This document summarizes a study on the effects of vacancy and copper doping on superconductivity in clathrate materials. Key findings include: 1) Copper doping of Ba8Si46 decreases the superconducting critical temperature strongly as copper content increases. Theoretical simulations also show copper doping decreases electronic density of states at the Fermi level. 2) Comparison of Ba8Ge46 and Ba8Si46 using theoretical simulations found their electronic structures are very similar, suggesting superconductivity is intrinsic to fully occupied silicon and germanium clathrates. 3) The absence of superconductivity in most germanium clathrates is suggested to arise from vacancy defects which result in

1. Physics Letters A 345 (2005) 398–408
www.elsevier.com/locate/pla
Vacancy and copper-doping effect on superconductivity
for clathrate materials
Yang Li a,b,∗
, Yang Liu a
, Ning Chen a
, Guohui Cao a
,
Zhaosheng Feng c
, Joseph H. Ross Jr. b
a Department of Physics, University of Science and Technology Beijing, Beijing 100083, China
b Department of Physics, Texas A&M University, College Station, TX 77843-4242, USA
c Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78541, USA
Received 26 April 2005; accepted 4 July 2005
Available online 18 July 2005
Communicated by J. Flouquet
Abstract
We present a joint experimental and theoretical study of the superconductivity and electronic structures in type-I Cu-doped
silicon clathrates and germanium clathrates. The superconducting critical temperature in Ba8Si46–xCux is shown to decrease
strongly with copper content increasing. These results are corroborated by CASTEP approach, first-principles simulations cal-
culated from the density-functional theory with plane waves and pseudopotentials. The simulations show that Cu-doping results
in a large decrease of electronic density of states in Fermi level, which can explain the superconducting critical temperature
decrease with Cu-doping in the BCS theoretical frame. Further, comparison of Ba8Ge46 and Ba8Si46 within the CASTEP ap-
proach shows that the superconductivity is an intrinsic property of the sp3 silicon and germanium clathrates without vacancy
in the cage framework. By analysis of the density of states (DOS) and reported experimental results of the Zintl-like Ba8Ge43,
a new mechanism of vacancy defect is suggested to explain the absence of superconductivity in Ge clathrates, which is of ben-
efit to eliminating the divarication between theoretical prediction and the experimental observation for superconductivity in Ge
clathrates. Keeping an entire Si and Ge cage structure without vacancy is the prerequisite for occurrence of superconductivity
in clathrates.
 2005 Elsevier B.V. All rights reserved.
PACS: 74.70.Wz; 73.61.Wp; 61.48.+c; 71.20.Tx; 81.05.Tp
* Corresponding author.
E-mail address: ylibp@hotmail.com (Y. Li).
0375-9601/$ – see front matter  2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.physleta.2005.07.015

2. Y. Li et al. / Physics Letters A 345 (2005) 398–408 399
1. Introduction
Group IV clathrate materials are extended Si, Ge
and Sn cage-like solids, which have received increas-
ing attention over the past few years. In such materials
with sp3 hybridized networks, alkali, alkaline earth
and Eu atoms can be encapsulated in the cages. The
discovery of superconductivity in the (Na, Ba)xSi46
based clathrates [1,2], new thermoelectric applica-
tions [3,4], the potential as a useful optical material [5]
as well as the potential for magnetic sensors and new
magnetic semiconductors [6–8], have further stimu-
lated interest in these novel materials. The study of
clathrates has opened a field of new materials with the
metals arranged in a nanoscale array [9], and with a
wide variety of properties ranging from insulators to
metals.
