Oxygen-induced surface states in YBa2Cu3O7

Vacuum/volume 41/numbers 4-6/pages 982 to 985/1990 Printed in Great Britain

0042-207X/9053.00 + .00 O 1990 Pergamon Press plc

Oxygen-induced surface states in YBa2Cu307 C C a l a n d r a , F M a n g h i and T M i n e r v a , Dipartimento di Fisica, Via Campi 213/,4, Modena, Italy

We present the results of theoretical calculations of the surface electronic structure of YBa2Cu30 z assuming different crystal terminations. Through a detailed analysis of the distribution of the valence charge near the surface we show that hole distribution may be significantly modified at the surface, due to the band narrowing and to the presence of surface states. The role of these modifications in determining the shape of the one-hole spectra is discussed.

1. Introduction

2. Charge distribution at basal plane surfaces

The recent reports of angle-resolved photoemission data on monocrystals of 1 - 2 - 3 superconducting compounds seem to support a description of the normal state of these materials as a Fermi liquid and show a dispersion of the main observed features as a function of the photoelectron parallel momentum, that may be consistent with a band picture 1-3. One of the main issues which are to be clarified for an understanding of the data is the role of the surface in determining the observed spectra. The importance of the surface and its quick degradation have been pointed out in a number of papers 4"5. The spectrum of the freshly cleaved surface is believed to reflect genuine features of the compound. However, no indications about the nature and the morphology of the surface have been provided up to now, except the fact that the cleavage occurs along the basal plane. This is not enough to specify the surface geometry, since more than one surface can be produced by cutting the crystal normal to the c-axis. In this paper we report on the results of theoretical calculations of the electronic density of states (DOS) and the correlated one-hole spectra for YBa2Cu30 7 assuming different crystal terminations. By comparing the results with those of a bulk band structure calculation we point out the natur, e of the surface-induced modifications and the differences in the spectra relative to the various surfaces. Since we have no information about the surface structure we assumed an ideal termination of the crystal i.e. without any changes in the atomic positions compared with an equivalent plane of the bulk. This is not the only factor that prevents a direct comparison with the experimental data: the neglecting of matrix elements effects and the approximations involved in the treatment of correlation may be equally important. Nevertheless we believe that our calculations are the first step in the direction of a description of the surface properties, since a knowledge of the ideal surface is required to understand any surface instability that may occur as a consequence of the cleavage. Since the theoretical approach and the method of calculations have been detailed in previous papers 6-s, we shall discuss the main results only, emphasizing the physical conclusions rather than the technical aspects.

The surfaces we have considered are shown in Figure 1. Cases A and B correspond to the crystal terminations obtained by breaking the Cu2-O4 bonds along the c-axis: the surfaces are composed of Ba-O4 and C u 2 - O 2 - O 3 ions, respectively. (Here and in the following we adopt the notation of Beno and coworkersg.) Case C corresponds to the surface obtained by removing a Y plane and is composed by Cu2-O2-O3 atoms. Clearly these are not the only surfaces that can be produced by cutting the crystal along the basal planes. Y-terminated crystals and surfaces produced by breaking the strong Cu1-O4 bonds could also be possible. However, we believe that cases A - C are adequate to illustrate the surface effects. The expected charge distribution near the surface is very different in the three cases. To elucidate this point we give in Table 1 the calculated electronic charge on the atomic sites in the bulk. It is interesting to notice how the Y and Ba electrons are distributed among the oxygens. One can easily evaluate from the table that Y gives 1.19 electrons to the 0 2 - 0 3 oxygens of the neighbouring planes. For each plane the charge provided by Cu2 atoms amounts to 1.57 electrons per planar cell, giving a total excess charge on the two oxygens equal to 2.76 electrons per planar cell, approximately 0.4 electrons less that the negative charge that can be calculated from the table. The missing charge is provided by the neighbouring Ba atoms, which in addition transfer about 1.6 electrons per Ba atom to the O i - O 4 chain oxygens. Although this description of the electronic charge is highly schematic and somewhat dependent upon the

