a Physics Department, Northeastern University, Boston, MA 02115. USA ... c University oflllinois at Chicago, 845 W. Taylor St., Chicago, IL 60607, USA.
PHYSICAG
Physica C 212 ( 1993 ) 347-351 North-Holland
Signature of the CuO2 plane related bands in YBa2Cu306.9 as seen by angle-resolved photoemission M. Lindroos a, A. Bansil a, K. Gofron b,c, J.C. Campuzano b,c, H. Ding b,c, R. Liu b and B.W. Veal b a Physics Department, Northeastern University, Boston, MA 02115. USA b Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, USA c University oflllinois at Chicago, 845 W. Taylor St., Chicago, IL 60607, USA
Received 19 April 1993
The intensity and polarization dependence of the spectral feature in angle-resolved photoemission (ARPES) associated with the CuO2 plane bands from the YBa2Cu307 (001) surface is computed for the first time within the band theory framework, and the corresponding polarization-dependent ARPES measurements are presented. The theoretical predictions are in remarkable agreement with the experimental features along the F-S line which have been interpreted as the signature of CuO2 plane bands crossing the Fermi energy. Our results clearly establish that the bulk CuO2 plane bands are indeed observed by ARPES, and indicate that the local-density-approximation based wave functions implicit in the band theory reasonably describe the physical situation.
An issue o f contention since the discovery o f the high-To superconductors ( H T S C ) has been the extent to which electron-electron correlations invalidate the conventional local-density-approximation ( L D A ) based b a n d theory framework for describing the electronic structure of these novel materials. In particular, in YBa2Cu307 ( Y 1 2 3 ) , the archetype of the new superconductors, b a n d theory predicts that four bands cross the F e r m i energy. O f the resulting four F e r m i surface ( F S ) sheets, the two large hole sheets (centered on the S-symmetry point in the Brillouin zone) arising from the CuO2 planes have drawn great interest, since the CuO2 planes are widely believed to play a central role in the occurrence of a high To. A considerable effort has been devoted to searching for the answer to the question: is the b a n d theory prediction of CuOz plane related FS's in the H T S C ' s correct? Angle-resolved photoemission ( A R P E S ) is the only spectroscopy so far which has claimed the existence o f such FS's with large Luttinger volumes, and this fact has been widely invoked as a significant constraint on physically relevant theories o f the electronic structure o f the H T S C ' s [ 1-
3].
The available ARPES evidence for the existence o f the CuO2 plane FS's is suggestive. It is based essentially on the observation that a spectral feature in the ARPES data crosses the F e r m i energy at a set o f kpoints which are in reasonable accord with FS's predicted by b a n d theory [ 4 - 8 ]. However, features in ARPES spectra are well known to arise from many diverse mechanisms, even in simple metals such as Cu and AI. The situation is far more uncertain in complex crystals in view o f the surface sensitivity o f the photoemission process, and the fact that relatively little experience exists in using ARPES as a probe o f the b a n d structure o f complex systems. Recall that the inelastic mean-free path of UV photoelectrons for the Y 123 (001 ) surface is less than one unit cell dimension along the c-axis, which raises serious questions concerning how, if at all, any particular Bloch state would manifest itself in the ARPES spectra. Thus, it is i m p o r t a n t to determine the signature o f the CuO2 plane bands in ARPES spectra as predicted by the b a n d theory framework. W i t h this motivation, we report in this article the first computation of the intensity and polarization dependence of
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M. Lindroos et aL /Signature o/"( "uO:plane related hands
