mlgl
PhysicaC 219 (1994) 17-20
North-Holland
Electronic structure of the mercury-based high-Tc compound with
four CuO2 layers: HgBa2Ca,,_1Cu.O2.+2 (n= 4)
C. Osvaldo Rodriguez
IFL YSIB, GrupoFtsica del S61ido, C C. 565, La Plata (1900), Argentina
R u b e n Weht and M a r i a n a Weissmann
Divisi6n Ftsicadel S61ido, CNEA, Avda Livertador 8250, BuenosAires (1429), Argentina
N.E. Christensen a n d E.L. Peltzer y Blanc~
Institute of Physics and Astronomy, Aarhus University, DK-8000Aarhus C, Denmark
Received28 October 1993
The electronicstructureof the tetrqonal ~ - b a s e d
compoundcontainingfour CuO2planes, HgBa2Ca~Cu4Oto(Hg1234),
has been made from fn'st principles, within the local-densityapproxima*Jon using the full potential linear muffin-tin orbital
method. The Hg-derivedband which dopes the CuO2 planes dips further below the Fermi energythan in the compoundswith
n=2 and 3 planes (this band stays above the Fermi energyfor nffi1), increasingthe degreeof rig character of all sheets of the
Fermi surface.
1. Introduction
The members of the family of the new mercury
compound superconductors belong to a homologous
series of formula HgBa2R,_ tCu~O2,+z+x. The work
of Putilin et al. [ 1 ] who reported superconductivity
in the first ( n = 1 ) member of the series, HgBa2CuO4+x (Hgl201), with a transition temperature of 94 K and x=0.06, stimulated considerable
interest in the Hg-based system. Putilin et al. [ 2 ] later
prepared compounds with n = 2 and R a rare-earth
element, which were not superconductors. Superconductivity appeared when the rare-earth elements
were replaced with Ca separating the CuO2 planes.
Schilling et al. [ 3 ] reported magnetic and resistivity
measurements in multiphased samples of HgBa2CaCu206+ x (Hg1212) and HgBazCa2Cu3Oe+ x
(Fig 1223) with transition temperatures of 124 K and
134 K, respectively. The structural arrangement for
the second member (Hg 1212 ) was then obtained by
X-ray diffraction [4], showing a small dimpling of
the CuO2 planes (around half of that in YBa2Cu3OT).
Synthesis and characterization of the third (Hg 1223 )
and fourth (Hg1234) members were obtained by
Antipov et al. [ 5 ] and even the existence of the phase
Hg1245 was detected in these preparations and in
the work of Cantoni et al. [6].
The crystal structure of rig1212 and Hg1223 have
recently been determined by neutron powder diffraction techniques [ 7-9 ]. The analysis of these data
showed that the oxygen composition corresponded
to x=0.28-0.35 and x--0.39-0.44 for Hg1212 and
Hg1223, respectively. The extra oxygen was found to
be located at the center of the squares formed by the
mercury atoms. No evidence was found of orthorhombic distortions, nor for substitution of some Hg
atoms by Cu, unlike the case of the one-layer compound. In Hg1223 the copper and oxygen atoms of
the central CuO2 layer were found to be coplanar.
The other two CuOz planes and the two corresponding planes in Hg1212 were also found to be almost
perfectly coplanar. For the case of Hg1234 only the
lattice parameters are known experimentally.
Similar to what happens to the analogous copper
oxide compounds based on thallium or bismuth the
superconducting transition temperature increases as
0921-4534/94/$07.00 © 1994ElsevierScienceB.V. All fights reserved.
SSDI 0921-4534(93)E1031-Z
18
C.O. Rodriguez et al. ~Electronic structure of HgBa2Ca._ lCunOzn+2 (n= 4)
the number of copper oxide layers, n, in the unit cell
increases from n = l , 3, and after that saturation
seems to be achieved. From the structural point of
view one can compare the mercury family to that of
thallium, T1Ba2R~_ICunO2n+3. There is, however, a
marked difference between the two classes of materials in the oxygen occupancy of the T1 and Hg layers. It is almost complete in the case of thallium but
grows from = 6 to 50% for the mercury compounds.
From the point of view of their electronic properties
the mercury compounds are closer to that of
Tl2Ba2Rn_lCunO2n+4 (the formal valence of two
T13+O2- layers is the same as a single Hg 2+ layer).
