fulltext

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The sliding bond mechanism for high-T

c

superconduction

in YBCO cuprate

P. BROVETTO, V. MAXIAand M. SALIS

INFN-GNSM - Cagliari, Italy

Istituto di Fisica Superiore, Università di Cagliari - Cagliari, Italy (ricevuto il 10 Dicembre 1996; approvato il 18 Febbraio 1997)

Summary. — The YBCO crystal cell consists of three superimposed perovskitic

cubes, the middle one holding yttrium at its centre. Divalent copper ions at the yttrium cube vertices are kept in lacunar oxygen octahedra. Copper ions exhibit unpaired electrons facing each other at opposite sides of the oxygen lacunae. These dangling electrons combine with opposite spins originating very faint covalent bonds which allow for superconducting pairs, as occurs for the Cooper pairs in metals. On this basis, simple calculations readily explain the real YBCO critical temperature. Moreover, the considerable effect of pressure on the critical temperature, shown by experiments, is also justified.

PACS 74.10 – Supercoductivity: Occurrence, potential candidates. PACS 74.20 – Theories and models of superconducting state.

1. – Introduction

We precede our arguments on high-Tc superconduction with a brief survey of the

pairing correlations in fermion systems. The Fermi-gas model, which neglects interactions between particles, is the simplest model that applies to many-body problems concerning fermions. This model maintains that fermions move in a self-consistent field which averages their mutual interactions. However, the real interactions cannot be reduced simply to a self-consistent field. After separation of the self-consistent part, there remains some interaction between the particles. This residual interaction is responsible for the formation of Cooper’s pairs in superconducting metals [1, 2] and of the pairing correlation in nuclear matter [3, 4]. In metals, the moving electrons drag nearby positive ions so that electric dipoles, which are lined up with the electron momenta, originate. These dipoles interact in such a way that quasi-bound electron pairs, with equal and opposite momenta near the Fermi surface, are made possible. This mechanism, which relies on the elastic properties of the lattice, can be properly described as an exchange of virtual phonons between moving electrons. In nuclear matter, the pairing correlation couples nucleons with 73

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opposite angular momenta, an effect that explains the energy gap observed in the spectra of even-even nuclei.

The most convenient method for dealing with the afore-mentioned pairing correlations is the canonical transformation of Bogolyubov [5]. Utilizing a linear substitution on annihilation and creation operators, a ground state of the system is obtained in which the original fermions are substituted by non-interacting quasi-particles. The density of states is modified and a forbidden energy gap of amplitude 2 D0appears across the Fermi surface. In metals, the presence of this energy

gap entails superconduction. Its half-amplitude D0is precisely the binding energy of a

Cooper pair. It has been shown that the energy gap is still present when the temperature is different from zero, that is for excited states of the fermion system [6-8]. The energy gap decreases as temperature increases, going to zero at a critical temperature Tcrelated to the zero-temperature gap by

D0` 1 .76 Q kTc.

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This is to say that Tc is the actual temperature of the superconductive transition.

The above arguments on pairing correlations are quite general. They can indeed be applied both to metals and nuclear matter without recurring to a specific pairing mechanism. This leads one to believe that high-Tcsuperconduction in cuprates is also to

be ascribed to a pairing effect. Different pairing intermediates, that is, phonons once again as in Cooper’s pairs, excitons, plasmons and polarons have so far been considered [9]. A mechanism based on spin waves has also been proposed and has received special attention [10]. Experiments on superconducting three-junctions rings, performed by epitaxially grown films of YBCO, have shown that the superconducting wave function is characterized by d-symmetry [11]. This result seems to rule out Cooper’s pairs, which are characterized by s-symmetry. And yet, nearly all the pairing mechanisms so far proposed are compatible with d-symmetry. In reality, neither symmetry nor other experiments have produced conclusive evidence in singling out the correct model. The most widely accepted opinion is that the true mechanism of high-Tc

superconduction still remains to be found. For this reason, we propose here a different model based on the exchange mechanism allowing electrons to combine in pairs with opposite spins thus originating covalent bonds. For definiteness, we will consider YBCO cuprate which perhaps remains the most interesting high-Tcsuperconductor.