the spectral feature associated with CuO2 plane bands near the Fermi energy in Y123, and show the results to be in remarkable agreement with the corresponding ARPES measurements. The computation of ARPES intensities in HTSC's has previously not been possible due to the complexity of their crystal structure. The present comparison between theory and experiment dearly establishes that the spectral signature of the bulk CuO2 plane bands is indeed observed in ARPES experiments. This result gives confidence in the interpretation of the data in this regard, and indicates that the LDA based wavefunctions implicit in the theory reasonably describe the physical situation, electron-electron correlations notwithstanding. Specifically, we have generalized the one-step photoemission approach [9,10] in order to treat systems with an arbitrary number of atoms in the unit cell. All existing work has been limited to a maxim u m of two atoms per layer unit cell [ 11 ], whereas the Y123 (001) surface requires at least three basis atoms, and a larger basis set for other low index faces. We emphasize that in the present one-step formulation, the photoemission process is treated as a single quantum mechanical event, and artificial distinctions between the processes of excitation, transport, and transmission o f the electron through the surface barrier invoked in the earlier ad hoc threestep model are removed [ 12 ]. As is evident already from the experience on simpler materials, quantitative predictions of the ARPES intensities are not possible within the three-step formulation, and the use of the one-step approach which properly accounts for multiple-scattering effects on the final as well as initial electron states is essential. Our new photoemission codes would also permit a first-principles treatment of ARPES spectra from complex materials more generally. The intensity of photoemitted electrons of a given energy E and emission direction kjl for incident radiation of frequency ~o can be written in the one-step formalism as [ 10 ] I=-
1_ I m ( k l I j [ G ] A G ~ A , G ;
Ilkll) ,
( 1)
where G2 and G~ are the one-electron Green's functions at the final state energy ( E + h c o ) and the initial state energy E, respectively; the superscripts
+ ( - ) i n d i c a t e forward (backward)propagation. A is the photon field operator. Practical photo-intensity computations assume a semi-infinite solid m which atoms arc represented by non-overlapping muffin-tin potentials, and the vacuum is separated from the bulk by a step V~...... the "inner potential". The analysis of form ( 1 ) proceeds most naturally via the use of multiple-scattering theory and low-energyelectron-diffraction techniques. The key quantities are the scattering matrices associated with a single layer; we have generalized the original equations of Pendry [10] for one atom per unit cell to the case of a general complex crystal. Note that since Y123 contains buckled layers, thc layer scattering matrices no longer possess mirror symmetry [ 13 ]. The layer scattering matrices permit the evaluation of the wavefields in terms of which the integrations of eq. ( 1 ) can be carried out to yield ARPES intensities. We have used the structural data of Beno et al. [ 14 ]. Our muffin-tin potentials for various sites are based on the use of the semi-relativistic self-consistent KKR methodology [15], and yield bulk band struclure and Fcrmi surfaces of Y123 in reasonable accord with the well-known results, relatively small differences between various band structures notwithstanding. Following c o m m o n practice, the self-energy corrections to the potential were incorporated via a semiempirical step potential at the surface, i.e. l i .... .= I R + i l ~ was taken to be 10.4 eV, estimated as the sum of the Fermi energy and the spectrometer work function. I1 was taken to be 2 eV for final states (electrons). For initial states (holes), an energy dependent value varying between 0.1 eV at the Fermi energy to about 1.0 eV at 3 eV binding energy was used. The present values of I,'] and [R are representative of measurements, but in any event, our conclusions are quite insensitive to these parameters. The experiments were carried out at the Alladin synchrotron, with a SEYA m o n o c h r o m a t o r giving a total energy resolution of 30 meV and an angular resolution of +1 . The photon beam was more than 94% linearly polarized in the horizontal plane 21.2 eV. We used twinned YBa2Cu30~.9 single-crystals [ 16 ], of typical dimensions I × I × 0.1 m m 3, exhibiting a sharp superconducting transition at 92 K, with a transition width of less than 2 K as determined by a S Q U I D magnetometer. The samples were carefully