We have previously studied the electronic structure of the Hg family with n = 1 - 3 [10,11]. Agreement has been obtained with the results of other authors [12-15].
In this paper we present a first-principles determination of the electronic structure for the stoichiometric structure of the member of the Hg family
with four ( n - - 4 ) CuO2 layers: Hg1234, within the
local-density approximation (LDA) using the full
potential linear muffin-tin orbital (FP-LMTO)
method [ 16,17 ]. These electronic structure calculations serve in the understanding of the normal and
superconducting state of the high-temperature superconductors. The band structures o f the stoichiometric compounds exhibit overall features similar to
those of other cuprate superconductors, with n CuO
antibonding bands crossing the Fermi energy (EF),
but with a difference: an antibonding band which
comes mostly from the hybridization of Hg p and d
and apical oxygen p states which lies slightly above
the Fermi level for Hgl201 and below it for Hg1212
and Hg1223. This makes stoichiometric Hgl201 a
Mort insulator. Doping in this compound is needed
to form the normal metallic state.
For the cases of n = 2 and n = 3 self-doping seems
to make these members metallic. The Hg layer hole
dopes the CuO2 layers in the stoichiometric materials. This is similar to the theoretical predictions in
Tl-based material [ 18-20], where a T1-O derived
band dips below EF for the entire series. The Fermi
surfaces (FS's) consist o f barrel-like sheets, and van
Hove singularities exist very close to EF. The density
of states increases and the FS sheets become drastically modified when the Fermi energy is moved
down in energy (this for example can be thought of
as the effect of hole doping) as it crosses the van Hove
singularities.
Our calculated electronic structure for Hg1234
shows a similar pattern, the Hg-derived band dipping further below E r and its hybridization increasing the Hg character of all sheets of the FS.
2. Method of calculation
Since the atomic positions of this compound are
not yet known, a structural model was set up for
Hg1234 based on the relative positions of atoms in
the infinite-layer compound CaCuO2 [ 21 ] and those
of Hg1223 in ref. [8]. The lattice dimensions,
a = b ffi3.85 A were chosen by averaging the experimental values for Hg1212 and Hg1223 [7,8], and
the positions in the z-direction scaled accordingly to
the experimentally known c-- 19 A lattice parameter
[5,221.
The FP-LMTO technique makes no shape approximation for the charge density or for the potential [ 16] for the valence electrons. Spherical harmonic components of the charge density are included
explicitly for angular momenta l~< 6, inside the MT
spheres. This same ! cut-off was used for the interpolation in the interstitial region with Hankel functions with energies - 1 and - 3 Ry. The basis functions are defined using a triple-~ set. The choice of
kinetic energies K2, associated with the envelope
Hankel functions is not critical and we have taken
them to be - 0 . 2 5 , - 1 . 0 and - 3 . 0 Ry. The core
electrons are allowed to relax. All calculations were
done within the LDA using the Barth-Hedin parametrization of the exchange-correlation energy and potential [23 ]. The basis set included 332 LMTO's per
cell. To obtain the desired precision it was necessary
to use 693 points in the irreducible Brillouin zone
(BZ) plus linear tetrahedral interpolation. The calculations needed to be carried out in two panels. The
following orbitals were taken as valence band electrons: Ba 5p and 6s, Hg 5d and 6s, Cu 3d and 4s, Ca 4s
and 3p, and O 2s and 2p. The Cu 3s and 3p, Ba 5s,
Ca 3s and Hg 5s and 5p were included as semicore.
Empty spheres were introduced to obtain a better
packing placed in a similar way as in the previous
calculations [ 10,11 ].
C O. R odriguez et al. / Electronic structure ofHgBa zCa._ tCu.O~. +z (n = 4)
3. Reults
The band structure of Hg1234, using our model
crystal structure is shown in fig. I. Bands for k==0
between high-symmetry points are shown in the left
part of the figure and bands for kz=~/c on the right.
These are joined by the r-z line,and a comparison
of both sides shows the dispersion in the z-direction.
Fermi surface (FS) cross-sections in the symmetry planes are shown in fig. 2. The difference of
crossings in the two squares shows again how dispersive the bands close to EF are in the z-direction.