2. – Electron pairing by covalent bonds

YBCO shows a variable Y Ba2Cu3O7 2d stoichiometry depending on the degree of

copper oxidization. With d 40, that is, with the highest oxidization degree, the stoichiometry can be written in the form: Y Ba2CuII2 CuIIIO7p2, p standing for an

oxygen lacuna. The YBCO orthorhombic cell (S.G. Pmmm, a04 3 .82 Å, b04 3 .86 Å,

c04 11 .68 Å) is composed by three superimposed perovskitic cubes, with copper at the

cube vertices and oxygen or oxygen lacunae at the edge midpoints. The middle cube, whose vertices hold the divalent copper, holds yttrium at its centre and the others hold barium. Owing to the oxygen lacunae, divalent copper shows a piramidal configuration and trivalent copper a planar configuration with respect to oxygen. With this cell structure, the lattice is cut into two equivalent parts by the planes orthogonal to the

c-axis crossing the yttrium atoms. In fig. 1, two neighbouring yttrium-containing cubes

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Fig. 1. – Schema showing two contiguous perovskitic cubes of the YBCO lattice holding yttrium ions (circles) at their centres. Copper ions, a and b, are indicated by means of the angular patterns of dz2orbitals. Lacunar oxygen octahedra are sketched by means of their edges. Oxygen lacunae

are indicated by crosses. Black dots represent the unpaired 3 d electrons in 11O2 and 21O2 spin states (arrows).

The divalent copper is characterized by the argon configuration followed by nine electrons in 3d-states. Therefore, just one d-state out of five remains half-filled. Taking into account that each copper ion engages a cubic volume with a side of about 3.9 Å, the density of unpaired electrons in the half-filled 3d-states is 1 .8 Q 1022cm23_{, that is about}

20% of the electron density in metal copper. This means that in the layer around the plane of yttrium ions a half-filled electron band capable of metal-like conductivity is present. Above the critical temperature, YBCO shows, indeed, a resistance increasing with temperature as in metals. However, it is also to be considered that, because of the oxygen lacunae along the lines joining the copper ions, electrons in the half-filled

d-states are able to combine with opposite spins, thus originating spin-singlet covalent

bonds (see fig. 1). The large distance between the copper ions, that is about 3.9 Å, makes these bonds very faint, but, in spite of this, still sufficient to explain the residual interaction responsible for the appearance of superconducting pairs. Actual energies of covalent bonds are, indeed, on the order of some eV, which, on a temperature scale, corresponds to some ten thousand K. Therefore, only a small fraction of this energy is required to explain an electron coupling which, on account of eq. (1), allows for Tc

values near 102_{K. With this interpretation, at temperatures below T}

c, electrons slide in

the layer around the yttrium ions, while they remain bound in pairs by residual covalent forces.

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To deal with covalent bonds, the classic method of Heitler and London can be readily applied. The two-electron symmetrical (spin-singlet) and antisymmetrical (spin-triplet) wave functions are [12, 13]

CS , A( 1 , 2 ) 4

1

k

_{2( 1 6S}2₎

[ua( 1 ) ub( 2 ) 6ua( 2 ) ub( 1 ) ] ,

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ua and ub standing for the wave functions of the d-electron belonging to the bound

copper ions and

S 4

ua( 1 ) ub( 1 ) dt1

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for the overlap integral. The corresponding energies are

WS , A4 2 W01 (Ze)2 rab 1 2 J 1J 86 (2SK1K 8) 1 6S2 , (4)

W0 standing for the energy of d-electrons in ua( 1 ) or ub( 1 ) states, (Ze)2O rab for the

Coulomb energy of the interacting copper ions, while

J 42Ze2

ua( 1 ) 2 r1 b dt1 (5) and J 84 e2

ua( 1 ) 2 ub( 2 ) 2 r12 dt1dt2 (6)

are Coulomb-like integrals for the interaction of electrons with ions and for the mutual interaction of electrons, respectively, and

K 42Ze2

ua( 1 ) ub( 1 ) r1 a dt1 (7) and K 84 e2

ua( 1 ) ub( 1 ) ua( 2 ) ub( 2 ) r12 dt1dt2 (8)

are exchange integrals. In the previous equations, Z means the effective nuclear charge of copper ions, r1 b the distance of electron 1 from ion b and r12 the distance

between the electrons. With the proposed interpretation, the superconducting forbid-den energy gap is iforbid-dentified with the triplet-singlet energy separation, that is

2 D04 WA2 WS.

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Owing to the large distance between a and b ions, the Coulomb-like integrals J and

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to be written as

D04 2( 2 SK 1 K 8 ) .