Inspired by the discovery of superconductivity in
alkali metal-doped C60 fullerene, efforts have been
made to explore the superconductivity of group IV
clathrates with particular attention to the sp3 hy-
bridized networks. The alkali-metal doped C60 ma-
terials are superconducting, for example for the stoi-
chiometries K3C60 (TC = 19.3 K) and Rb3C60 (TC =
29.6 K) [10,11]. In contrast to carbon, silicon and
germanium do not form sp2-like networks. There-
fore, superconductivity of Si clathrate superconduc-
tors with sp3 network should be unique. As a precur-
sor research, the Caplin group studied the electronic
conductivity and magnetic susceptibility of clathrates
of silicon, containing Na atoms as guests [9], and
found there is no superconductivity in this kind of
materials. For K7Si46, no diamagnetic behavior in-
dicative of superconductivity was found in studies
down to 2 K [12]. However, when doped with Ba,
(Na, Ba)xSi46 and (K, Ba)xSi46 clathrates exhibit su-
perconductivity with TC ∼ 4 K [1,12,13]. The calcu-
lation of the band structure for Na2Ba6Si46 showed a
strong hybridization between the Si46 band and Ba or-
bital, resulting in a very high density of states at the
Fermi level N(EF ) ∼ 48 states/eV [14]. The strong
hybridization of the Ba state with the Si46 conduction-
band state and the high N(EF ) is believed to play a
key role in the superconductivity of these compounds.
By the high-temperature-high-pressure method, the
quality of samples was later improved. Applying a
pressure of 3 GPa and at 800 ◦C to prepare sam-
ples [2], Ba8Si46 showed a superconducting transition
Fig. 1. The structure of Ba8Si46 and Ba8Ge46. The open frame-
works of clathrates are characterized by their cage structure. The
group IV elements form the basis for condensed fullerene-like poly-
hedral units consisting of five- and six-membered rings. These
frameworks built from Si (or Ge) adopt cage-like structures around
guest atoms Ba. The type-I clathrate structures observed to date de-
fine dodecahedral and tetrakaidecahedral sites for the guest metal
atoms.
(TC) at 8 K. The silicon clathrates with Ba encapsu-
lated in Si20 dodecahedra were identified as the su-
perconductors [1,2]. This superconductor is unusual
in that the structure is dominated by strong covalent
bonds between silicon atoms, rather than the metallic
bonding that is more typical of traditional supercon-
ductors. Isotope effect measurements reveal that su-
perconductivity in Ba8Si46 is of the classic kind, aris-
ing from the electron–phonon interaction [15].
The type-I clathrates, as shown in Fig. 1, with the
general chemical formula of M8Si46 or M8Ge46 (M =
alkali or alkaline-earth), are materials containing 20-
atom and 26-atom polyhedra arranged on a simple cu-
bic lattice, and an A15 unit cell (space group Pm¯3n).
There are eight cages per cell, which can accom-
modate at maximum eight endohedral alkali/alkaline-
earth guest atoms. Unlike the intercalated fullerides,
doped clathrates are air-stable because dopants reside
inside the Si or Ge cages. Ge atoms at the crystal-
lographic 6c positions bridging the Ge20 fullerenes
were found to have defects, and can readily be re-
placed by transition metals such as Cu, Zn, Mn, Fe,
Ni and Au [7,16–21]. It can be expected that new

3. 400 Y. Li et al. / Physics Letters A 345 (2005) 398–408
electronic properties will be achieved by regulating
the 6c-site elements. The hybridization behavior of al-
kali or alkaline-earth atoms is sensitively influenced
by this special position in the cubic lattice. The elec-
tronic properties of the clathrates are thus expected to
depend on the nature and the extent of metal substitu-
tion.
We are interested in the effect of transition metal
doping such as Cu on the superconductivity of Ba8Si46
and Ba8Ge46, as well as the change of electronic struc-
ture in clathrates. Experiments have demonstrated that
Cu can be placed at the 6c site in clathrates [7,
16]. Therefore, investigation of Cu doping can in-
crease our understanding of the electronic structure
and superconducting mechanism in clathrate materi-
als.