The band structure is highly two-dimensional, but
less than for Hg1223. The FS consists basically of
n = 4 (the number of CuO2 planes) largebarrelsheets
centered around the M - A line and a small electronlike sheet around the X - R line which comes from
the Hg-plane derived band. This Hg-derived band
dips below Ev further than for Hg1212 and Hg1223.
2
.~...
~.
,5
": ,: -.:.
-
.::
/
..,.o
o
-
-1
-l.5
-2
I"
M
X
r'Z
A
R
19
Its hybridization to the n CuO2 sheets is also
increased.
The four FS sheets in fig. 2 come from linear combinations of n CuO2 plane-derived bands characteristic of cuprate superconductors (basically, understood as antibondlng pda bands of a simple tightbinding model, in the nearest-neighbor approximation). How the simple two-dimensional, perfectly
nested FS from each plane transforms to the rounded
squares of fig. 2 can be found in a previous study
[24]. In Hg1234, there are two inner barrels whose
character is mostly related to those CuO2 planes
which are adjacent to the planes containing the apical oxygens. The other n - 2 outer barrels are related
to the remaining CuO2 planes. Due to the strong hybridization with the Hg-derived band the barrel
sheets get much distorted near the intersections with
the XMAR plane (and equivalent ones). One can
observe that because the Hg-derived band dips deep
below EF the electron-like sheet intersects one of the
CuO2 sheets. For the k== 0 plane they are allowed to
cross. As soon as kx~0 they cannot cross anymore
making the FS lose part of its 2D character. As already mentioned this marks a difference to the behavior of Hg1223.
Figure 3 shows the total electronic density of states
(DOS) in the vicinity of EF. As seen in fig. 1 there
are van Hove saddle points at X and R in the BZ.
Two peaks appear in fig. 3 at ~ - 0.11 and - 0.40 eV
from Er. These are derived from two of the four saddle points which occur in the X-R line, derived from
the CuO2 bands. The value of the DOS is enhanced
to ~5.3 and 9.9 state/(eVunit cell), respectively,
Z
Fig. I. Band structureforHg1234. Thesymmetrypointsare:
rffi(0,0, 0),Mr(I, I, 0)~/aandX=(l, 0, 0)x/~Z=(0, 0,
l)z/~ A=(I, I, a/c)~/aandR=(l, O, a/c)~/a (aand care
thetetragonallatticeconstan¢).
I2
10
8
I]I
%
MA
6
4
2
XR
Z
0
Fig. 2. Intersection of the I D A Fermi surface of Hg1234 with the
upper half of the Brillouin zone boundaries.
t
~.4
i
~.3
t
~.2
i
~.1
i
0.1
Fig. 3. Total DOS of I-Ig1234 in the vicinity of E~.
0.2
20
C.O. Rodriguez et al. ~Electronic structure of HgBazCaa_lCuaO2n+z (n= 4)
compared to the DOS at EF, N ( E F ) = 4 . 3 2 states/
(eVunit cell). The interaction of the Hg-derived
band with the CuO2 band which has the saddle point
closest to Ev for kz=O at X causes the saddle point
to move away from the X - R line for kz#0. The peak
in DOS around - 0.11 eV is broad.
Our calculations were based on a structural model
which used the experimentally determined structure
of Hg1223 [8] and adding an extra CuO2 and Ca
plane based on the structure of the infinite-layer
compound [ 21 ]. We believe this model will be close
to the actual crystal structure. We have anyhow tested
the validity of our conclusions by realizing an additional calculation based on a model structure which
used the crystal structure of Hgl 212 as determined
by an early experiment using X-rays which proposed
a dimpling in the CuO2 planes [ 4 ] (this dimpling
was not observed on any of the newer experiments
which used neutron scattering techniques). The proposed dimpling was half o f that in YBa2Cu307crystals. Although the use of this model altered the detafls of the band structure it did not modify any of
the qualitative features already described here.
4. Conclusions
The main conclusion which we can infer from the
results presented in this paper and previous studies
[ 10,11 ] is that the electronic structure for any member with n > 1 of the stoichiometric compounds of
the Hg family will produce a FS consisting of n large
barrel sheets (derived from the CuO2 planes) and a
small electron-like sheet (which derives from the Hg
plane). This Fig band dips below Ev further and its
hybridization to the CuO2 related sheets is bigger as
n increases. There are two inner barrels associated
with the CuO2 planes adjacent to the apical oxygens.
