In conclusion, our calculations reveal the itinerant magnetism

1
In conclusion, our calculations reveal the
itinerant magnetism triggered by simple defects
in graphene and stable over the wide range of
concentrations. It is notable that the
itinerant magnetism does not require the presence
of highly reactive unsaturated dangling bonds.
Both ferromagnetic and antiferromagnetic
scenarios of the magnetic correlation
are possible with the second being more probable
for truly disordered systems. The reconstruction
of vacancy defects was found to be responsible
for the partial suppression of magnetic moments
and for the broadening of defect bands. We argue
that the defect-induced itinerant magnetism is
responsible for the experimentally observed
high-TC ferromagnetism of irradiated graphite
samples.
2
In conclusion, I have shown the crucial role
of single-atom defects in combination with a
sublatticediscriminating mechanism for developing
ferromagnetic order in graphene-based materials.
In graphite, the role of such a mechanism is
played by the stacking order of graphene layers.
This suggestion is confirmed by the ab initio
investigation of hydrogen chemisorption
and vacancy defects in proton-bombarded graphite.
The results of this study pave a way for
tailoring carbon-based magnetic materials by
means of irradiation and chemical treatment of
graphite and other graphene derivatives.
3
The effects of impurities on the magnetism of
electrons on a half-filled honeycomb lattice are
studied using the self-consistent T-matrix
approximation and an exact diagonalization
analysis. Staggered susceptibility is found to be
enhanced by vacancies it logarithmically
diverges as T !0 even in the absence of
electronelectron interaction. It is found that
this strong enhancement of staggered susceptibilit
y is brought about by resonance states at zero
energy (zero modes) induced by vacancies. Possible
magnetic states induced by vacancies are
discussed.
4
It is shown that a strong impurity potential
induces short-range antiferromagnetic
(ferrimagnetic) order around itself in a Hubbard
model on a half-filled honeycomb lattice. This
implies that short-range magnetic order is
induced in monolayer graphene by a nonmagnetic
defect such as a vacancy with full hydrogen
termination or a chemisorption defect
5
It is shown that a non-magnetic vacancy
introduced to a two-dimensional graphite
(graphene) sheet enhances response function to a
staggered field even when Coulomb interaction
between electrons is ignored. This strongly
implies that a vacancy introduced to a graphene
sheet induces short-ranged antiferromagnetic
order around it.
6
Two-dimensional carbon, or graphene, is a
semimetal that presents unusual low-energy
electronic excitations described in terms of
Dirac fermions. We analyze in a self-consistent
way the effects of localized impurities or
vacancies and extended edges or grain boundaries
defects on the electronic and transport
properties of graphene. On the one hand, point
defects induce a finite elastic lifetime at low
energies with the enhancement of the electronic
density of states close to the Fermi level.
Localized disorder leads to a universal,
disorder independent, electrical conductivity at
low temperatures, of the order of the quantum of
conductance. The static conductivity increases
with temperature and shows oscillations in the
presence of a magnetic field. The graphene
magnetic susceptibility is temperature dependent
unlike an ordinary metal and also increases
with the amount of defects. Optical transport
properties are also calculated in detail. On the
other hand, extended defects induce localized
states near the Fermi level. In the absence of
electron-hole symmetry, these states lead to a
transfer of charge between the defects and the
bulk, the phenomenon we call self-doping. The
role of electron-electron interactions in
controlling self-doping is also analyzed. We also
discuss the integer and fractional quantum Hall
effect in graphene, the role played by the edge
states induced by a magnetic field, and their
relation to the almost field independent surface
states induced at boundaries. The possibility of
magnetism in graphene, in the presence of
short-range electron-electron interactions and
disorder is also analyzed.
7
We study the magnetic properties of
nanometer-sized graphene structures with
triangular and hexagonal shapes terminated by
zigzag edges. We discuss how the shape of the
island, the imbalance in the number of atoms
belonging to the two graphene sublattices, the
existence of zero-energy states, and the total
and local magnetic moment are intimately related.
We consider electronic interactions both in a
mean-field approximation of the one-orbital
Hubbard model and with density functional
calculations. Both descriptions yield values for
the ground state total spin S consistent with
Liebs theorem for bipartite lattices. Triangles
have a finite S for all sizes whereas hexagons
have S 0 and develop local moments above
a critical size of 15 nm.
