050007 2013 S. A. Grigera E. M. Forgan, School of Physics & Astronomy,
University of Birmingham, U.K. 050007

We review experimental results, from transport to magnetization measurements,
on different graphite samples, from bulk oriented graphite, thin graphite
films to transmission electron microscope lamellae, that indicate the
existence of granular superconductivity at temperatures above 100 K. The
accumulated evidence speaks for a localization of the superconducting phase(s)
at certain interfaces embedded in semiconducting crystalline regions with
Bernal stacking order.

# Invited review: Graphite and its hidden superconductivity

P. Esquinazi[inst1] E-mail<EMAIL_ADDRESS>
(25 January 2013; 10 October 2013)

††volume: 5

99 inst1 Division of Superconductivity and Magnetism, Institute for
Experimental Physics II, Fakultät für Physik und Geowissenschaften,
Universität Leipzig, Linnéstrasse 5, D-04103 Leipzig, Germany.

##  1 Introduction

Over the past decade, our interpretation of the magnetic and transport
properties of ordered graphite bulk samples has experienced a change respect
to the partially accepted general description of their intrinsic properties.
The description of graphite one finds in the not-so-old literature tells us
that it is a kind of (semi)metal with a finite Fermi energy and carrier
(electron plus hole) densities per graphene layer at low temperatures
$n_{0}\sim 10^{10}\ldots 10^{12}~{}$cm-2, see e.g., [1, 2, 3]. However, real
samples are not necessarily ideal, we mean defect-free, and therefore those
carrier densities are not necessarily intrinsic of ideal graphite. The
exhaustive experience accumulated in gapless and narrow band semiconductors
[4] already indicates us how important defects and impurities (not necessarily
magnetic ones but, for example, hydrogen) are in determining some of the
measured properties. Therefore, taking experimental data of real samples as
intrinsic, without knowing their microstructure and/or defect concentration,
was indeed a misleading assumption in the past. This assumption has
drastically influenced the description of the band structure of graphite we
found nowadays in several books and publications. For example, if graphite has
a finite Fermi energy $E_{F}$ (whatever the majority carriers are), as assumed
everywhere, up to seven free parameters have to be introduced [2, 5, 6] to
describe the apparently ideal band structure of Bernal graphite with the well-
known ABAB stacking order of the graphene layers.

The impact of well defined two-dimensional interfaces inside graphite samples
[7, 8] had not been realized until recent studies of the transport properties
as a function of thickness of the graphite sample provided a link to the
microstructure of the samples obtained by transmission electron microscope
(TEM) studies. We also have to add the sensitivity of the graphite transport
properties to very small amount of defects [9]. Those results [7, 9] do not
only indicate us that at least a relevant part of the carrier densities
measured in graphite is not intrinsic but also that the metallic-like behavior
of the electrical resistance does not reflect ideal, defect-free graphite
[10]. An anomalous vanishing of the amplitude of the Shubnikov-de Haas (SdH)
oscillations decreasing the thickness of the graphite samples was published,
more than 10 years ago, [11] without attracting the necessary attention,
although those results already suggested that the SdH oscillations are
probably not intrinsic of the graphite structure. These results are supported
by the absence of SdH oscillations, i.e., no evidence for the existence of a
Fermi surface, found recently in bulk oriented samples of high grade and high
purity but without internal interfaces [12]. All these results indicate that
the internal microstructure of the graphite samples play an important role, a
microstructure that was neither characterized nor considered in the discussion
of the measured properties of different graphite samples, from highly oriented
pyrolytic graphite (HOPG) to Kish or natural graphite, even in nowadays
literature [6, 13, 14].

What does this have to do with superconductivity? If we start searching for
superconductivity in graphite by measuring the behavior of the electrical
resistance ($R$) with temperature ($T$) and magnetic field ($H$), for example,
it should be clear that the knowledge of the intrinsic, normal state
dependence is needed. Otherwise, we may misleadingly interpret an anomalous
behavior due to, for example, the influence of non-percolative, granular
superconducting regions embedded in a (normal state) graphite matrix, as
intrinsic of the material, clearly missing an interesting aspect of the
sample. A reader with expertise in superconductivity might not be convinced
that such a mistake could be ever made. However, the ballistic transport
characteristics of the graphene layers in ideal graphite with their huge
mobility and mean free path [15, 16, 17, 18] provide a high conductivity path
in parallel; such that it is not at all straightforward by simple experiments
to realize and prove the existence of superconductivity at certain regions in
some, not all, graphite samples. One needs indeed to do systematic experiments
decreasing the size of the graphite samples (but not too much) to obtain clear
evidence for the embedded or “hidden” superconductivity.