M. Lindroos et al. / Signature of Cu02 plane related bands
oriented by Laue diffraction and cleaved in situ in a vacuum of 2 × 10-~o Torr at 12 K. The orientation was confirmed by the observed symmetry of sharp photoemission features around high symmetry points (X, Y, and S) in the Brillouin zone (BZ). Our purpose, as noted, is to investigate how the intensity of the ARPES spectral peak associated with the CuO2 planes changes when the polarization vector of the incident light is rotated in the crystal a-b plane [ 17 ]. Figure 1 gives two sets of spectra, both obtained from the same specimen when the light is incident at an azimuthal angle ¢ = 4 5 ° to the a-axis so that the F-S line in the BZ lies in the plane of incidence. In fig. 1 (a), the detector also lies in the incidence plane and different kll values along F-S are scanned by changing the polar angle of the detector. In fig. 1(b), we once again scan krstates along the F-S line, but now the detector is moved by 90 ° so that the emitted electrons are observed in a plane perpendicular to the plane of incidence. It is straightforward to show that, for a general orthorhombic lattice, the spectra of fig. 1 (b) will be identical to the case where, instead of the detector, the incident light beam is rotated by 90 ° . In short then, the electric field vector of the incident light, in addition to a component along the crystal z-axis, possesses a compo-
A//F-S
AZF-S -~Y
349
nent along the F-S direction in fig. 1 (a), but perpendicular to F-S in fig. 1(b). We also obtained a third set of spectra using a different specimen which was mounted such that the incident beam is aligned along the crystal a-axis. Now the electric field possesses a component along the b-axis [18 ], in addition to the component along the z-axis. Taken together, we thus have three sets of spectra with polarization parallel, perpendicular, and at 45 ° to the F-S direction. The polar angle 0 of the incident light in all measurements was 50 ° with respect to the surface normal. Other measurements carried out using a range of 0 values show that the spectral feature associated with the CuO2 plane bands is insensitive to the zcomponent of the polarization vector, A:. Significantly, this experimental observation is in accord with our computations which indicate that the CuO2 plane bands are not excited by Az. For this reason, we have mostly ignored Az in our discussion, as for example is implicit in the directions of polarization vectors given in fig. 1. Our theoretical and experimental results can be discussed with reference to figs. 1-3. Specifically, we are concerned with the feature lying between 0 and 0.3 eV binding energies in fig. 1 (b), which has been widely interpreted as the signature of two CuO2 plane bands moving across the Fermi energy [4-7,19]. Figure 2 (a) illustrates the polarization dependence
S
Experiment q I
4o
J I r
I'
I '
I ~ I J i
Theory ~ I r
/\
T I '
"3
2o
I ' I '[~!T',
I '
I
' I i, rl
'
0o
(a ~)
8o 6° 4°
.= 1.6 1.2 0.8 0.4 0. Binding Energy (eV)
1.6 1.2 0.8 0.4 0. Binding Energy (eV)
Fig. 1. ARPES spectra from YBa2Cu306.9 for polarization parallel (a) and perpendicular (b) to the F - S direction. The insets show the Fermi surface of Y 123 projected on the F - X - S - Y plane [25 ]. The solid dots in the insets give the k u for various spectra (the polar angle of the detector is indicated next to each spectrum). The double arrow denotes the polarization direction of the incident light. The thick curves for a polar angle of 8 ° are used in fig. 2(a).
0.8
0.6 0.4 0.2 0 Binding Energy (eV)
0.8
0.6 0.4 0.2 0 Binding Energy (eV)
Fig. 2. Typical experimental and theoretical ARPES spectra for .4 IIF-S and A ± F - S in the vicinity of the Fermi energy displaying the polarization dependence of the CuO2 plane band feature. The experimental data in fig. 2(a) give the 8 ° spectrum of fig. 1. The insets show the spectra over a larger binding energy range.
350
M. Lindroos et al. /Signature of ('uOe plane related band~
Y
. . . .