8
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9
Here, we propose a modified strategy for
generating fractal structures with large spin
based on a building block consisting of a
spin-polarized triangular fragment, the same as
in the WMK proposal.
10
We address the electronic structure and magnetic
properties of vacancies and voids both in
graphene and graphene ribbons. By using a
mean-field Hubbard model, we study the appearance
of magnetic textures associated with removing a
single atom vacancy and multiple adjacent atoms
voids as well as the magnetic interactions
between them. A simple set of rules, based on the
Lieb theorem, link the atomic structure and
the spatial arrangement of the defects to the
emerging magnetic order. The total spin S of a
given defect depends on its sublattice imbalance,
but some defects with S0 can still have local
magnetic moments. The sublattice imbalance also
determines whether the defects interact
ferromagnetically or antiferromagnetically with
one another and the range of these magnetic
interactions is studied in some simple cases. We
find that in semiconducting armchair ribbons and
two-dimensional graphene without global
sublattice imbalance, there is a maximum defect
density above which local magnetization
disappears. Interestingly, the electronic
properties of semiconducting graphene ribbons
with uncoupled local moments are very similar to
those of diluted magnetic semiconductors,
presenting giant Zeeman splitting.
11
Theoretical calculations, based on the hybrid
exchange density functional theory, are used to
show that in graphene, a periodic array of
defects generates a ferromagnetic ground state at
room temperature for unexpectedly large defect
separations. This is demonstrated for defects
that consist of a carbon vacancy in which two of
the dangling bonds are saturated with H
atoms. The magnetic coupling mechanism is
analysed and found to be due to an instability in
the -electron system with respect to a long-range
spin polarization characterized by alternation in
the spin direction between adjacent carbon
atoms. The disruption of the -bonding opens a
semiconducting gap at the Fermi edge. The size of
the energy gap and the magnetic coupling strength
are strong functions of the defect separation and
can thus be controlled by varying the
defect concentration. The position of the
semiconducting energy gap and the
electron effective mass are strongly
spin-dependent and this is expected to result in
a spin asymmetry in the transport properties of
the system. A defective graphene sheet is,
therefore, a very promising material with an
in-built mechanism for tailoring the properties
of future spintronic devices.
12
An electronic phase with coexisting magnetic and
ferroelectric order is predicted for graphene
ribbons with zigzag edges. The electronic
structure of the system is described with a
mean-field Hubbard model that yields results very
similar to those of density functional
calculations. Without further approximations, the
mean-field theory is recasted in terms of a BCS
wave function for electron-hole pairs in the edge
bands. The BCS coherence present in each spin
channel is related to spin-resolved electric
polarization. Although the total electric
polarization vanishes, due to an internal phase
locking of the BCS state, strong magnetoelectric
effects are expected in this system. The
formulation naturally accounts for the two gaps
in the quasiparticle spectrun, 0 and 1, and
relates them to the intraband and interband
self-energies.
13
Local magnetic moment formation on edges of
graphene is studied using the Hubbard model on a
honeycomb lattice. The Coulomb interaction is
treated with the mean field approximation.
Realistic edges of graphene are composed of
zigzag and armchair parts. It is found that, on a
zigzag part of length na larger than 3a, where a
is the lattice constant, local staggered moment
whose magnitude is proportional to the length of
the zigzag part, is developed, i.e., a zigzag
part of length 3a is sufficient for generation of
local magnetism. This also means that one has to
get rid of zigzag parts of n 3 to suppress local
edge magnetism of graphene.
14
Theoretical calculations, based on the hybrid
exchange density functional theory, are used to
show that in graphene, a periodic array of
defects generates a ferromagnetic ground state at
room temperature for unexpectedly large defect
separations. This is demonstrated for defects
that consist of a carbon vacancy in which two of
the dangling bonds are saturated with H
atoms. The magnetic coupling mechanism is
analysed and found to be due to an instability in
the -electron system with respect to a long-range
spin polarization characterized by alternation in
the spin direction between adjacent carbon
atoms. The disruption of the -bonding opens a
semiconducting gap at the Fermi edge. The size of
the energy gap and the magnetic coupling strength
are strong functions of the defect separation and
can thus be controlled by varying the
defect concentration. The position of the
semiconducting energy gap and the
electron effective mass are strongly
spin-dependent and this is expected to result in
a spin asymmetry in the transport properties of
the system. A defective graphene sheet is,
therefore, a very promising material with an
in-built mechanism for tailoring the properties
of future spintronic devices.