The findings about superconductivity in Ge clath-
rates have thus far been inconsistent. Unlike Si clath-
rates, there has been no unambiguous evidence of bulk
superconductivity in Ge clathrates. A majority of re-
searchers have found that Ge clathrates are semicon-
ducting, without superconducting transitions down to
2 K [22]. A report about superconducting transition
(TC = 7 K) in Ba8Ge30Ga16 [23] corresponded to a
small superconducting fraction, rather than bulk super-
conductivity. This could have resulted from BaGe2, as
an impure phase [22]. In our experiments, we have ob-
served superconducting transitions near 8 K for some
almost pure phase samples of Ge clathrates and dilute
Fe-doped clathrates [24]. Because of the small super-
conducting volume fraction (< 5%), it is difficult to
determine unambiguously whether the Ge clathrates
are superconducting. It is possible that there are un-
known superconducting phases in the samples. For
instance, in our early research [25,26], we observed
an onset superconducting transition at TC = 10 K in
(Ge, Ba)-containing phases. The complications of Ge
clathrates make understanding the superconductivity
mechanism difficult.
As a comparison with superconducting Si clath-
rates, the investigation of electronic structures of Ge
clathrate and its 3d-doping should be significant and
helpful to clarify the controversy for superconductivity
in Ge clathrates. The exploration of superconductivity
of various Ge-based compounds might not only shed
light upon particular electronic structure, but also pro-
vide a new way to look for new superconductors with
higher critical temperature in group IV.
In this Letter, we report a joint experimental and
theoretical study of Cu substitution in Ba8Si46 and
Ba8Ge46 clathrates. With increasing Cu content, the
TC decreases rapidly. For Ba8Ge40Cu6, there is no
evidence of superconductivity for temperature as low
as 1.8 K. We also used first-principles calculations to
build up a detailed picture of the atomic and elec-
tronic structure of Cu doped clathrates. Our calcula-
tion method, so-called CAmbride Serial Total Energy
Package (CASTEP), is based on the density-functional
theory (DFT) pseudopotential approach, which has al-
ready proved highly successful in many silicon inter-
metallic materials [27]. By comparing the electronic
structures of Cu-free and Cu-doped silicon clathrates,
our theoretical results show that Cu-doping gives rise
to a lower density of states (DOS) at Fermi-level. The
destructive effect of Cu-doping on superconductivity
in Si-clathrate comes from the decreasing of density
of states at Fermi-level and the localization of elec-
trons on Cu, in agreement with the experimental ob-
servations of decreasing TC. Further, comparison of
Ba8Ge46 and Ba8Si46 within the CASTEP approach
shows that the electronic structure are very similar,
which supports that the superconductivity is an in-
trinsic property of the sp3 silicon and germanium
clathrates. As a consequence, ideal fully-occupied ger-
manium clathrates are predicted to exhibit critical tem-
peratures similar to silicon clathrates. However, in the
majority of Ge-clathrate samples, the absence of su-
perconductivity arises from the vacancy effect; the
non-entire Ge-cage structure results in a small DOS
at the Fermi level.
2. Experimental results
Our synthesis of Ba8Si46–xCux and Ba8Ge46–xCux
is based on the multistep melting of bulk Ba and
Cu and Si (or Ge) powders under argon atmosphere
and sequent solid-state reaction [6,7]. The samples
were characterized and analyzed by X-ray diffrac-
tion (XRD) with graphite monochromated Cu Kα ra-
diation, and transmission electron microscopy (TEM)
(JEOL JEM-2010 at 100 kV). The obtained samples
were analyzed for magnetic properties by a SQUID
magnetometer (quantum design MPMS-XL).
Analysis by powder X-ray diffraction showed char-
acteristic type-I clathrate reflections, with a few per

4. Y. Li et al. / Physics Letters A 345 (2005) 398–408 401
Fig. 2. X-ray refinement for Ba8Si42Cu4. Upper curve: data and
fit, with difference plot below. Ticks show peaks indexed accord-
ing to the type I clathrate structure. Inset: the lattice parameters of
Ba8Si46–xCux (x = 2, 4, and 6), showing an increasing trend with
Cu doping.
cent diamond Si in Ba8Si46–xCux samples. Structural
refinement of the powder X-ray diffraction data were
carried out using the GSAS software package [28,29],
giving Cu occupying 6c Si sites and lattice parame-
ters consistent with previous work on Cu-doped Ge
clathrates [16,30].