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As for the real form of states ua and ub, any d-state might be considered in principle.

However, states dz2 and d_x2_{2 y}2 are surely well-suited for originating covalent bonds,

since they exhibit prominent lobes which can be directed along the line joining the copper ions (see fig. 1) [14]. Consequently, the overlapping electron density ua( 1 ) ub( 1 )

thickens in a narrow region between the ions. By utilizing reasonable assumptions, this allows us to reduce the evaluation of integrals K and K 8 to a simple problem of electrostatics. Calculations are greatly facilitated and the problem, although with limited accuracy, can be handled in an analytical way. The procedure is reported in appendix. Taking into account the values of K and K 8 given in eqs. (A.20) and (A.25), respectively, it follows from eqs. (1) and (10)

1 .76 kTc4 6 S2

k

Z 2 1 10log

g

35 12 Q ZD 3 a0

h

l

e2 D , (11)

D standing for the distance rabbetween the interacting copper ions and a0for the Bohr

radius. The overlap integral, reported in eqs. (A.10) and (A.11), is

S 4 1 315

g

ZD 3 a0

h

6 exp

k

₂ZD 3 a0

l

, (12)

for dz2states. For dx22 y2states, eq. (12) once again holds, but the factor 1 O315 is to be

substituted by 1 O420. Equations (11) and (12) allow us to evaluate the critical temperature Tcif the actual value of the effective nuclear charge Z is known. Assuming

wave functions of the form rp

exp [2ra], we have [15]

a 4 (Znuc2 s) O n ,

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where Znucmeans the real nuclear charge, s the screening constant and n the principal

quantum number. For a 3 d-shell with one screened and eight screening electrons, we have s( 3 d) 413.589410.269338415.7438. It follows: a(3d) 4 (29215.7438)O34 13.2562O3. The screened nuclear charge Zsc is related to a( 3 d) by a( 3 d) 4ZscO ( 3 a0),

which, being a04 0 .529 Å, leads to Zsc4 7 .01. This result applies to isolated copper ions.

In the present case of ions lying inside a crystal lattice, the situation is different. It must in fact be kept in mind that YBCO shows a layered structure consisting of planes of yttrium ions and oxygen lacunae alternating with layers bearing oxygen, copper and barium ions (see fig. 1). The yttrium-lacuna planes exhibit a net positive charge, the interposed layers an equivalent negative charge. Thus, electrons in the bonding 3 d-lobes experience an electric field which attracts them towards these planes. To evaluate this field, let us consider a copper ion lying at the centre of a regular oxygen octahedron. The fields originated by the oxygen ions are mutually balanced so that the electric field, as well as the electric field gradient, vanishes at the octahedron centre. Therefore, oxygen lacunae are equivalent to double positive charges lying on the yttrium planes. Since lacunae are situated at the centre of squares of four yttrium ions, simple geometrical considerations lead to

Zsce r2 3 d 2 2 e (D O22r3 d)2 2 12 e(D O22r3 d) ( 3 D2 O 4 2 Dr3 d1 r3 d2 ) 4 Ze r2 3 d , (14)

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r3 dstanding for the 3 d-shell radius. The meaning of this equation is simple: the copper

ion electric field Zsce Or3 d2 is decreased by the crystal field originated by the oxygen

lacuna and the surrounding square of yttrium ions so that the strength of field acting on the bounding 3 d-lobe becomes Ze Or2