15
We investigate the effect of edge defects
vacancies and impurities substitutional dopants
on the robustness of spin polarization in
graphene nanoribbons GNRs with zigzag edges by
using density-functionaltheory calculations. The
stability of the spin state and its magnetic
moments is found to continuously decrease with
increasing the concentration of the defects or
impurities. The system generally becomes
nonmagnetic at the concentration of one edge
defect impurity per 10 Å. The spin suppression is
shown to be caused by the reduction and removal
of edge states at the Fermi energy. Our analysis
implies an important criterion on the GNR samples
for spintronics applications.
16
Using a first-principles density-functional
electronic structure method, we study the energy
gaps and magnetism in bilayer graphene
nanoribbons as a function of the ribbon width and
the strength of an external electric field
between the layers.We assume AB Bernal stacking
and consider both armchair and zigzag edges and
two edge alignments distinguished by different
ways of shifting the top layer with respect to
the other. Armchair ribbons exhibit three classes
of bilayer gaps which decrease with increasing
ribbon width. An external electric field between
the layers increases the gap in narrow ribbons
and decreases the gap for wide ribbons, a
property which can be understood semianalytically
using a -band tight-binding model and
perturbation theory. The magnetic properties of
zigzag edge ribbons are different for the two
different edge alignments, and not robust for all
exchange-correlation approximations considered.
Bilayer ribbon gaps are sensitive to the presence
or absence of magnetism.
17
Based on first-principles calculations, we showed
that repeated heterostructures of zigzag
graphene nanoribbons of different widths form
multiple quantum well structures. Edge states of
specific spin directions can be confined in these
wells. The electronic and magnetic state of the
ribbon can be modulated in real space. In
specific geometries, the absence of reflection
symmetry causes the magnetic ground state of
whole heterostructure to change from
antiferromagnetic to ferrimagnetic. These quantum
structures of different geometries provide unique
features for spintronic applications.
18
We study the influence of pentagons, dislocations
and other topological defects on the
magnetic properties of a graphene lattice in a
Hartree Fock mean field scheme. The ground state
of the system with a number of vacancies
belonging to the same sublattice in the non
frustrated lattice has been usually found to
follow the Lieb theorem and be equal to the
number of uncoordinated atoms in the lattice for
any value of the Coulomb repulsion U. We show
that the presence of a single pentagonal ring in
a large lattice is enough to alter this behavior
and a critical value of U is needed to find
the polarized ground state. Glide dislocations
made of a pentagon-heptagon pair induce more
dramatic changes on the lattice and the critical
value of U needed to polarize the ground state
depends on the density and on the relative
position of the defects and there is a region in
parameter space where the polarized and
unpolarized ground states coexist.
We study the stability and evolution of various
elastic defects in a flat graphene sheet and the
electronic properties of the most stable
configurations. Two types of dislocations are
found to be stable glide dislocations
consisting of heptagonpentagon pairs, and
shuffle dislocations, an octagon with a
dangling bond. Unlike the most studied case of
carbon nanotubes, Stone Wales defects seem to be
dynamically unstable in the planar graphene
sheet. Similar defects in which one of the
pentagonheptagon pairs is displaced vertically
with respect to the other one are found to be
dynamically stable. Shuffle dislocations
will give rise to local magnetic moments that can
provide an alternative route to magnetism in
graphene.
19
We performed ab initio calculations, using
density functional theory, to study spin
polarization in carbon nanostructures with
disclinations. The results indicate that
compounds with positive and negative Gaussian
curvature may exhibit a net magnetic moment in
the ground state. Additionally, we can conclude
that, carbon compounds that display an odd number
of pentagons and heptagons, present polarization
in the ground state.