A sample of Ba8Si42Cu4 with almost pure phase
was analyzed by X-ray diffraction measurements at
room temperature as shown in Fig. 2. Ba8Si42Cu4
crystallizes into the cubic space group Pm¯3n (No.
223) with dimensions of a = 1.03257 nm. The ex-
periment pattern is in agreement with the simulated
one for the entire 2θ region. R values for the fit are
Rwp = 0.081, Rp = 0.063. No impurity phase was ob-
served clearly, under the X-ray diffraction resolution.
The measured structural parameters are selected as the
input data for the model simulations, which will be
discussed below in Section 3.
Experiment shows that Cu-doping results in a sup-
pression of TC for Ba8Si46, and reduction in the super-
conducting fraction. Fig. 3 presents the magnetization
of Ba8Si46–xCux (x = 4) as a function of tempera-
ture, under conditions of zero field cooling (ZFC) and
field cooling (FC) at 50 Oe. The ZFC magnetization
data were taken on heating after sample cooling in
zero applied field, and the FC magnetization was mea-
sured as a function of decreasing temperature in the
applied field. The enhancement of the diamagnetism
Fig. 3. DC magnetic susceptibility of Ba8Si42Cu4 verus temper-
ature measured in H = 50 Oe. Data are shown for conditions of
zero field cooling (ZFC) and field cooling (FC) at 50 Oe. Insets are
magnified views of the temperature region near TC, for the sake of
clarity. The starting superconducting transition is observed at 2.9 K.
below TC(H) originates from the screening supercur-
rents (ZFC regime) and the Meissner effect of mag-
netic flux expulsion (FC regime). Fig. 3 demonstrates
a difference between χm in ZFC and FC. The inset of
Fig. 3 gives a detailed view of the data obtained for
H = 50 Oe in a vicinity of the TC = 2.9 K. As can
be seen from this plot, both in ZFC and in FC, χm
become more diamagnetic at T < TC. Such magne-
tization behavior is characteristic of superconductors.
Nevertheless, the TC (= 2.9 K) of Ba8Si42Cu4 is much
lower than that of pure Ba8Si46 (TC = 4–8 K) [2].
As shown in Fig. 3, the irreversibility behavior of
the sample in ZFC and FC regime show that the tran-
sition belongs to the type II superconductors. Under
an applied field of 50 Oe, the diamagnetic susceptibil-
ity is small below TC, indicating that superconducting
fraction is low. We also find out that the magnetic
field suppresses the magnitude of superconducting re-
sponse easily. In addition, we found no evidence in
Ba8Si40Cu6 for a transition to a superconducting state
in measurements down to 1.8 K, which is consistent
with a previous report [20]. This demonstrates that the
substitution of Cu heavily suppresses superconductiv-
ity in Si clathrates.
As shown in Fig. 4, magnetization versus applied
field for Ba8Si42Cu4 is characteristic of a type II su-
perconductor because of the hysteresis. In our case, the
lower critical field Hc1, defined as the minimum of the

5. 402 Y. Li et al. / Physics Letters A 345 (2005) 398–408
Fig. 4. M–H hysteresis of Ba8Si42Cu4 at 2 K, with the starting magnetization curve inset at the right. Left inset: an expanded view covering
from −5 kOe to +5 kOe.
M–H curve, is 30 Oe for Ba8Si42Cu4. This value is
much smaller than that of BaGe2 (Hc1 = 170 Oe) [25].
On the assumption that the flux associated with a sin-
gle core is πλ2Hc1, and this should be equal to the
flux quantum ΦO, so one can estimate the penetration
depth λ to be about 1.48 × 10−5 cm. Further, the irre-
versibility field Hirr at 2 K can reach about 4 kOe as
shown in the left inset of Fig. 4. This value is much
smaller than that of the BaGe2, Hirr = 10 kOe [25].
Nevertheless, superconductivity in the sample is lo-
calized within grains or islands large enough to carry
vortices.