A note on samples: The internal ordering or mosaicity of the graphite
crystalline regions inside commercial HOPG samples is given usually by the
grade. For example, the highest ordered pyrolytic graphite samples have is a
grade “A”, which means a rocking curve width $\Delta\sim 0.4^{\circ}\pm
0.2^{\circ}$ (“B”, $\Delta\sim 0.8^{\circ}$, etc.). Interestingly, and due to
the contribution of two dimensional highly conducting internal interfaces
between crystalline regions [7, 10], the highest grade, i.e., smaller rocking
curve width, does not always mean that the used sample provides the intrinsic
transport properties of ideal graphite. The characterization of the internal
structure of usual HOPG samples, as well as the thickness dependence of $R(T)$
to understand the transport and the magnetic properties of graphite, indicate
that these two dimensional interfaces are of importance. The existence of
rhombohedral inclusions [19, 20] (stacking order ABCABC instead of ABAB of the
usual Bernal graphite structure) in HOPG as well as in Kish graphite samples
can also have a relationship with the hidden superconductivity in graphite,
following the theoretical work in Ref. [21]. According to literature (see
e.g., Fig. 2-2 in Ref. [8]), the density of interfaces parallel to the
graphene layers in Kish graphite, in regions of several microns length, is
notable. Therefore, quantifying the perfection of any graphite sample through
the resistivity ratio between 300 K and 4.2 K [8] is not necessarily the best
criterion to be used if we are interested on the intrinsic properties of the
graphene layers in graphite, because of the high conductivity of the
interfaces in parallel to the graphene layers of the sample [10]. Two examples
of the interfaces we are referring to can be seen in Fig. 1. On the other
hand, commercial HOPG bulk samples are of high purity with average total
impurity concentrations below 20 ppm. Especially the existence of magnetic
impurities are of importance if the Defect-Induced Magnetism (DIM) is the main
research issue. Their concentration remains below a few ppm for high grade
HOPG samples [22].

The graphite flakes discussed in this work were obtained by exfoliation of
HOPG samples of different batches, by careful mechanical press and rubbing the
initial material on a previously cleaned substrate. As substrate, we used
p-doped Si with a 150 nm SiN layer on top. We selected the flakes using
microscopic and micro-Raman techniques to check their quality. More details on
the preparation can be taken from Ref. [7] and other publications cited below.

This review is organized as follows. In the next section we discuss the
experimental data for $R(T,H)$ from different graphite samples published in
the last 12 years and argue that the first hints on unusual superconducting
contribution can be already found in those measurements. In section III, we
discuss the anomalous hysteresis in the magnetoresistance, a first clear
indication for embedded granular superconductivity. Section IV, deals with the
Josephson behavior measured in TEM lamellae whereas section V deals with the
granular superconducting behavior found in the magnetization of water-treated
graphite powder as well as in bulk HOPG samples for fields normal to the
interfaces found inside those samples. In the last section, section VI, before
the conclusion, we discuss possible origins for the superconducting signals on
the basis of earlier and recent experimental and theoretical work.

##  2 The behavior of the resistance vs. temperature at different applied
magnetic fields

In this section, we discuss the behavior of the resistance $R(T,H)$ of
different HOPG samples including Kish graphite. The data we present here were
taken from [7, 23, 24] and a quick search in literature demonstrates that
these data are reproducible and can be found in different publications, see,
e.g., [2, 25, 26, 27]. Figure 2(a) shows the $R(T)$ for different bulk
graphite samples of different grades (rocking curve width) and for one sample
(HOPG-1) at zero and under a magnetic field applied normal to the main area,
i.e., normal to the graphene planes of the sample. This figure reveals a
general behavior, namely that the lower the resistivity $\rho$ of the HOPG
sample, the more metallic-like its temperature dependence. It is appealing to
assume that these characteristics, low $\rho$, low $\Delta$ and the metallic
behavior are clear signs for more ideal graphite. Therefore, from the measured
$R(T)$, we may conclude that sample HOPG-3 is more ideal than sample HOPG-1
and the latter being more ideal than sample HOPG-2, see Fig. 2(a). This is
indeed the usual interpretation found in several reviews in the literature,
see e.g., [28, 8].

From a quick look at all the curves in Fig. 2, however, one recognizes a
striking similarity between them, although we are comparing different samples
with different thickness and some of the curves were measured under a magnetic
field applied normal to the graphene layers of the samples; also normal to the
interfaces commonly found in some ordered samples [8, 7].

