Van Hove singularities and the role of doping in the stabilization, synthesis and superconductivity of HgBa2Can−1CunO2n+2+δ

PHYSICA

Physica C 216 (1993) 273-283 North-Holland

Van Hove singularities and the role of doping in the stabilization, synthesis and superconductivity of HgBaECa._ 1 C U n O E n + 2 + J D.L. Novikov and A.J. Freeman Science and Technology Center for Superconductivity, Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208-3112, USA

Received 9 August 1993

The electronic structure and Fermi surface of the recently discovered HgBa2Ca._~CunO:.+2+6superconductors have been determined using the full potential linear muffin-tin orbital method and precise structural information determined with neutrons by Radaelli et at. Whereas for stoichiometric HgBa2CuO4 (Hg-1201) the only band crossing the Fermi energy derived from the Cu-O antibonding state is half-fiUed, an additional Hg-O band that crosses EF exists in the case of HgBa2CaCu206 (Hg-1212) and HgBa2Ca2CuO4Os(Hg- 1223). Thus, stoichiometric HgBa2CuO4is expected to be a Mott insulator with dopants essential for forming the normal metallic state that leads to superconductivity at 95 K, in contrast to two other members of the Hg family that are expected to be "self-doped" to a metallic normal state. As in Hg-1201, the electronic structure is two-dimensional and is dominated by van Hove singularities (vHS's) to which EF is pinned by dopants whose calculated concentration is found to agree well with that determined by Radaelli et at. for Hg-1212 for their maximum T¢= 128 K sample. Finally, predicted doping levels for stabilizing a large volume of the high-ToHg-1223 phase - and hence its highest T~ - are made on the basis of pinning Er to the vHS.

1. Introduction The recent discoveries of superconductivity at 94 K in the single layer CuO2-compound HgBa2CuO4+6 (Hg-1201) by Putilin [ 1 ] and reproduced by Wagner et al. [ 2 ] has been followed rapidly by the synthesis and measurement o f the multi-layer compounds HgBa2Ca,_ iCu,O2,+2+a. Thus, superconductivity at 133 K in a mixed material containing HgBa2CaCu206+6 (Hg-1212) and HgBa2Ca2CuaOs +a (Hg- 1223) was reported by Schilling et al. [ 3 ]; X-ray data on Hg- 1212 were reported in ref. [4] and more precise neutron powder diffraction results on Hg- 1212 were presented in ref. [ 5 ] and at 135-140 K in the same kind o f materials by Gao [ 6 ] and Meng [ 7 ]. Along with the superconductivity found in the "infinite layered" (IL) (SrxCal_x) CuO2 systems [8] these discoveries have stimulated intense activity in investigating and understanding this new record-breaking class o f superconductors. Apart from the fact that these materials are very promising for practical applications due to their higher irreversibility line [6,9], their simple

structure and composition may also provide a good opportunity to explore the underlying physics o f highTc superconductivity phenomena observed in the layered cuprate materials. Strong similarities in their crystal structure i.e. Hg-1201 containing one C u - O layer per unit cell, Hg-1212 two layers, Hg-1223 three layers and the IL material an "infinite" number of C u - O layers (which means absence o f H g - O blocks in the structure), allow for a study of their systematics and an attempt at least to trace correlations between some features o f the band structure and the observed Tc values. In previous publications [ 10,11 ] we reported detailed results o f full potential linear muffin-tin orbital ( F L M T O ) band structure calculations o f IL and Hg-1201 superconductors along with an analysis o f the Fermi surface (FS) topology in those compounds. We found strong correlations between the pinning o f the Fermi level to the vicinity of the van Hove saddle-point singularity (vHS) by dopants and the m a x i m u m value of To. In this paper we report results o f band structure calculations o f two other members o f the Hg-

0921-4534/93/$06.00 © 1993 Elsevier Science Publishers B.V. All fights reserved.