3. Theoretical results
In order to explain the effect of Cu doping on su-
perconductivity, first-principles calculations for the
periodic boundary systems were carried out by means
of ab initio pseudopotential theory within the local
density approximation (LDA). We used the CASTEP
code in order to solve the pseudopotential Schrödinger
equation self-consistently. Besides the Cu-doped Si
clathrates mentioned above, Cu-doped germanium
clathrates were also calculated, and densities of states
of these phases will be discussed below.
The total energy pseudopotential method we used
was developed by Payne et al. [31]. This method is
based on DFT in describing the electron–electron in-
teraction and on a pseudopotential description of the
electron–core interaction, and has been publicized as
CASTEP. It gives the sum of electronic energy of a
large system, as well as its band structure. Transfer-
ability and robustness of the assumed pseudopotentials
of each element seem to be confirmed by success in
reproducing the physical properties such as lattice pa-
rameters of many compounds. Therefore, it can be ex-
pected to give the relative stability of different crystal
structures.
Wave functions were expanded in plane-wave ba-
sis sets with a kinetic energy cutoff of 300 eV for all
systems studied. We adopted the ultrasoft pseudopo-
tential. Calculated final structural data and inequiv-
alent atomic positions of each model in the cal-
culation are listed in Table 1 [2,7,16,21]. The in-
put structural parameters were obtained from ex-
perimental parameters by the geometry optimization
function. All of the lattice constants calculated here

6. Y. Li et al. / Physics Letters A 345 (2005) 398–408 403
Table 1
Calculated equilibrium structures and inequivalent atomic positions for clathrate phases of Ba8Si46, Ba8Si40Cu6, Ba8Ge46 and Ba8Ge40Cu6.
The notation of atomic positions follows that of the International Tables for Crystallography
Symmetry
Pm¯3n (No. 223)
Ba8Si46 Ba8Si40Cu6 Ba8Ge46 Ba8Ge40Cu6
Lattice
constant a (nm)
1.03280 1.03370 1.07436 1.06778
6c (Si, Ge or Cu) x = 0.25, y = 0.5, z = 0 x = 0.25, y = 0.5, z = 0 x = 0.25, y = 0.5, z = 0 x = 0.25, y = 0.5, z = 0
16i (Si, Ge) x, y, z = 0.1864 x, y, z = 0.1866 x, y, z = 0.185 x, y, z = 0.185
24k (Si, Ge) x = 0.3056, y = 0.1199, z = 0 x = 0.3099, y = 0.1187, z = 0 x = 0.307, y = 0.12, z = 0 x = 0.308, y = 0.12, z = 0
2a (Ba) x, y, z = 0 x, y, z = 0 x, y, z = 0 x, y, z = 0
6d (Ba) x = 0, y = 0.25, z = 0.5 x = 0, y = 0.25, z = 0.5 x = 0, y = 0.25, z = 0.5 x = 0, y = 0.25, z = 0.5
are shown in Table 1, and are found to be slightly
smaller than those of the experimental values, which
is a usual result of the LDA approximation. We as-
sumed Cu to be located on the 6c site, as previ-
ously supposed [16]. Spin-polarization was not con-
sidered.
The band structure and density of the states for
Ba8Si46, Ba8Si40Cu6, Ba8Ge46 and Ba8Ge40Cu6 are
shown in Fig. 5. The sixteen valence electrons from
Ba atoms and 3p electrons from Si atoms in Ba8Si46
contribute to form the conduction-band edge above the
fundamental energy-gap with width about 1 eV. There
is no contribution from 5p states were included in
the barium pseudo-potential around Fermi-level. The
DOS exhibits a metal character. The Fermi level EF is
located on a peak of DOS with N(EF ) = 40 states/eV,
which is comparable to previous theoretical calcula-
tions [32].