20
The phase diagram of a biased graphene bilayer is
computed and the existence of a ferromagnetic
phase is discussed both in the critical on-site
interaction Uc versus doping density and versus
temperature. We show that in the ferromagnetic
phase the two planes have unequal magnetization
and that the electronic density is hole-like in
one plane and electron-like in the other. We give
evidence for a first-order phase transition
between paramagnetic and ferromagnetic phases
induced by doping at zero temperature.
21
Magnetic zigzag edges of graphene are considered
as a basis for novel spintronics devices despite
the fact that no true long-range magnetic order
is possible in one dimension. We study the
transverse and longitudinal fluctuations of
magnetic moments at zigzag edges of graphene from
first principles. We find a high value for the
spin wave stiffness D 2100 meV A2 and a
spin-collinear domain wall creation energy Edw
114 meV accompanied by low magnetic anisotropy.
Above the crossover temperature Tx 10 K, the
spin correlation length / T1 limits the
long-range magnetic order to 1 nmat 300 K while
below Tx, it grows exponentially with decreasing
temperature. We discuss possible ways of
increasing the range of magnetic order and
effects of edge roughness on it.
22
Within the Hartree Fock RPA analysis, we derive
the spin wave spectrum for the weak ferromagnetic
phase of the Hubbard model on a
honeycomb lattice. Assuming a uniform
magnetization, the polar (optical) and
acoustic branches of the spin wave excitations
are determined. The bipartite lattice geometry
produces a q-dependent phase difference between
the spin wave amplitudes on the two sub-lattices.
We also find an instability of the uniform weakly
magnetized configuration towards a weak
antiferromagnetic spiraling spin structure, in
the lattice plane, with wavevector Q along the K
direction, for electron densities n gt 0.6. We
discuss the effect of diagonal disorder on both
the creation of electron bound states and the
enhancement of the density of states, and the
possible relevance of these effects to
disorder-induced ferromagnetism, as observed in
proton-irradiated graphite.
23
We present an ab initio density functional theory
study of the magnetic moments that arise in
graphite by creating single carbon vacancies in a
three-dimensional 3D graphite network using full
potential, all electron, spin polarized
electronic structure calculations. In previous
reports, the appearance of magnetic moments
was explained in a two-dimensional graphene sheet
just through the existence of the vacancies
itself Carbon-Based Magnetism, edited by F.
Palacio and T. Makarova Elsevier, Amsterdam,
2005 D. C. Mattis, Phys. Rev. B 71, 144424 2005
Y. Kobayashi et al., ibid. 73, 125415 2006 R.
Yoshikawa Oeiras et al., ibid. to be published
P. O. Lehtinen et al., Phys. Rev. Lett. 93,
187202 2004. The dependence of the arising
magnetic moment on the nature and geometry of the
vacancies for different supercells is reported.
We found that the highest value of magnetic
moment is obtained for a 331 supercell and that
the highly diluted 551 supercell shows no
magnetic ordering. The results obtained in this
paper are indicative of the importance
of interlayer interactions present in a 3D
stacking. We conclude that this should not be
underestimated when vacancy-based studies on
magnetism in graphitic systems are carried out.
24
We present an ab initio density functional theory
study of the magnetic moments that arise in
graphite by creating single carbon vacancies in a
three-dimensional 3D graphite network using full
potential, all electron, spin polarized
electronic structure calculations. In previous
reports, the appearance of magnetic moments
was explained in a two-dimensional graphene sheet
just through the existence of the vacancies
itself Carbon-Based Magnetism, edited by F.
Palacio and T. Makarova Elsevier, Amsterdam,
2005 D. C. Mattis, Phys. Rev. B 71, 144424 2005
Y. Kobayashi et al., ibid. 73, 125415 2006 R.
Yoshikawa Oeiras et al., ibid. to be published
P. O. Lehtinen et al., Phys. Rev. Lett. 93,
187202 2004. The dependence of the arising
magnetic moment on the nature and geometry of the
vacancies for different supercells is reported.