3 d, Z standing for the effective charge to be

accounted for. Of course, this entails the spherical symmetry of the electric field around the copper ions being removed and the bonding 3 d-lobes being somewhat stretched towards the yttrium-lacuna planes. Equation (14) can be rewritten as

Z 4Zsc2 2 [D O (2r3 d) 21]2 2 12[D O (2r3 d) 21] [ 1 2DOr3 d1 3 D2O ( 4 r3 d2) ]3 O2 , (15)

which, for D 43.9 Å and by assuming r3 d4 0 .69 Å, that is the standard radius of the

divalent copper ions [16] leads to Z 46.15. Thus, the correction due to the crystal field corresponds to about 12% of the Zsc value, due mainly (i.e. 8.6%) to the effect of the

oxygen lacunae.

The correction just examined deserves some remarks. It constitutes a first approximation which should be substituted by a more accurate treatment. This might be based on perturbative methods. This kind of approach, however, would require complex numerical calculations which are out of place in the present preliminary account of the high-Tc problem. In any case, it is worthwhile noting that direct

experimental evidence of the presence of a crystal field has been obtained by means of Mossbauer spectroscopy. By substituting 5% of the copper ions with trivalent iron, a spectrum showing a large quadrupole splitting, originated just by the crystal field spoken of, was recorded [17].

Fig. 2. – Expected YBCO critical temperature as a function of the effective nuclear charge Z. The dashed line marks the abscissa Z 46.15.

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Fig. 3. – Rise of YBCO critical temperature originated by a decrease in size of the perovskitic cubes.

In fig. 2, the computed Tc values are plotted vs. Z. It appears that Tc increases

steeply when Z drops below 6.5. For Z 46.15, we have Tc4 51 K with dx2

2 y2orbitals

and Tc4 90 K with dz2orbitals. Even though the good agreement of this latter figure

with experimental value is to be regarded as fortuitous (YBCO shows indeed Tc` 92 K)

the data of fig. 2 prove that critical temperatures on the order of 102K can be readily explained by the proposed pairing mechanism. However, the most significant result is the large increase in Tc originated by a slight decrement of distance D. In fig. 3, Tc is

reported vs. D in the interval from 3.90 Å to 3.80 Å. In this interval, Tc values rise by

more than 30 K. It follows that critical temperature is expected to be quite sensitive to high pressures capable of decreasing ion distances. Such an effect is a peculiarity of the pairing mechanism considered here, which is essentially controlled by the magnitude of the overlap integral S.

3. – Discussion and conclusions

When dealing with the theory of superconduction in cuprates, the main goal is obviously to explain how Tc succeeds in reaching values on the order of 102K. For this

reason, in applying the devised model, approximations which, in principle, avoid overestimations of the Tc value have been considered. Indeed, the Heitler and London

approximation in all likelihood underestimates the bonding energy, as occurs for the hydrogen molecule. Moreover, in evaluating D0by means of eq. (10), the contribution of

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integrals J and J 8 has been neglected. If included, this contribution would increase energy D0 by a small term S2( 2 J 1J 8). However, other approximations less clear in

nature and which might act in the opposite way have inevitably been introduced. Let us quote, in this connection, the evaluation of the exchange integrals K and K 8 and the effect of the crystal electric field. Errors of different origins probably counterbalance each other.

Another point worth considering is the possible hybridization of 3 d-orbitals with 4 s-orbitals, whose energy is indeed not much different. If this occurs, the negative lobes of 3 d-orbitals decrease with a corresponding increase in the positive ones, thus allowing for higher values of the overlap integral S , that is, according to eq. (11), of Tc.

For this reason, the value Tc4 51 K corresponding to dx2_{2 y}2orbitals might increase to

the actual YBCO critical temperature. On the other hand, the mixing of 3 d and 4 s orbitals can be cited also in explaining some uncertain results on the symmetry of the superconducting wave function, which indicate a contribution of s-waves [18]. This means that although dz2 orbitals are more effective in originating superconducting

electron pairs, dx2_{2 y}2 orbitals may also play this role. The identification of the true

orbitals responsible for electron pairing remains an open question.