A direct comparison of the band structures and
DOS of Cu-free and Cu-doped clathrate shows that
the DOS of Ba8Si40Cu6 is much different than that of
Ba8Si46 both in the valence band and the conduction
band. Cu-doping results in a Fermi level shift down-
wards about 0.7 eV (not shows in Fig. 6) due to the
decrease of total electron content. On the other hand,
Cu-doping also significantly narrows the fundamental
energy-gap; a bunch of new defect energy levels ap-
pear in the fundamental energy-gap due to hybridiza-
tion of Cu 3d and Si 3p. Moreover, there is a large
additional DOS feature in valence band to form a big
peak at −2.5 eV. The density of states N(EF ) reaches
about 90 states/eV. These findings show that Cu 3d
states are strong hybridized with the valence band
states of Ba and Si, which may help to stabilize the
structure over and above the Zintl bond-filling mech-
anism. The simulation shows a lower total energy for
Ba8Ge40Cu6, implying that the Cu-substituted phase
is more stable. In experiment, the pure phase samples
of Cu-doped clathrates can be synthesized relatively
easier than those of Ba8Si46 requiring a high pressure
atmosphere.
In contrast to Ba8Si46, the conduction-band den-
sity of states of Ba8Si40Cu6 has also been strongly
changed. There is a significant decrease in the den-
sity of states at the conduction-band edge. The Fermi
level of Ba8Si40Cu6 is located close to the foot of
a DOS peak as shown in Fig. 5(b). The density of
states is only 15 states/eV, much lower than that in
Ba8Si46 (N(EF ) = 40 states/eV). This is aided by
the strong hybridization between the Cu states and the
cage structure orbitals. Thus Cu replacing Si on the
6c site strongly decreases the Fermi-level density of
states. It has been known that a high DOS at the Fermi
level is critical for the occurrence of superconductiv-
ity Cu-doping results in a decrease of N(EF ), and to a
rapid reduction in superconductivity observed experi-
mentally, as described above.
To offer further insight and contrast, we have per-
formed simulations for Cu-doped and Cu-free ger-
manium clathrates, which have framework structures
identical to the silicon clathrate. The DOS of Ba8Ge46
and Ba8Ge40Cu6 are shown in Fig. 5(c) and (d).
N(EF ) of Ba8Ge46 is very similar to that of Ba8Si46
(Fig. 6(a)). There is a high DOS peak at the Fermi
level in Ba8Ge46, which as a characteristic is asso-
ciated with the presence of superconductivity in the
cage structure [32–34]. From this result we would
predict that Ba8Ge46 would also be a superconduc-
tor. The comparison of Ba8Si46 and Ba8Ge46 sup-
ports the idea that the superconductivity is an intrin-

7. 404 Y. Li et al. / Physics Letters A 345 (2005) 398–408
Fig. 5. Band structures and density of states for (a) Ba8Si46, (b) Ba8Si40Cu6, (c) Ba8Ge46, and (d) Ba8Ge40Cu6. Density of states is calculated
using 0.1 eV Gaussian broadening of the band structure. Energy is measured from the Fermi level, which is denoted by broken horizontal lines.
sic property of the sp3 silicon and germanium net-
works [35]. As a consequence, germanium clathrates
are predicted to yield critical temperatures similar to
silicon clathrates. It is likely that lack of superconduc-
tivity in Ge clathrate comes from vacancies in the Ge
framework and corresponding DOS reduction. Indeed,
our previous experimental works have shown that the
Zintl mechanism prefers a specific Cu and vacancy
concentration, giving stabilization and semiconduct-
ing or semimetallic behavior [7]. In addition to a low-
ering of the DOS the band structure will be modified
to produce a vacancy level for Ge clathrate believed to
contain vacancies in the framework due to weaker Ge–
Ge bonding relative to Si–Si bonding [36]. For the Ge
clathrate with vacancies there is no big characteristic
DOS peak associated with occurrence of superconduc-
tivity, which will be discussed below.
Cu-doping also results in a N(EF ) decreases
from 45 states/eV in Ba8Ge46 to 15 states/eV in
Ba8Ge40Cu6, which implies no superconductivity
probably occurs. Our early experimental results
showed that no superconducting signals were observed
in Ba8Ge40Cu5 clathrate [7], and the temperature de-
pendence of resistivity shows a semiconductor-like
behavior, in agreement with our calculation of band
structure and density of states; Ba8Ge40Cu5 thus is
likely to be semiconductor with a narrow gap less
than 0.4 eV, as shown in Fig. 5(b) and (d).