We found that the highest value of magnetic
moment is obtained for a 331 supercell and that
the highly diluted 551 supercell shows no
magnetic ordering. The results obtained in this
paper are indicative of the importance
of interlayer interactions present in a 3D
stacking. We conclude that this should not be
underestimated when vacancy-based studies on
magnetism in graphitic systems are carried out
25
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26
The magnetic properties of the hydrogenated
single-walled carbon nanotubes SWNTs have been
studied by the first-principles calculations. It
is found that different distributions of hydrogen
atoms on the SWNT surfaces have a significant
effect on the magnetic order of the hydrogenate
SWNTs. More importantly, it has been shown that
in general there exist two types of the hydrogen
adsorption sites on the SWNT external
surface, forming two different structures of the
hydrogenated SWNTs, i.e., the so-called AA and AB
structure, among which the latter has lower total
energy than the former. The flat bands appear at
the Fermi energy in the AA structures, favoring
spontaneous magnetism, but not in the AB
structures, making the composite system
always stay in the nonmagnetic ground state.
27
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28
We apply first-principles calculations to
investigate the interplay between electronic and
magnetic properties of carbon nanotubes with line
defects. We consider three types of defects
lines of COC epoxy groups, and defects
resulting from the substitution of the oxygen
atoms by CH2 or C2H4 divalent radicals. We find
that the line defects behave as pairs of coupled
graphene edge states, and a variety of electronic
and magnetic ground states is predicted as a
function of defect type, nanotube diameter, and
a possibly applied transverse electric field.
29
Density-functional calculations of electronic
structure, total energy, structural distortions,
and magnetism for hydrogenated single-layer,
bilayer, and multilayer graphenes are performed.
It is found that hydrogen-induced magnetism can
survive only at very low concentrations of
hydrogen single-atom regime whereas
hydrogen pairs with optimized structure are
usually nonmagnetic. Chemisorption energy as a
function of hydrogen concentration is calculated,
as well as energy barriers for hydrogen binding
and release. The results confirm that graphene
can be perspective material for hydrogen storage.
Difference between hydrogenation of graphene,
nanotubes, and bulk graphite is discussed.
30
Hydrogen interactions with undefective and
defective graphitic structures were investigated
by firstprinciples simulations. Structural
vacancies were identified to promote the
dissociation of molecular hydrogen with a reduced
activation barrier of 0.63 eV, compared to 2.38
eV for a perfect graphene. However, the vacancies
bind the hydrogen too strongly for spill-over
mechanisms to be effective. An isolated vacancy
in a graphene can bind four hydrogen atoms, but a
metastable and magnetic structure binds six
hydrogen atoms at the vacancy site at room
temperature. The thermodynamics, magnetic
properties, and hydrogen binding energies vary
with graphene layer spacing. A metastable
structure becomes energetically favorable for a
layer spacing of 3.19 Å, while the binding of
hydrogen becomes exothermic at a layer spacing of
2.72 Å. This phenomenon suggests the possibility
of using hydrogen-rich carbon structures for
reversible magnetic and hydrogen storage
applications.
31
We predict the existence of antiferromagnetic
ordering in the one-dimensional dangling-bond
wires fabricated on a hydrogen-terminated C001
surface. Our spin-polarized density-functional
theory calculations show that the
antiferromagntic configuration, where the spins
of adjacent dangling bonds point in opposite
directions, is favored over the ferromagnetic
one. Using the broken symmetry method, we
estimate an exchange coupling constant of 31 meV
between adjacent spins. It is thus shown that
unpaired electrons in sp3-bonded diamond yield
magnetic moments which interact
antiferromagnetically with each oth
32

33

• The concentrations of various elements in ppm
• Fe 43.70,
• Cr 7.60,
• Mn 12.70,
• Ti 1.61,
• Zn 59.60,
• Cu 110.00,
• Al 102.00,
• Ba 0.85,
• Ca 485.00,
• Mg 59.60,
• Si 8.50,
• Other elements, such as Co, Ni, K, Li, Pb, Sr,
  and V, have not been detected by ICP. According
  to the ICP result, the magnetic impurity of Fe is
  43.70 ppm in CMTs. If assuming the worst case in
  which all the Fe was in its FM elemental forms,
  the saturation magnetic moments per unit mass
  caused by Fe is estimated as 0.0096 emu/g, which
  is only 3.1 of the total measured magnetization
  value 0.314 emu/g at 300 K in CMTs.