All the previous arguments deal with the divalent copper ions. But the YBCO cell also includes a trivalent copper ion, whose 3 d-shell contains eight electrons. Therefore, the presence of unpaired electrons capable of originating covalent bonds cannot be asserted a priori. Nevertheless, trivalent copper may still exhibit two unpaired electrons capable of originating two bonds. In this case, the situation would be similar to that of divalent copper, although with a quite different lattice framework. This would probably originate a different superconductive transition with a different Tc. In any

case, it appears unnecessary to dwell here on this uncertain matter, since divalent copper already yields a suitable field to discuss superconduction.

We now come to the expected effect of pressure on the actual value of Tc. Many

papers have appeared up to now on this argument, concerning different cuprates. Measurements on YBCO of standard stoichiometry Y Ba2Cu3O7 2d and with different

partial substitutions of yttrium and barium atoms indicate a pressure effect of 0.96 K OGPa for PE0.6 GPa [19]. This figure is thought to last unchanged up to pressures less than 20 GPa. Other measurements have shown higher values of dTcO dP

which vary from 4 to 7 K OGPa for oxygen-deficient samples of YBCO [20-23]. A large effect of pressure on Tc has actually been observed with Hg Ba2Ca2Cu3O8 1dcuprate.

At zero pressure, this material exhibits the largest Tcfound till now, that is, Tc4 135 K.

Under a pressure of 15 GPa its critical temperature increases up to 153 K, which corresponds to dTcO dP 4 1 .2 K O GPa [24]. These experimental results yield a

qualitative evidence in favour of the mechanism proposed here. However, few data suitable for a quantitative comparison are available on the dependence of cell size on pressure. Measurements performed at pressures up to more than 12 GPa on samples of stoichiometry Y Ba2Cu3O6.85 indicate linear compressibility dDOdP`0.006 ÅOGPa [25].

Since data in fig. 3 yield dTcO dD 4 450 K O Å with dz2 orbitals and dT_cO dD 4

260 K OÅ with dx2

2 y2 orbitals, this compressibility leads to dTcO dP 4 2 .7 K O GPa

and dTcO dP 4 1 .6 K O GPa for the quoted orbitals, respectively. Other measurements

for pressure up to about 0.6 GPa on samples of stoichiometry Y Ba2Cu3O6.93

have been reported, which lead to a greater compressibility, that is dD OdP4 0.017 ÅOGPa [26]. With this compressibility, we obtain dTcOdP47.8 KOGPa and dTcOdP4

4 .5 K OGPa for dz2 orbitals and d_x2

2 y2 orbitals, respectively. These figures likely

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are considerably influenced by the oxygen content, the calculated dTcO dP values appear

to be in acceptable agreement with experimental ones.

We deem it useful to conclude our arguments on high-Tc superconduction by

comparing the electron coupling mechanism proposed here with the Cooper coupling mechanism. In both cases, electron coupling is mediated by the ion lattice. In metals, the displacement of positive ions acts as a source of virtual phonons, thus giving rise to attractive forces which allow electrons to move in pairs. In cuprates, copper ions intervene by means of their Coulomb field which, owing to exchange integrals K, couples the electrons in singlet states. This originates the residual interaction which allows electron pairs to slide along the yttrium-lacuna planes as free quasi-particles. In our opinion, electron coupling by means of faint covalent bonds represents the simplest and most conservative hypothesis. The dangling electrons on the facing copper ions (see fig. 1) actually show a marked tendency to combine in singlet states, as everywhere occurs with dangling electrons of free radicals. After all, the coupling mechanism proposed here relies on the old and well-established idea of Lewis’ electron pairs, dating back to 1916 [27].