274

D.L. Novikov, A.J. Freeman / vHS's and the role of doping

Ba2Can-lCUnO2n+2+6 family, that demonstrate the highest Tc's and investigate further the possible role of dopants in stabilizing the structure and the effects of pinning EF tO the vHS on the observed To. For completeness, we compare these results to the earlier obtained results for Hg-1201, but here redone with more precise parameters. Unlike the case for Hg1201, we find that in Hg-1212 and Hg-1223, an additional Hg-O-derived band crosses EF and so is partially occupied in their stoichiometric compositions. While this allows these materials to become metallic in their normal state (i.e., self-doped), it also means that higher doping levels are required to pin EF to the van Hove singularity and thus to achieve a maximum T¢. Our calculated doping level for pinning to the vHS in Hg-1212 is found to be in very good agreement with the neutron results of RadaeUi et al. [ 5 ], as it was for the case of Hg- 1201 [ 10 ] and the infinite layer material [ 11 ], (Sr~ _xCax)l_yCu02. Thus, our results lend strong support to our earlier finding that the vHS may play a dominant role in the superconductivity of these quasi-2D high-T~ systems. Further, they again call attention to vHS-based excitonic pairing mechanisms for superconductivity, as emphasized in the recent work of Markiewicz [ 12 ], Newns et al. [ 13 ] and Bok [ 14 ]. Finally, these findings also may be useful in predicting a synthesis pattern and doping levels for stabilizing a large volume of Hg-1223 and hence its maximum T~.

2. Method and approach To determine the electronic structure of these compounds, we used the full potential linear muffintin orbital (FLMTO) method [16] within the local density approximation (LDA) and the CeperlyAlder form of exchange-correlation potential. In these calculations no shape approximations are made to either the charge density or the potential. The structural parameters for Hg-1201 were determined in ref. [ 2 ]. The lattice parameters for Hg1212 were first published in ref. [4], where Putilin et al. [ 4 ] reported that the Hg- 1212 structure contains "distorted" Cu-O planes, with oxygen atoms shifted by about 0.17 A from their "in-plane" positions towards each other. But recent investigations [ 5 ] of Hg- 1212 using neutron powder diffraction do

not confirm the conclusions made in ref. [4]. Here we report results using the crystal parameters for Hg1212 from ref. [ 5 ], with the very small "buckling" parameter of 0.01 A found there. Since no reliable data on the Hg-1223 system are available, we "deduced" the crystal structure of this material from the Hg-1212 data by adding an additional undistorted Cu-O plane and keeping the a parameter equal to that found in ref. [5] for Hg-1212. The lattice constants used in our calculations, atomic positions and some computational parameters are listed in table 1. The FLMTO calculations were performed in the spin-restricted scalar-relativistic mode with atomic Ba5p66s 2, Hg5dl°6s 2, Cu3dl°4s I, Ca4s 2 and O 2s22p 4 levels treated as valence band electrons and Ba 5s 2, Hg 5s25p 6 and Cu 3s23p 6 treated as semicore states (in a second energy window). It is well known that the LMTO scheme of band calculations works well for close-packed structures. In order to get a more close-packed structure, empty spheres were introduced at the sites listed in table 1. We carefully chose the MT-radii based on the spatial distribution of the self-consistent charge density over the unit cell. We preferred to use the set of radii shown in table 1 since these attribute charge densities centered at different atoms to their corresponding spheres, leaving only relatively smooth variations of the charge density over the interstitial region. Such a choice of the sphere radii allows the packing parameter (VMr/Vtotal) tO remain around 0.59 percent for all compounds considered. We used the triple-kappa basis set for each type of atom with angular momentum, l, up to 2 for Hg, Cu and O and up to 3 for Ba and Ca for x2= - 0 . 0 1 Ry, and up to 1 for x2= - 1.0 and up to 0 for x2= - 2 . 3 Ry. Wave functions with/max = 1 were associated with empty spheres for the first kappa value only. The charge density was calculated exactly in muffin-tin spheres for angular momentum components up to l = 6. The same l cut-off was used when interpolating in the interstitial region over Hankel functions with energies - 1 and - 3 Ry. Calculations done for l= 5 do not show any difference in band positions (the total energy curve shows only a rigid shift of about 10 mRy), which indicates good convergence of our results with/max- Note that the band structure for Hg1201 presented here differs slightly from that published by us in ref. [ 11 ]. The main source of the dif-

D.L. Novikov, A.J. Freeman / vHS's and the role of doping

275

Table 1 Lattice parameters, MT-sphere radii and number of atoms per unit cell for Hg- 1201 and 1212 used in the FLMTO calculations. For Hg1223, all coordinates are taken equal to those of Hg-1212 by adding an extra Cu-O and Ca layer Type

Atom

x

y

z

R~rr, a.u.

No.