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Table 1. Occupancies of Cu d, Y d and O p shells for the atoms belonging to the external cell in the three surfaces and in the bulk Atom

Case A

Case B

Case C

Bulk

Cu z 02 03 O4 Cut Ot Y

9.43 5.63 5.67 5.96 9.08 5.55 0.62

9.36 5.56 5.62 5.86 8.96 5.49 0.62

9.56 5.51 5.50 5.75 8.67 5.27 0.62

9.43 5.57 5.62 5.88 9.06 5.53 0.62

C Calandra et al:

Surfacestates in YBa2Cu307 N~

Cu~=~03

_w~

02

04 01

0~02 Y

A

C

[3

Figure 1. Surfaces of YBa2Cu307 crystal considered in the present work.

theoretical model Hamiltonian, it can be used to predict some of the features of the charge distribution near the surface. Consider first case A. The external B a - Q ions are almost coplanar and have opposite charges. With the removal of the C u 2 - O 2 - Q plane above the outermost Ba layer an electron charge of about 0.4 electrons becomes available and is transferred to the underlying oxygens, particularly to 04. As a consequence that B a - O 4 layer behaves as a corrugated nonpolar surface in agreement with what can be predicted on the basis of simple valence models m. These conclusions are confirmed by the calculations, shown in Table 1, giving the calculated occupancies for the atoms belonging to the outermost cell in case A. As to the case B, we expect the removal of the Ba layer to leave a Cu2-O2-O3 plane with a significant electron deficiency compared with the bulk. To keep the oxygen charge nearly constant this deficiency is compensated by a transfer of electronic charge from the Cu atoms, as indeed may be observed in the results of Table 1. Notice that not only the copper atoms belonging to the surface show an increased number of holes in the d band, but also the chain coppers. This is not surprising, since the role of the chains is essentially to behave as a hole reservoir for the planes. On the basis of the same arguments one can predict even larger effects in case C, where the breaking of Y - O bonds leaves the surface with a strong electron deficiency compared to the bulk. Electronic charge is then transferred from the underlying planes, primarily from Ba and Cu sites. Again this is confirmed by the results of the calculations reported in the table. The most interesting aspect of these results is the strong increase in the Cul 3d hole number near the surface and the comparatively slight variations in the oxygen occupancies. We will show that these results have important consequences in the one-hole spectra.

3. Local densities of states

In this section we show that the modifications of the orbital occupancies taking place in the external layers are a consequence of two effects: (a) the surface band narrowing i.e. the reduction in band width that occurs at the surface due to the reduced atomic coordination; (b) the presence of surface localized features in the electronic structure. To illustrate these points we give in Figure 2 a comparison between the bulk and the surface density of states in the three cases under consideration. The surface DOS was obtained by adding the contributions of all the planes belonging to the outermost cell. One can notice that major changes take place on passing from the bulk to the surface. In the first place the density of states at the Fermi energy E v is generally modified: it drops significantly compared to the bulk value in case A, while it is enhanced in cases B and C. Second, although there is a general correspondence between the main groups of peaks in the bulk and those in the surface DOS, the surface curves display peaks that are somewhat narrower and better defined. Third, the relative intensities of the main peaks are considerably different in the three cases and with respect to the bulk. For example in case A the structures between - 6 and - 4 eV are reduced in comparison with those located between - 4 and - 3 . 5 eV. No such behaviour is found in the other cases. The origin of these modifications is better understood by looking at the contribution of every specific atom to the local DOS, particularly for the surface atoms. For example in case C, this analysis, not reported here for space limitations, would show that the increase of the DOS at Ev, observed in Figure 2(C), is almost entirely due to oxygen-induced surface states. Moreover, the pronounced maximum at about 1.3 eV binding energy observed in the total DOS for case C corresponds to a