Figure 1: Transmission electron microscope pictures of two different kinds of
interfaces and their distribution in HOPG samples. The TEM pictures were taken
from two different lamellae, each about 300 nm thick and with the electron
beam nearly parallel to the graphene planes of the samples. (a) The interfaces
are recognized at the borders of crystalline regions of different gray colors.
Taken from [7]. (b) Interfaces found in a HOPG sample used for magnetization
measurements (see section V)that reveals hysteretic behavior in field and
temperature. Taken from [29].

Let us start discussing the metallic-like behavior of $R(T)$ of sample HOPG-3
in Fig. 2(a). This sample behaves as the HOPG-UC sample shown in (c) at zero
magnetic field, having also a maximum at $T\sim 150~{}$K. A “better” metallic
character shows the HOPG sample in (b) or the Kish graphite sample in (d),
without any maximum in the shown temperature range. Is this metallic-like
behavior really intrinsic of ideal graphite?

The following experimental evidence does not support such interpretation:
First, for samples from the same batch, the metallic character of $R(T)$
vanishes in the whole temperature range when the sample thickness is below
$\sim 50~{}$nm [11, 7, 27], see Fig. 2(b).
Second, the metallic-like behavior vanishes in the whole temperature range
after applying a magnetic field of the order of 1 to 2 kOe, an interesting
behavior known as the Metal-Insulator Transition (MIT) [23, 26, 25], see Figs.
2(a), (c) and (d). Note that such magnetic field strength influences mainly
the metallic-like region, see e.g., the change of sample HOPG-1 in Fig. 2(a)
at zero and at 1 kOe field, an interesting behavior noted first in [30] and
interpreted as due to superconducting instabilities.

At those field strengths, i.e., $H\sim 1~{}$kOe, the obtained $R(T)$ curves,
for samples showing at zero field a metallic-like behavior, resemble the
semiconducting-like curves obtained for sample HOPG-2 (Fig. 2(a)) or for
samples with small thickness (Fig. 2(b)). At fields higher than a few kOe, the
rather large magnetoresistance of graphite starts to play the main role and
the $R(T)$ curve increases in the whole temperature range.

Finally, all these results added to the existence of well defined interfaces
in the metallic-like HOPG samples as well as in Kish graphite, with distances
in the $c-$axis direction usually larger than $\sim 30$ nm, indicate that the
metallic-like behavior is due to the contribution of these interfaces and it
is not intrinsic of the graphene layers of ideal graphite [7, 10]. Therefore,
explanations of the MIT based on ideal graphite band models with a large
number of free parameters [25, 26] are certainly not the appropriate ones.

All the different $R(T)$ curves for different samples shown in Fig. 2 and at
zero field can be very well understood assuming the parallel contribution of
semiconducting graphite paths in parallel to the one from the highly
conducting interfaces [10]. The saturation of the resistance at $T\rightarrow
0$ K is interpreted as due to the finite resistance of the sample surfaces
(the free one and the one on the substrate) short circuiting the intrinsic
behavior of the bulk graphene layers at low enough temperatures.

Figure 2: (a) Normalized resistance vs. temperature for three different HOPG
bulk samples. The bottom, metallic-like curve corresponds to the sample
HOPG-3, the curves above correspond to HOPG-1 ($H=0$), HOPG-1 ($H=1~{}$kOe),
and HOPG-2. The grade and resistivity values are HOPG-1 ($\Delta=1.4^{\circ}$,
resistivity at 300 K $\rho(300$K$)=45~{}\mu\Omega$cm), HOPG-2
($\Delta=1.2^{\circ}$, $\rho(300$K$)=135~{}\mu\Omega$cm) and HOPG-3
($\Delta=0.5^{\circ}$, $\rho(300$K$)=5~{}\mu\Omega$cm). Taken from [23]. (b)
Similar to (a) but for HOPG samples from the same batch but with different
size, namely (thickness $\times$ length $\times$ width) L5: $12\pm 3~{}$nm,
$27~{}\mu$m, $14~{}\mu$m, L2A: $20\pm 5~{}$nm, $5~{}\mu$m, $10~{}\mu$m, L8A:
$13\pm 2~{}$nm, $14~{}\mu$m, $10~{}\mu$m, L8B: $45\pm 5~{}$nm, $3~{}\mu$m,
$3~{}\mu$m, L7: $75\pm 5~{}$nm, $17~{}\mu$m, $17~{}\mu$m, HOPG: $17\pm
2~{}\mu$m, $4.4~{}$mm, $1.1~{}$mm, taken from [7]. (c) and (d) Resistance of
bulk graphite samples vs. temperature at different applied fields normal to
the graphene layers. The sample in (c) is a HOPG bulk sample from Union
Carbide of grade A and the sample in (d) is Kish graphite. Taken from [24].