Hg-1201 a= 7.322 a.u. c/a=2.455

Hg Ba Cu O( 1) 0(2) ES( 1) ES(2) Hg Ba Ca Cu O(1 ) 0(2) ES( 1) ES(2) ES(3) Cu (2) 0(3)

0.0 0.5 0.0 0.5 0.0 0.5 0.5 0.0 0.5 0.5 0.0 0.5 0.0 0.5 0.5 0.5 0.0 0.0

0.0 0.5 0.0 0.0 0.0 0.0 0.5 0.0 0.5 0.5 0.0 0.0 0.0 0.0 0.5 0.5 0.0 0.0

0.0 0.732 1.228 1.228 0.510 0.250 0.0 0.0 0.723 1.643 1.235 1.238 0.515 0.250 0.0 1.642 2.050 2.050

2.03 3.30 1.82 1.82 1.70 1.78 2.00 2.05 3.40 2.86 1.82 1.82 1.70 1.61 1.86 1.10 1.82 1.70

1 2 1 2 2 4 1 1 2 1 2 4 2 4 1 1 1 2

Hg-1212 a=7.285 a.u. c/a= 3.285

Hg- 1223 c/a=4.1006

ference comes from/max = 4 used there, which affects the position o f some bands above the Fermi energy. The Brillouin-zone integrations were carded out by the tetrahedron method using a 637 k-point mesh (corresponding to 2 4 X 2 4 × 2 4 regular divisions along the kx-, ky- and kraxes respectively) for Hg1201 and a 455 k-mesh for Hg-1212 and Hg-1223 in the ~6 irreducible wedge.

3. Results

3.1. Band structure The self-consistent F L M T O band-structure results near the Fermi energy are plotted in fig. 1 for stoichiometric Hg-1201, Hg-1212 and Hg-1223, respectively, along some high symmetry lines in the simple tetragonal Brillouin zone, where X = ( n / a , 0, 0), M = (n/a, n/a, 0), R = (n/a, O, n / c ) and A = (n/a, n/a, n/c). The total and angular-momentum projected DOS for the different atoms inside their MTspheres are displayed in fig. 2 for defect-free Hg- 1201, Hg-1212 and Hg-1223. The band structures o f these c o m p o u n d s are on the whole very similar to each other and to that o f

the IL compound. In each case, a CuO2-derived freeelectron-like dpo antibonding band per CuP2 layer crosses the Fermi energy in the planes parallel to the basal ( X M F ) plane. In Hg-1201, this CuP2 band is exactly half-filled in the undoped case indicating that it must be an antiferromagnetic insulator according to the M o t t - H u b b a r d description. For Hg-1212 and Hg- 1223 (found also for the latter by Singh [ 15 ] using the full potential linearized augmented plane wave method) there is an additional band crossing E r at the X and R points (around the X - R line) in the BZ. It is composed predominantly from Hg p, Ba p,d and the 2p- states o f the apical oxygen ( 0 ( 2 ) ) . This band is present in the Hg-1201 band structure also, but is located ~ 0 . 2 eV above the Fermi level at the X-point. The downward m o v e m e n t of this band with an increasing number o f layers is caused by hybridization between the Ca 4p and Ba p states that pushes this band down. This fact can be proven in a simple way. We carried out the same calculations including Ca 3p states in the valence panel and dropping the Ca 4p orbitals. In this case, this H g - O band does not change its position at all and remains above the Fermi energy, as for Hg-1201. Figures 4 and 5 show contour maps in different planes o f the square o f the wave

276

D.L. Novikov, A.J. Freeman / vHS's and the role of doping 3

3

I~

i

w

w

-3

r

X

M

r Z

R

A

Z

(a)

F

X

M

FZ

R

A

Z

(b)

> v

C

uJ

-1

-2-

-3

i

F

X

M

FZ

R

A

Z

(c) function at the X point in the BZ corresponding to this Hg-O band in Hg-1201 and Hg-1212. The antibonding character of the Hg-O interaction is dearly seen along with considerable Ba-O bonding interactions. Thus, the influence of Ca atoms situated between Cu-O layers on the energy position of the Hg-

Fig. 1. FLMTO energy-band results along high-symmetrydirections in the simple tetragonal BZ for (a) Hg-1201, (b) Hg-1212, and (c) Hg-1223.