sp-hybridized structure
34
Carbon powder was produced by a pulsed arc
ignited between two carbon electrodes submerged
in ethanol, and was comprised of both micro- and
nano-particles. The measured magnetic properties
of the mixed raw powder at 20 and 300 K were
saturation magnetization Ms 0.900.93 emu/g,
residual magnetization Mr 0.022 and 0.018
emu/g, and coercive force Hc 11 and 8 Oe,
respectively. The data lead to conclusion that
the powder consisted of ferromagnetic particles
with a critical temperature much higher than 300
K. Magnetic particles in solution were separated
by means of bio-ferrography. It was found that
the magnetically separated particles included
chains of 3050 nm diameter spheres, and
nanotubes and nanorods with lengths of 50250 nm
and diameters of 20 30 nm. In contrast, the
residual particles which passed through the
bio-ferrograph consisted of 1 lm and larger
micro-particles, and nano-particles without any
definite shape
35
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36
The irradiations with 10 MeV O ion beam
Figure 4 shows the curves of magnetization versus
applied magnetic field recorded for ion
irradiated and pristine C60 films at 15 K.
Magnetization measurements were also performed at
5, 15, 50, 100, 200, and 300 K.In this
temperature range, no significant change of the
ferromagnetic signal was observed.The results
show that the saturation magnetization increases
with the ion fluence and the saturation
magnetization reaches 0.54 emu/cm3 for the
fluence of 51013 O ions/cm.2
Fig. 4. Magnetization measurement on pristine and
ion irradiated C60 film at indicated fluences.
37
It is shown that polycrystalline fullerene thin
films on hydrogen-passivated Si111 substrates
irradiated by 2 MeV protons display
ferromagneticlike behavior at 5 K. At 300 K, both
the pristine and the irradiated film show
diamagnetic behavior. Magnetization data in the
temperature range of 2300 K in 1 T applied
field, for the irradiated film show much stronger
temperature dependence compared to the pristine
film. Possible origins of ferromagneticlike
signals in the irradiated films are discussed.
38
PbC nanocomposites consisting of pyrolytic
carbon nanospheres and Pb nanoparticles
were produced by discharging a mixture of Pb and
graphite powders in an ethanol and Ar atmosphere.
Raman spectrum and x-ray photoelectron
spectroscopy indicated that the carbons in the
PbC nanocomposites are in both ordered and
disordered forms. The Pb atoms in the PbC
nanocomposites were removed by the treatment of a
65 HNO3 solution to form carbon nanocomposites
in order to have a comparison. X-ray diffraction
data and magnetic measurements revealed the
magnetism of the nanosized pyrolytic carbon with
different degrees of crystallization, in which
disordered carbon with a (0 0 2) interlayer
spacing of 0.342 nm is diamagnetic, while the
oriented pyrolytic graphite with a spacing of
0.337 nm shows ferromagnetism. The saturation
magnetization of highly oriented pyrolytic
graphite (HOPG) nanospheres is enhanced by about
two orders of magnitude, compared with that
of bulk HOPG. Spin-glass behaviour of HOPG
nanospheres may be caused by complex competing
interactions between magnetic moments in
nanosized HOPG.
Figure 3. (a) and (b) TEM images of the PbC
nanocomposite. HRTEM images of (c) Pb
nanoparticles with different thicknesses of PbO
shells and (d) pyrolytic carbon nanospheres.
39
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40
Magnetic measurements up to 1200 K on
iron-contaminated multiwalled carbon nanotube
mats. Extensive magnetic data consistently show a
ferrromagnetic transition at about 1000 K and a
ferromagnetic-like transition at about 1275 K.
The ferromagnetic transition at about 1000 K is
associated with an Fe impurity phase and its
saturation magnetization is in quantitative
agreement with the Fe concentration measured by
an inductively coupled plasma mass spectrometer.
On the other hand, the saturation magnetization
for the ferromagnetic-like phase at 1275 K is
about 4 orders of magnitude larger than that
expected from the measured concentration of Co or
CoFe.We show that this ultrahigh-temperature
ferromagnetic-like transition is not consistent
with ferromagnetism of any e-carbon phases,
carbon-based phases, or magnetic impurities.
Alternatively, the observed magnetic behavior of
ultrahigh-temperature ferromagnetic-like phase
can be consistently explained in terms of the
paramagnetic Meissner effect orbital
ferromagnetism due to the existence of
Josephson junctions in a granular superconduct