X
e" Fig. 3. The computed intensity of the CuO2 plane band feature as a function of the azimuthal angle of polarization of the incident light (solid curve) for a fixed value ofktl (along the F-S direction ). The experimental results are given by filled circles on which the direction of the polarization vector is shown by double arrows. The normalization between theory and experiment was determined by setting the peak height in fig. 2(a) for A L [ ' - S equal to that of the corresponding theoretical peak in fig. 2(b ). o f this feature in detail with the help of the 8 curves (thick lines) o f figs. l ( a ) and ( b ) . Figure 2 ( b ) , which gives the corresponding c o m p u t e d spectra, shows that the shape and polarization d e p e n d e n c e of the spectral feature associated with the CuO2 plane bands is r e m a r k a b l y similar to the measurements. The results o f fig. 2 are typical in that the calculated and measured spectra at nearby &l values display a similar behavior: the intensity of the CuO2 plane bands is small for A][F-S and large for A Z F - S . Figure 3 makes a quantitative comparison between the c o m p u t e d and measured polarization dependences, and the agreement is seen to be excellent. F o r this purpose, great care was taken in obtaining experimental intensities. The actual value of the beam current at the time o f m e a s u r e m e n t was taken into account for each spectral run. In all cases, the sample completely intercepted the beam. The m e a s u r e m e n t s have been repeated on different samples, and at different times, and results very similar to those o f fig. 3 have been obtained. The agreement between theory and experiment seen in fig. 3 is highly robust to variations such as small changes in the value o f / q , a n d / o r whether or not some reasonable background (several different types were tried) is subtracted from
the spectra in making such a comparison [20]. This study gives insight into the i m p o r t a n t question o f surface termination in Y123. Ba-termination is suggested by the fact that Ba-core level shifts have been reported in Y123 [21 ]. This result, however, does not rule out the presence o f other atoms on the surface, and does not d e t e r m i n e which of the two Bat e r m i n a t i o n s is prevalent The real surface may, o f course bc an a d m i x t u r e o f various ideal terminations. Although we carried out c o m p u t a t i o n s for six possible ideal terminations a d m i t t e d by the Y123 structure, all theoretical results in this article refer to the BaO/CuO2 termination, i.e. a BaO layer followed by the CuO2 plane layer. The reason is that we find that only this termination yields theoretical spectra which possess a shape similar to the measurements over the larger binding energy range of about 2 eV. As the insets in fig. 2 show, both theory' and experiment display the CuO2 plane peaks near Ev, followed by a much larger peak around 1 eV. The differences in the absolute positions o f the peaks seen in the insets are c o m m o n in first-principles contparisons of this sort even in simpler materials, and may reflect effects o f electron-electron correlations missing from the present LDA based calculations, and also of possible deviations of a real surface from the ideal one assumed here [22]. One may be tempted to conjecture that the agreement o f fig. 3 merely reflects the s y m m e t r y properties of the lattice and thus does not test the charactcr of the underlying LDA band theory based wave functions. In this connection we have repealed the calculations for other bands in Y123 (e.g. the C u - ( ) chain bands and the S-centered pillbox: none ofthesc bands has, however, so far been identified in ARPES spectra, some hints notwithstanding) and found that the associated azimuthal intensity plots like those of fig. 3 possess many different shapes, and even for tile same band, this signature can v a w between different terminations. For these reasons the presently observed agreement is nol a simple consequence of the s y m m e t r y of the wave functions forced by that o f the crystal lattice [23]. In summary, we have shown that the detailed shape and polarization dependence of the spectral feature associated with CuO2 plane bands, as predicted by the band theory framework, is in remarkable accord with the A R P E S measurements. This agreement not
M. Lindroos et al. / Signature of Cu02 plane related bands
only gives confidence in the interpretation of the ARPES data establishing the presence and size of the FS's, but also constitutes a discriminating test of the underlying band theory based wavefunctions implicit in the computations. The value of polarization dependent photoemission studies, especially when combined with first-principles computations, is emphasized by this work. Our computations also show that, of the six possible terminations, the ARPES spectra from the Y123 (001) surface are well described by the BaO/CuO2 ideal surface termination, i.e. by assuming a BaO layer followed by a CuO2 plane layer [25].
Acknowledgement We thank Roy Benedek for substantive conversations. This work was supported by the DOE under contract W-31-109-ENG-38, including a subcontract to Northeastern University, NSF grants DMR 8914120, DMR8809854, a travel grant under the US-Finland program of the NSF, and the Academy of Finland. The Synchrotron Radiation Center is supported by NSF grant DMR 8601349. We also benefited from the allocation of supercomputer time at NERSC and Pittsburgh Supercomputer Center.