O band can be understood as an indirect interaction involving Ba p states. The same is true for Hg-1223. Thus, it turns out that in the family of the Hg-based compounds considered here, Hg- 1212 and Hg- 1223 have "self-doped" band structures, that move the CuO dpt~ antibonding band away from half-filling. This

277

D.L. Novikov, A.Z Freeman / vHS's and the role of doping

c.J C" "7 i

> .1--,

0 n

32 Tot~ 24 16 8 0 Hg -1 1 0 Ba 6s, 5p 1 0 Cu 3d 4 0 0(1) 2p 4 0 0(2) 2p 4 0 -6 -10 -8

i EF

C,3 c

"7 I

>

if)

0

121

/ ~ -4

-2

0

2

(a)

o c i

>

ffl

E © a

EF

I

Ba 6s, 5p Ca 6s, 5p

o(1) 2

p

~

~

0(2)/~2p _ ~ -8

-6

~4 -4

-2

0

2

(b) A,, ~, ~

~

EF

I

I

;,,

I

I

~

~

0(2) 2p

4 0 4 0

Cu(2) 3d ~

4 0

-10

Tot~

Energy (eV)

Energy (eV)

32 24- Total 16 8 0 1 0 1 %i s,s 0 Ca 6s, 5p 1 0 6 0 o(1) 2 4

32 24 16 8 0 1 0 1 0 1 0 4 0 4 0 4 0

0(3! 2p -10

-8

I -6

-4

Energy (eV)

(c)

-2

0 Fig. 2. Total and MT-projected density of states for defect-free (a) Hg-1201, (b) Hg1212, and (c) Hg-1223 (with Er the zero of energy).

278

D.L. Novikov, A.J. Freeman / vHS's and the role of doping

2.50

r"'--"---'T~

O

EF

1.4I

E'F

(a)

2.25

.~1.2 e-

5

l

>

I

EF

(b)

.~ 2.00

"~ 1.0

(#3 © 0.8 D

O 1.75 D : Ae=0.38 ,'-,-

0.6 -0.6

-0.4 -0.2 -0.0

0.2

0.4

Energy (eV)

1.50~

-0.4

-0.2 -0.0 0.2 Energy (eV)

0.4

32II /i/I

}t//

i

'\ o

-0.4

-0.2 -0.0 0.2 Energy (eV)

0.4

band pattern is reminiscent of the case for the T1based superconductors (TI2Ba2Ca,_ iCu,O4 + 2,, n = 1, 2, 3 ) [ 17-I 9 ], the crystal analog of the Hgbased materials, where the T1 6s-O 2p band is found to be located always below EF. From fig. 1, it is seen that the band structure of these materials is strongly two-dimensional, as it is for the other C u - O layered cuprate superconductors. There are van Hove saddle point singularities at the

Fig. 3. Expanded total DOS in the vicinity of EF for the stoichiometric case for (a) Hg-1201, (b) Hg-1212, and (c) Hg-1223. Ae values refer to the number of boles needed to put the Fermi energy onto the (first) vHS labeled E~.

X and R points in the BZ that give rise to peaks in the total DOS close to EF (cf. fig. 2). The blown up total DOS's in the EF region are displayed in fig. 3 for Hg-1201, Hg-1212 and Hg-1223. As seen from fig. 2, the valence bands extend over an 8 eV region for each compound, with the bottom part composed mainly of Hg 5d states. As stated above, EF for the undoped systems falls in the region of antibonding Cu 3d-O 2p states. According to the individual muf-

D.L. Novikov, A.J. Freeman / vHS's and the role of doping

Hg

Hg 0(2)

0(2) 0

0(2)

279

Hg

Hg

0(2)

0(2)

Cu

Cu

Cu

Cu

0(2)

0(2)

Q

0(2)

r

Hg

Hg (a)

Hg (b)

Hg

Fig. 4. Square of the wave function at the X point in the BZ normalized to two electrons per unit cell in the (110) plane for ( a ) Hg- 1201 and (b) Hg-1212. Contours start from 10 -Se/a.u.3 and increase successively by a factor of x/~.

fin-tin projected DOS results, these states are associated with Cu and O(1 ) (in-plane oxygen) states for Hg-1201 and Hg-1212 and with Cu( 1), Cu(2)O ( 1 ), O (3) states with a small admixture of Hg p0 ( 2 ) states for Hg-1223.