The difference between Cu-doped and Cu-free
clathrates in term of hybridization can be also per-
ceived from the different valence electron density dis-
tributions in Ba8Si40Cu6 and Ba8Si46. The electronic
charge distributions in real space are shown in the con-
tour maps of the valence electron densities of Ba8Si46,

8. Y. Li et al. / Physics Letters A 345 (2005) 398–408 405
Fig. 6. Contour maps of the valence-electron densities of (a) Ba8Si46, (b) Ba8Si40Cu6, (c) Ba8Ge46, and (d) Ba8Ge40Cu6 on the (100) plane.
Ba8Si40Cu6, Ba8Ge46 and Ba8Ge40Cu6 on the (100)
plane as shown in Fig. 6. The two Ba sites of each fig-
ure correspond to those the center of the Si20 cages.
Comparing Ba8Si46 with Ba8Si40Cu6, no distinct dif-
ferences are observed in valence electron densities on
the Ba and Si 16i and 24k sites. However, the presence
of Cu on the 6c sites (which bridge the Si20 and Si24
cages) leads to a higher charge distribution between
the 6c site and its neighbors on the Si framework,
which shows that the interaction of Cu with the frame-
work is strong. This shows that Cu orbitals hybridize
strongly with the Si cage states.
To show the effect of Cu substitution on the charge
distributions at the Fermi level states, which plays
a crucial role in superconductivity, contour maps of
the electron densities at the Fermi level are shown in
Fig. 7. For Cu-free clathrates, the electrons are distrib-
uted relatively evenly on the Si (or Ge) 6c, 16i and
24k framework sites. In contrast, the electron distrib-
ution is much more localized on the 6c sites occupied
by Cu atoms in Ba8Si40Cu6. The localization of elec-
tron at Fermi level has been shown to be an important
factor in the suppression of superconductivity [37,38].
Our results show that this may also contribute to the
absence of superconductivity in Cu-doped clathrates.
4. Discussions
Isotope effect measurements have revealed that
superconductivity in Ba8Si46 is of the classic kind,
arising from the electron–phonon interaction [15].
In the conventional Bardeen–Cooper–Schrieffer the-
ory for phonon-mediated superconductivity, TC can

9. 406 Y. Li et al. / Physics Letters A 345 (2005) 398–408
Fig. 7. Contour maps of the electron densities at the Fermi level of (a) Ba8Si46 and (b) Ba8Si40Cu6 on the (100) plane.
be estimated in term of the Debye temperature ΘD
and the electron–phonon coupling constant λ: TC =
1.13ΘD exp(−1/λ). Furthermore, λ can be expressed
as the product of N(EF ) and the average electron pair-
ing interaction, V . Therefore an increase in N(EF ) is
associated with the occurrence of superconductivity.
For example, from the electronic structure calculations
of K3C60 and Rb3C60, these fullerene compounds ex-
hibit a high N(EF ), which is known to be critical for
the occurrence of the superconductivity [14,32–34]. In
addition, the comparison of N(EF ) between Na8Si46
and Ba8Si46 has shown that the strong hybridization
of Ba states with the Si46 conduction-band makes
N(EF ) large with Ba as the dopant, which plays a key
role in the superconductivity of barium-doped silicon
clathrate compounds [14,32].
As mentioned above, the calculations show that
N(EF ) is similar for Ba8Ge46 and Ba8Si46. A large
peak at Fermi level of Ba8Ge46 implies occurrence of
superconductivity. However, most observations show
no bulk superconductivity in type-I Ge clathrate sam-
ples. Ba8Ge46, however, is always found to include
vacancies in the Ge cage framework.