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C Calandra et ah Surface states in YBa2Cu307

r l l l l l l

II

I I , I I

l l l l l l l l l ' C

I r J

~ l l l l l , i l t

t

I I ~ l l ~ l l L ,

-8

-4

I

I

0 E - EI(eV)

interactions. An extension of this method to include multiplet and surface effects has been discussed by two of the present authors s. Here we present the results of the application of such approach to the three surfaces under consideration. To derive a spectrum that can be compared with the experimental EDCs one has to take into account the finite escape depth of the photoelectrons. To account for this effect we calculated the hole self-energy by adding the contributions of every atomic layer with a weight given by an exponential attenuation factor corresponding to escape depths 2 = 4,~ and 2 = 30 ,~. The first spectrum is representative of the surface behaviour, while the second one has a more significant bulk contribution. The theoretical spectra are reported in Figure 3 for the three cases. Notice that the correlated spectra extend down to about - 14 eV, well below the single particle band bottom. In particular the structure located at about - 13 eV below Er arises from the d s Cu satellite. The intensity and shape of this structure is strongly dependent upon the surface. It is wider and has a more complex shape in case C than in the other cases. This is primarily a consequence of the higher number of d holes found in the d shell of Cu~ atoms near the surface (see Table 1) and of the modifications of the copper d band in the outermost planes. On passing from the low to the high escape depth curve the maximum around - 13 eV becomes more pronounced and the satellite acquires the shape characteristic of the bulk. As to the main structures, lying between EF and --5 eV, we notice that the first peak, located around - 1.7 eV, is larger and more asymmetric on the high binding energy side in cases B and

Figure 2. Comparison between the bulk DOS and the DOS of the external cells in the three cases.

narrow surface localized Cu d state, which is responsible for the sharp peak found in the partial DOS at the same energy. Also the narrowing of the maximum in the structures around - 3 eV observed in Figure 2(C) is a consequence of the strong reduction of the intensities of both C u d and O p partial surface DOS at this energy with respect to the bulk. By similar comparison it is possible to understand the different behaviour of the bulk and surface DOS in the three cases and to point out the relati~,e importance of the surface states in determining the electronic structures of the first few layers.

i i i i i I i i i i i i i i, i ./"

/'X

4. One-hole spectra

Although the local densities of states provide quite a detailed description of the behaviour of an electron near the surface, they are not directly comparable with the outcomes of spectroscopical measurements. Indeed, even assuming that transition matrix elements do not play an important role and can be taken constant, the self-enery effects arising from the Coulomb correlation cannot be neglected. If we limit our consideration to the photoemission data, in order to obtain theoretical spectra that can be compared with the measured energy distribution curves (EDC), one has to calculate the one-hole spectral function, which is connected to the self-energy'L An approximate approach to calculate this quantity, based on a Hubbard model Hamiltonian, which includes intra-site Coulomb interaction between two holes on the same oxygen or copper ion, has been developed by Chang and coworkers 12. The self-energy is evaluated using the so called t-matrix approximation, which is valid in the limit of low density of holes for any value of the Coulomb 984

AtI ~ i 1 i i~ i 1i i /]i i~ i L~

- 15

- 10

-5

Figure 3. Correlated one-hole spectra for the three surfaces. Full line curves are evaluated using an escape depth 2 = 4 A, dotted line curves with 3. = 30 A.

C Calandra et al: Surface states in

YRa2CLI307

C than in case A, where the difference between the two spectra are more pronounced. This peak is mainly C u d in character, although the oxygen contribution cannot be neglected due to the large Cu d - O p hybridization, that characterizes these compounds. Its shape does not change appreciably on changing 2 for a C u 2 - O 2 - O 3 termination, but is considerably narrower for small 2 when the surface is terminated by B a - O 4 atoms. To a large extent this is due to the modifications of the oxygen states near the Fermi energy, which is more pronounced when C u 2 - O 4 bonds are cut. The structure at higher energy lies around - 3.7 eV in case A, where it has an intensity comparable with the main peak, and above 4 eV in cases B and C. It shows the minimum intensity with respect to the main peak in case B, where it does not differ appreciably from the bulk emission. The enhancement compared to the bulk found in cases A and C is primarily a consequence of the pressure of oxygen induced surface states at these energies. In case A this effect is particularly strong and leads to a considerable narrowing of this structure compared to the bulk.

Acknowledgements We acknowledge finantial support from Ministero Pubblica Istruzione and technical assistance from C I C A I A .

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