3.2. Density of states The blown up total DOS's (fig. 3) display peaks in the vicinity of EF resulting from the vHS at the X and R points in the BZ. We see clearly the split peak due to the (first) vHS at the X and R points in Hg1201 and Hg-1212. The peak in the DOS from the additional Hg-O band that is above EF in Hg-1201 is seen to move down in energy and become occupied in Hg-1212 and Hg-1223, where it overlaps the vHS peak and yields the higher DOS value above E~ (the position of the (first) vHS). In previous papers [ 10,11 ], we correlated the highest Tc that was

reached in the hole doped IL [8] and Hg-1201 [2] systems with moving EF toward the vHS. Indeed, the number of"holes" needed to place EF exactly on the vHS estimated using the simple rigid-band approximation was found to be in strikingly good agreement with that observed experimentally. Following the same rigid-band approximation, we estimated the number of electrons one needs to remove from Hg1212 and Hg-1223 in order to hit the vHS (the very first vHS counting from EF). The numbers are displayed on fig. 3 for Hg-1201, Hg-1212 and Hg-1223. Note that they rise gradually from Hg-1201 to Hg1223 (0.38, 0.50 and 0.60). But if we consider the number of holes per Cu-O layer, they change in the reverse order, 0.20 for Hg-1223, 0.25 for Hg-1212 and 0.36 for Hg-1201. This is expected from the fact that the Hg-O bands are also emptied with doping. As expected, the value of the total DOS at the vHS (in states/eV unit cell) increases correspondingly to

280

D.L. Novikov, A.J. Freeman / vHS's and the role of doping

0(1)

0(1)

0(1)

o(1)

0(1)

0(1)

(a)

(b)

Fig. 5. Square of the wave function at the X point in the BZ normalizedto two electrons per unit cell in the (100) plane for (a) Hg-1201 and (b ) Hg-1212. Contours start from 10 - 5e/a.u.3 and increase successivelyby a factor of x/'2. the increase of the number of C u - O layers per unit cell ( 1.45 for Hg-1201, 2.3 for Hg-1212 and 3.34 for Hg-1223). However, considering the total DOS per C u - O layerwe see a gradual decrease of the total DOS per layer at the vHS from Hg-1201 to Hg-1223, at which point the total DOS approaches that for the IL compound for the onset of its vHS. If we try to correlate the value of the DOS at the vHS with possible changes in To, we can expect Tc to rise along with increasing the number of interacting C u - O planes in this Hg-based family of superconductors. We mention here that model calculations [ 20 ] show that the coupling between C u - O layers may provide conditions for the T~ enhancement. 3.3. Fermi surfaces and Fermi velocities

Let us turn to the topology of the Fermi surface in the systems considered. For the stoichiometric material, the simple band structure at E F in Hg-1201 gives rise to the simple square barrel FS (cf., fig. 6)

which displays very little dispersion along FZ. The situation changes in Hg-1212 (cf. fig. 7) and Hg-1223 (cf. fig. 8), where not only do additional co-axial FS sheets arise (due to increase of the number of C u O layers), but we also see electronic pockets with the shape of a tube around X - R caused by the H g - O band moving down below the Fermi level. Again assuming a rigid-band behavior for the band structure and doping the systems by the appropriate number of holes, we can move E~ onto the vHS. The resulting changes in the FS geometry can be seen from fig. 6(b) for Hg-1201, fig. 9 for Hg-1212 and fig. 10 for Hg-1223. The outer sheet of the FS in each compound becomes pinched at the X or R point. And at this point, the system of co-axial "hole" cylinders reaches its maximum volume without becoming broken. As expected, in the case of Hg-1212 and Hg1223, the electron pockets around the X - R direction disappear with doping. Additionally, we estimated Fermi velocities at EF for the undoped cases and at the energy correspond-

D,L. Novikov, A.J. Freeman I vHS's and the role of doping

r

(z)

x (R)

(a)

F

281

X i

X (R)

r (z)

X (R)

X (R) .... ....

"a . . . . . . . . . . . . . . .

'. . . . . . . . . . . . . .

Z

R

(b)

"1"I

iI

Fig. 6. The Fermi surface for Hg- 1201 in the basal (FXM) plane (dashed line) and (ZRA) plane (solid line) at different hole doping levels: (a) undoped case, (b) doping for maximum To.

F

X

Fig. 8. The Fermi surface for Hg-1223 (undoped case).

F

X

X

Z

R

Fig. 7. The Fermi surface for Hg-1212 (undoped case).

Z

R

Fig. 9. The Fermi surface for Hg-1212 (at the first vHS).

282

D.L. Novikov, A.J. Freeman / vHS's and the role of doping

F

tron-like b a n d to the total D O S at the v H S accompanying a decrease o f group velocities in the Hg-1201, Hg-1212, Hg-1223 series.