The other n - 2 outer barrels are related to the remaining CuO2 planes. The Hg layer hole dopes the
CuO2-derived bands away from half filling. Stoichiometric Hgl201 ( n = l ) represents a special case in
that it is not self-doped: the Hg-derived band is close
to EF but does not dip below it.
We have benefited from the interaction with W.E.
Pickett and D.J. Singh. This work was supported by
Consejo Nacional de Investigaciones Cientificas y
T6cnicas de la Repdblica Argentina, by the Commission of the European Communities, Contracts no.
S/CI1"-913141 and CI1"-CT92-0086 and by the
Danish Research Council under grant nr. 11-9685-1
and 11-9001-3.
References
[ 1] S.N. Putilin, E.V.Antipov,O. Chmaissemand M. Marezio,
Nature (London) 362 (1993) 226.
[2 ] S.N. Putilin, J. Brynts¢and V,E. Antipov,Mater. Rcs. Bull.
26 (1991) 1299.
[3] A. Schilling, M. Cantoni, J.D. Guo and H.R. Ott, Nature
(London) 363 (1993) 56.
[4] S.N. Putilin, E.V. Antipovand M. Marezio, PhysicaC 212
(1993) 266.
[ 5] E.V. Antipov,S.M. Loureiro, C. Chaillnut, J.J. Capponi, P.
Borde~J.L. Tholence,S.N. Putilin and M. Marezio,Physica
C215 (1993) 1.
[6] M. Cantoni, A. Schilling, H.U. Nicsscn and H.R. Ott,
PhysicaC 215 (1993) II.
[7] E.V. Antipov, J.J. Capponi, C. Chaillout, O. Chmaisscm,
S.M. Loureiro, M. Marezio, S.N. Putilin, A. Santoro and
J.L. Tholence, PhysicaC 218 (1993) 348.
[8]0. Chmaissem, Q. Huang, E.V. Antipov, S.N. Putilin, M.
Marezio, S.M.Loureiro,J.J. Capponl,J.L. TholenceandA.
Santoro, PhysicaC 217 (1993) 265.
[9] P.G. Radaelli, J.L. Wagner, B.A. Hunter, M.A. Beno, G.S.
Knapp, J.D. Jorgensen and D.G. Hinks, Physica C 216
(1993) 29.
[ 10] C.O. Rodriguez,Phys. Rev. B, to be published.
[ 11] c.o. Rodriguez,N.E. Christe~sen and E.L. Peltzery BlancA,
PhysicaC216 (1993) 12.
[ 12] D.J. Singh, PhysicaC 212 (1993) 228.
[13] D.L.NovikovandAJ. Freeman, PhysicaC212 (1993) 233.
[ 14] D.J. Singh, Phys. Rev. B 48 (1993) 3571.
[ 15] D.L.NovikovandAJ. Frceman,PhysicaC 216 (1993) 273.
[ 16] M. Methfessel, Phys. Rev. B 38 (1988) 1537.
[ 17] M. Methfessel, C.O. Rodriguezand O.K. Andersen, Phys.
Rev. B 40 (1989) 2009.
[ 18 ] J. Yu, S. Massida and A.J. Freeman, PhysicaC 152 (1988)
273.
[19] D.R. Hamann and L.F. Matheiss, Phys. Rev. 38 (1988)
5138.
[20 ] D.J. Singhand W.E.Pickett, PhysicaC 203 (1992) 193.
[21 ] T. Siegrist, S.M. Zahurak, D.W. Murphy and R.S. Roth,
Nature (London) 334 (1992) 231.
[22] The atomic z-coordinatesare: z(Hg)=0, z(Cu)=0.2482,
z(Cub)--0.4166, z(O2) =0.2494, z(O2b) =0.4166,
z(Ba) =0.1477, z(Ol) =0.1030, z(Ca) =0.3294,
z(Cab)=0.5, in units of the corresponding c lattice
parameter.
[23 ] U. yon Barth and L. Hedin, J. Phys. C 5 (1972) 1629.
[24 ] C.O. Rodriguez,A.L Liechtenstein,O. Jepsen, I. M~in and
O.K. Andersen, J. Comput. Phys., to be published.