AP P E N D I X

a) The overlapped charge density. – The radial part of dz2and d_x2_{2 y}2orbitals is

R32(r) 4 4 9k30

g

Z a0

h

3 O2

g

Zr 3 a0

h

2 exp

k

₂ Zr 3 a0

l

, (A.1)

Z standing for the effective nuclear charge and a0 for the Bohr radius. The angular

parts are, respectively,

f20(z Or) 4 k5 4 kp 3 z2 2 r2 r2 (A.2) and f22(x Or, yOr) 4 k15 4 kp x2 2 y2 r2 . (A.3)

In the following, for brevity’s sake, we will consider only the dx2_{2 y}2orbital, since the

results, barring a factor 2 Ok3 , apply to the dz2orbital as well. By putting y21 z24 l2,

we have r 4x

k

1 1 (lOx)2` x 1l2

O 2 x , which entails a factor exp [2Zl2O 6 a0x]

appearing in the radial part of the dx2_{2 y}2orbital. Consequently, the probability density

decreases quickly as the distance l from the x-axis grows larger. This is to say that

r ` x and y ` 0 , so that the factor f22can be reduced to a constant value. In this way,

the electron state ua( 1 ) can be written in the form

(A.4) ua( 1 ) 4 1 9k_{2 p}

g

Z a0

h

(A.6)

which is a quantity showing a maximum when j 40, that is when x1 a4 x1 b4 D O 2 .

Taking into account that significant contributions to r( 1 ) arise when l2

b2 x_{1 a}x1 b and

12

35 3 a0

ZD .

(A.13)

In this way, and taking into account eq. (A.10), eq. (A.7) becomes

r( 1 ) 4 1 96 pD3

g

ZD 3 a0

h

7 exp

k

₂ZD 3 a0

l

Q F(Q1) 4 35 8 p Q ZD 3 a0 Q S D3 Q F(Q1) , (A.14)

with F(Q1) 41, or F(Q1) 40, for Q1 inside, or Q1 outside, the ellipsoid volume,

respectively. This approximation is justified by the fact that the most significant terms appearing in the expression of r( 1 ) are the factors preceding F(Q1). Indeed, the main

dependence on ion separation D is related just to these very factors. With eq. (A.14), the problem of evaluating the bonding energy can be reduced to a simpler problem of electrostatics.

c) Evaluation of integral K. – Utilizing eqs. (7) and (A.14), the integral K takes

the form K 42Ze2

r( 1 ) r1 a dt14 2Ze2 35 8 p ZD 3 a0 S D3 Q

F(Q1) r1 a dt1. (A.15)

According to known equations, the electric potential at point P(x , y , z) lying inside a prolate ellipsoid of major semiaxis a and minor semiaxis b filled with a unitary charge density, is given by [28]

F(Q1) r1 a dt14 2 p[R 2 2 Ax22 B(y21 z2) ] (A.16) with R 4 b 2 2 e log 1 1e 1 2e , A 4

g

b a

h

2 ₁ e3

u

log

o

1 1e 1 2e 2 e

v

, B 4 1 2( 1 2A) , (A.17)

e 4

k

1 2 (bOa)2_{standing for ellipsoid eccentricity. Utilizing eq. (A.13) and taking into}

account that a 4DO2, we have (bOa)2

4 ( 38 O 35 )( 3 a0O ZD), which, being a0bD , is a

small quantity. We thus have e ` 1 2b2

O 2 a2, which allows us to write

R 4b2_log

g

2 a b

h

, A 4 b2 a2

k

log

g

2 a b

h

2 1

l

. (A.18)

In this way, the potential at point x 42DO2, y4z40, that is the point-position of ion

a, turns out to be

F(Q1 ) r1 a dt14 2 p[R 2 A(D O 2 )2] 4 72 p 35 Da0 Z . (A.19)

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Substituting in eq. (A.15) and remembering eq. (A.10), we thus obtain

K 423SZe

2

D .

(A.20)

d) Evaluation of the integral K 8. – Taking into account the overlapped charge

density, eq. (8) can be written as

K 84 e2

r( 2 )

y

r( 1 ) r12

dt1

z

dt2,

(A.21)

which, barring a factor 1 O2, represents the electrostatic energy of the overlapped charge distribution. By considering, as for eq. (A.16), a unitary charge density lying inside the ellipsoid volume, we have

_F(Q₂₎

_y

F(Q1)

r12

dt1

z

dt24 2 p

[R 2Ax22 B(y21 z2) ] dx dy dz ,

(A.22)

where x, y, z now mean the coordinates of point Q2, the integration being extended on

the ellipsoid volume. That is, performing some calculations and utilizing eqs. (A.17),