Thus it appears that vacancy can explain the ab-
sence of superconductivity in Ge clathrates. Our pre-
vious work about Cu-doping Ge clathrates has demon-
strated Zintl concept is available, and it also has been
widely accepted that Ba–Ge clathrates follows the
Zintl–Klemm concept [39], assuming that each Ba do-
nates two electrons to the framework, satisfying the
Fig. 8. Density of states for Ba8Ge43. The valence level occurs be-
tween conductivity band and valence band, and N(EF ) is much
smaller than that of Ba8Ge46 and Ba8Si46.
tetrahedral bonding requirements of the framework
with four electrons per site. There must be vacancies
in Ge framework. A stable Ba–Ge type-I clathrate of
composition Ba8Ge43, with three framework vacan-
cies per unit cell, has been prepared, and found to
be semiconductor [21], but with one less vacancy per
cell than expected, due to a slightly smaller electron
transfer from Ba. The analogous Ba–Sn clathrate is
predicted to be stable in the composition Ba8Sn42 [40].
We calculate the band structure and state of density
for Ge clathrate with 3 vacancies in the framework. In
our model, the lattice parameter is set a = 10.6778 Å.

10. Y. Li et al. / Physics Letters A 345 (2005) 398–408 407
For 6c sites, three Ge atoms occupy (0,0.25,0.5),
(0,0.75,0.5) and (0.5,0,0.25) sites while other 3 sites
are empty. As shown in Fig. 8, a new vacancy level
is formed between the valence band and conductive
band. The unique properties of Ba8Ge43 band struc-
ture can be attributed to the existence of vacancy ef-
fect, since Ge clathrates follow Zintl–Klemm concept
due to weaker Ge–Ge bonding unlike the Si clathrates.
The DOS at Fermi level is about 20 states/eV which is
much smaller than that of Ba8Si46 and Ba8Ge46. Small
DOS at EF is expected to suppress superconductivity,
as observed experimentally. On the other hand, we un-
ambiguously observed superconducting transitions at
about 8 K for some samples with almost pure phase of
Ge clathrates and dilute Fe-doped clathrate [24], how-
ever resistance drop cannot reach zero, and the theo-
retical superconducting volume fractions according to
measured magnetism under zero-field-cooling regime
are rather small, just only several percents, which are
much less than that of Ba8Si46 clathrate, which can
reach 100% [2]. We alternatively explain the small su-
perconducting fraction arises from that the entire Ge-
cage structure without vacancy is formed in a very few
parts of samples. The local composition incoherence
probably could be produced in the samples preparing
process. Therefore, it is probable to achieve supercon-
ductivity in Ge clathrates only by means of unique
methods such high-pressure or to adjust the composi-
tions to obtain an integrated Ge-cage structure, which
with high DOS peak and without localization of elec-
tron at Fermi level. This allows us to draw important
conclusions about the effect of on superconductivity in
Ge-clathrate materials; the entire Ge-cage framework
in clathrates is the prerequisite for occurrence of su-
perconductivity.
In summary, we report the results of CASTEP
theoretical calculations performed for Cu-doped Si
and Ge clathrates and joint measurements of super-
conducting properties. Results demonstrate the de-
ductive effect of Cu-doping on superconductivity in
clathrate compounds. In Cu-doped clathrates, the Cu
state is found to be strongly hybridized with the cage
conduction-band state. Cu doping leads to an enhance-
ment of p–d coupling. In contrast to the conduction
band of Ba8Si46, in which the EF level locates on
a big DOS peak with 40 states/eV, the Fermi level
of Ba8Si40Cu6 is found to be with lower the density
of states (∼ 15 states/eV), which should be an im-
portant effect on the non-superconductivity observed
in Cu-doped silicon clathrates. It is expected that the
electronic density of states around the Fermi level de-
creases with the Cu concentration in clathrates. A new
mechanism of vacancy defect is suggested to explain
absence of superconductivity in Ge clathrates.
Acknowledgements
This work was supported in part by the Young
Teachers Program of MOE China (EYTP), National
Natural Science Foundation of China (Grant No.
50372005), the Robert A. Welch Foundation (Grant
No. A-1526), the National Science Foundation (DMR-
0103455) and CRDF (Cooperative Grant No. 2566).
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