format from:

http://arxiv.org/ps/cond-mat/0007283v4