_F(Q₂₎

_y

F(Q1) r12 dt1

z

dt24 2 p

2a 1a

0 bk1 2x2_{O a}2 (R 2Ax2 2 Br2) 2 pr dr dx 4 (A.23) 4 4 p2

g

2 3Rb 2 a 2 2 15Ab 2_a3 2 4 15Bb 4_a

h

4 8 15p 2_ab4 1 e log 1 1e 1 2e . This result is obtained without approximations. By substituting the eccentricity with

e ` 1 2b2

O 2 a2, utilizing eq. (A.13) and putting a 4DO2, we obtain

_F(Q₂₎

_y

F(Q1) r12 dt1

z

dt24 1728 p2 6125 D3a02 Z2 log

g

35 12 Q ZD 3 a0

h

. (A.24)

Finally, taking into account eq. (A.14), simple substitutions lead to

K 84 3 5 S 2_log

g

35 12 Q ZD 3 a0

h

e2 D , (A.25)

which is the result searched for. It is to be noted that eqs. (A.20) and (A.25) apply both to dx2_{2 y}2and d_z2orbitals, provided that the proper S value given in eqs. (A.10) or (A.11)

is utilized.

R E F E R E N C E S

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[2] BARDEENJ., COOPERL. N. and SCHRIEFFERJ. R., Phys. Rev., 108 (1957) 1175. [3] BOHRA., MOTTELSONB. R. and PINESD., Phys. Rev., 110 (1958) 936.

[4] BELYAEVS. T., Mat. Fys. Medd. Dan. Vid. Selsk., 31, no. 11 (1959).

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[6] GOR₈KOVL. P., Sov. Phys. JETP, 7 (1958) 505. [7] ALEKSEEVA. I., Sov. Phys. Usp., 4 (1961) 1, 23.

[8] ZIMAN J. M., Principles of the Theory of Solids (Cambridge University Press) 1965, Chapt. 11.

[9] See for instance, RUVALDS J., Supercond. Sci. Technol., 9 (1966) 905 and references therein.

[10] SCALAPINOD. J., Phys. Rev., 250 (1995) 329.

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[12] PAULINGL. and WILSONE. B., Introduction to Quantum Mechanics (McGraw-Hill Book Co., New York) 1935, Chapt. XII.

[13] SLATER J. C., Quantum Theory of Matter (McGraw-Hill Book Co., New York) 1968, Chapt. 21.

[14] GRAYH. B., Electrons and Chemical Bonding (W. A. Benjamin Inc., New York) 1964. [15] CLEMENTIE. and RAIMONDID. L., J. Chem. Phys., 38 (1963) 2686.

[16] See for instance, Table of Periodic Properties of the Elements (Sargent-Welch Scientific Company, Chicago) 1966.

[17] CHEREPANOVV. M., CHUEVM. A., YAKIMOVS. S., GONCHAROV V. YA. and SMIRNOVS. A., JETP Lett., 47 (1988) 424.

[18] MULLERK. A., Nature, 377 (1995) 133.

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[20] MURAYAMAC., MORIN., YOMOS., TAKAGIH., UCHIDAS. and TOKURAY., Nature, 339 (1989) 293.

[21] SCHIRBERJ. E., GINGLEYD. S., VENTURINIE. L. and MOROSINB., Phys. Rev. B, 35 (1987) 8709.

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[24] CHUC. W., GAOL., CHENF., HUANGZ. J., MENG R. L. and XUEY. Y., Nature, 365 (1993) 323.

[25] SUENAGAKAZUFUMIand OOMIGENDO, Physica C, 185-189 (1991) 1297.

[26] JORGENSEN J. D., PEI SHIYOU, LIGHFOOT P., HINKS D. G., VEAL B. W., DABROWSKI B., PAULIKASA. P., KLEBR. and BROWNI. D., Physica C, 171 (1990) 93.

[27] LEWISG. N., J. Am. Chem. Soc., 38 (1916) 762.

fulltext

The sliding bond mechanism for high-T

superconduction

in YBCO cuprate

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