X

4. Role of doping in synthesis and superconductivity

Z

We h a d found previously for the IL a n d Hg-1201 superconductors that there was a strong correlation between the pinning o f EF to the v H S by the d o p a n t s a n d the m a x i m u m value o f To. The new d a t a b y Radaelli et al. for Hg-1212 [ 5 ] allow us to investigate whether these predictive correlations work also for the case o f Hg- 1212. N e u t r o n diffraction d a t a o f Radaelli et al. give evidence that the p r i m a r y doping m e c h a n i s m in these materials, as in Hg-1201, is prov i d e d by oxygen a t o m s in an interstitial position, the 0 ( 3 ) position. Its occupancy varies up to 0.22 for their oxygenated sample with Tc = 126 K (slightly reduced from their as-synthesized sample with T¢= 128 K ) . " T h e a d d i t i o n a l defect site O ( 4 ) , which h a d a significant occupancy for the one-layer material was found to be almost empty. This result suggests that the complex defect p r o p o s e d for the one-layer material is not present in this case." O u r calculated n u m b e r o f electrons needed to pin EF to the vHS is 0.50, hence the oxygen doping o f 0.25, is in very good agreement with experiment especially when one considers the nature o f the real material with its possible very small a m o u n t o f ad-

[q

Fig. 10. The Fermi surface for Hg-1223 (at the first vHS). ing to the " f i r s t " v H S in each c o m p o u n d . Partial integrated F e r m i velocities along with a partial cont r i b u t i o n o f each sheet o f the FS to the D O S are presented in table 2. These group velocities are relatively high a n d o f o r d e r o f those for YBa2Cu307 [ 21 ]. We find that there is a tendency to increase the partial c o n t r i b u t i o n o f the highest C u - O free-elec-

Table 2 Partial contribution to the density of states at Er, N( EF) (in states per Ry-spin unit cell ) from each sheet of the Fermi surface and partial integrated Fermi velocities, ( v2 ) t/2 ( 107 cm / s), at stoichiometry (first number ) and at the van Hove singularity (second number). Numbers 1, 2, 3 correspond to different co-axial sheets of the FS counting from the center

1

2

3

"Hg-O" band

4.5/5.3 1.64/1.66 0.03/0.04

5.9/10.2 1.53/1.45 0.14/0.24

-

4.3/0.64/0.04/-

4.8/5.1 1.62/1.63 0.02/0.02

5.1/5.7 1.61 / 1.58 0.04/0.10

6.7/11.9 1.55/1.41 0.12/0.21

3.83/0.85/0.04/-

Hg-1201 N(EF)

(v 2 ) t/2 = (v~) 1/2 (v 2 ) t/2

5.0/9.6 1.63/1.49 0.11/0.25

Hg-1212 N(Ev)

(v~) 1/2= (v 2 )t/2 ( v2 ) 1/2 Hg-1223 N(EF)

(v 2 ) l/z= (v 2 )1/2 (v 2 ) t/2

D.L. Novikov, A.J. Freeman / vHS's and the role of doping

ditional dopants or defects to that at the O (3) site. Thus we see that as in the case of the IL and Hg1201 systems, the as-synthesized samples with the maximum Tc for the two-layer Hg-1212 material appear to result from the pinning Of EF tO the vHS when the proper doping is allowed for. The additional oxygen doping required to stabilize Hg-1212 and Hg1223 appears also to explain the difficulty of avoiding multi-phase samples in the synthesis process and of obtaining large volumes of the single phase sought. It is important, in this context, to recall that by contrast synthesis of Hg-1201 is surprisingly easy and is found to form over a large range of synthesis conditions employing different precursors; apparently because of the lowered total hole doping (i.e. oxygen content) needed to pin EF to the vHS. In a similar fashion, we may use our predicted doping level (0.60 holes or 0.30 oxygen atoms) for pinning EF to the vHS for Hg-1223 as a predictor for the synthesis conditions needed to possibly produce a large volume fraction of this phase. Since an increase in Tc is expected for single.phase samples once the optimized doping levels are achieved, we may expect Tc's well beyond those obtained so far for the small-volume samples of this phase currently available. We therefore propose an additional source of oxygen (eg., from AgO) to be incorporated directly into the synthesis process in order for the system to be able to be grown at dopant levels required for EF tO hit the vHS.

Acknowledgements We thank J.D. Jorgensen, P.G. Radaelli, D.G. Hinks and J. Wagner for helpful discussions and encouragement, A.V. Postnikov for discussions and M. Methfessel for his FLMTO code. This work was supported by the National Science Foundation (through the Northwestern University Science and Technology Center for Superconductivity, Grant No. DMR

283

91-20000, and by a grant of computer time at the Pittsburgh Supercomputing Center).

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