References [ I ] T h e r e is a very large literature dealing with the issues mentioned in this paragraph. References [2] and [3] constitute recent volumes with extensive citations. [ 2] Fermiology of High-To Superconductors, eds. A. Bansil, A. J. Arko, R. Benedek, V.J. Emery and L.C. Smedskjaer, J. Phys. Chem. Solids 52 (1991) December. [ 3 ] Electronic Structure and Fermiology of High-To Superconductors, eds T. Takahashi, A. Bansil and H.K Katayama-Yoshida, J. Phys. Chem. Solids 53 (1992) December. [4] J.C. Campuzano et al., Phys. Rev. Lett. 64 (1990) 2308. [ 5 ] R Liu et al., Phys. Rev. B 45 ( 1992 ) 5614. [6] J.G. Tobin et al., Phys. Rev. B45 (1992) 5563. [ 7 ] G. Mante et al., Phys. Rev. B 44 ( 1991 ) 9500. [ 8 ] P.A.P. Lindberg et al., Surf. Sci. Rep. 11 (1990) 1. [9] C. Caroli et al., Phys. Rev. B 8 (1973) 4552. [ 10] J.B. Pendry, Surf. Sci. 57 (1976) 679;
351
J.F.L. Hopkinson, J.B. Pendry and D.J. Titterington, Computer Phys. Commun. 19 ( 1981 ) 69. [ 11 ] See, e.g., C.G. Larsson, Surf. Sci. 152/153 (1985) 213. [ 12] See, e.g., C.N. Berglund and W.E. Spicer, Phys. Rev. A 136 (1964) 1030. [13] F. Maca and M. Scheffier, Computer Phys. Commun. 52 (1988) 381. [ 14 ] M.A. Beno et al., Appl. Phys. Lett. 51 ( 1987 ) 57. [ 15 ] A. Bansil, S. Kaprzyk and J. Tobola, MRS Proc. 253 (1992) 505; A. Bansil and S. Kaprzyk, Phys. Rev. B 43 ( 1991 ) 10335; S. Kaprzyk and A. Bansil, Phys. Rev. B 42 (1990) 7358. [ 16] It would obviously be better to use untwinned crystals. However, straightforward symmetry arguments show that, insofar as emission along the F-S direction in Y123 is concerned, the effects of polarization can he studied via twinned specimens. [ 17 ] The simplest approach is obviously to use normally incident linearly polarized light and rotate the sample and the detector synchronously. Such a measurement, however, is not possible with our experimental setup. [ 18] For our twinned specimen, of course, the a- and b-axes are indistinguishable. [ 19 ] Theoretically, the spectra when followed as a function of k I also show two peaks crossing the Fermi energy corresponding to the two CuO2 plane bands. In fig. 2(b), one of these plane band peaks has moved above the Fermi energy. [ 20 ] The theoretical results of fig. 3 neglect Az. We have, however, carried out a number of calculations in which the effects of Az are included, and find that the presence of Az generally yields somewhat less symmetric curves than those of fig. 3. [21 ] R Liu et al., Phys. Rev. B 40 (1989) 2650. [221 Also, our wave functions may not have the right admixture of Cu 3d and O 2p states. Notably, ARPES spectra from Y123 do not display a superconducting gap. The present results suggest that the surface of Y 123 is metallic. [23] An analysis of the formalism also indicates that there is no such relationship. [24] J. Yu et al., Phys. Lett. A 122 (1987) 203; W.E. Pickett, R.E. Cohen and H. Krakauer, Phys. Rev. B 42 (1990) 8764; O.K Andesen et al., Physica C 185 ( 1991 ) 147. [251 The most sensible picture that comes to mind is that the crystal cleaves along the planes containing Cu-O chains, yielding randomly dispersed fragments of the chains on the BaO/CuO2 surface. In this way, two essentially identical surfaces would be obtained, as seems to be the case experimentally, since ARPES data from most such cleavages from various groups are quite the same. After this work was completed, an STM study just reported by Edwards et al. [ Phys. Rev. Lett. 69 ( 1992 ) 2967 ] appears to reach a similar conclusion concerning the surface termination. Apparently, CuO chain fragments do not affect the ARPES spectra much.