The question is now whether parts of these interfaces hide superconducting
regions. It is certainly appealing to suggest that the huge MIT at fields
normal to the interfaces (and below $\sim 2~{}$kOe) is related to Josephson-
coupled superconducting regions embedded in some of the interfaces. Note that
the huge anisotropy of the MIT (parallel fields to the interfaces main plain
do not affect the electrical transport) already implies that the regions
responsible for the MIT must be laying parallel to the graphene layers [31].
Without the knowledge on the existence of these interfaces, an interpretation
of the low field MIT based on the influence of superconductivity has been
discussed in detail in the reviews [32, 24]. In those reviews, one can
recognize the remarkable similarity between the scaling approaches used to
characterize the magnetic-field-induced superconductor-insulator quantum phase
transition [33] or of the field-driven MIT in 2D electron (hole) systems [34]
and the one obtained for the MIT observed in graphite. As we will see in the
next sections, the experimental evidence obtained in the last recent years
indicates that granular superconductivity exists within some of those
interfaces, indeed.

If superconducting patches exist embedded in parts of the interfaces or in
other two dimensional regions of the bulk ordered samples, one expects to
measure some signs of granular superconductivity, as for example nonlinear
$I-V$ curves or hysteresis in the magnetoresistance. However, this is not
really observed in bulk large samples. There are at least two reasons for the
apparent absence of these expected phenomena. One is the distribution of the
input current between the ballistic channels given by the graphene layers [17,
18], the metallic, normal conducting parts of the interfaces and the regions
where the superconducting patches exist. In other words, the usual maximum
currents used in transport experiments reported in bulk samples may have been
small enough so that the current through the superconducting regions remained
below the critical Josephson one. The other reason is the experimental voltage
sensitivity to measure the possible irreversibility in the magnetoresistance
due to the existence of pinned vortices or fluxons. We will see in the next
section that part of these problems can be overcome decreasing the sample
size; in this way, one obtains the voltage signals from the regions of
interest with enough sensitivity.

Apart from the large magnetic field sensitivity of the metallic-like
resistance measure in bulk graphite samples with interfaces, is there any
further hint for the existence of granular superconductivity in those $R(T)$
curves? Yes, this hint is related to the thermally activated function
($\propto\exp(-E_{a}/k_{B}T)$ with $E_{a}$, a sample dependent effective
thermal barrier $\sim 30~{}$K) one needs in order to fit the metallic-like
contribution below $T\sim 200~{}$K [10]. This function is relevant in spite of
only a factor five increase of the resistance between low and high
temperatures, see Fig. 2. Skeptical readers can convince themselves about its
relevance taking a similar example, as the exponential function used to fit
the increase, by a similar factor, of the ultrasonic attenuation with
temperature below $T_{c}$ in conventional superconductors. We note that this
exponential function has already been used to describe the increasing
resistance of bulk graphite samples with temperature and it was speculated to
be related to some superconducting-like behavior in graphite [32]. It is clear
that this function is not the usual one, one expected for metals or semimetals
and that cannot be understood within the usual electron-phonon interaction
mechanisms, nor in two dimensions. A similar dependence has been observed in
granular AlGe [35], which shows for a particular Al concentration a
superconductor-semiconductor transition similar to that reported in Ref. [10]
or, after an appropriate scaling in temperature, to some of the curves shown
in Fig. 2. The observed thermally activated behavior might be understood on
the basis of the Langer-Ambegaokar-McCumber-Halperin (LAMH) model [36, 37]
that applies to narrow superconducting channels in which thermal fluctuations
can cause phase slips. This interpretation gets further support from the
evidence we discuss in the following sections.

##  3 Hysteresis in the magnetoresistance

In order to reveal by transport measurements the existence of granular
superconductivity in some regions of the graphite samples, we need to increase
the sensitivity of the measured voltage to those regions. To achieve this, we
decrease the size of the sample enhancing in this way the probability to get
some measurable influence of this phenomenon in the voltage. The work in Ref.
[38] reported the first observations of an anomalous irreversible behavior in
the magnetoresistance (MR) in a few tens of nm thick and several micrometer
large multigraphene samples. Hysteresis in the magnetoresistance is a key
evidence on the existence of either magnetic order (domains with their walls,
for example) or vortices/fluxons and therefore on the existence of
superconductivity. Because defects as well as hydrogen can trigger magnetic
order in graphite, a first attempt would be to relate the measured hysteresis
in the MR with the existence of magnetic order and magnetic domains, for
example. However, the data exhibited anomalous hysteresis loops in the MR
[38], similar to those observed in granular superconductors with Josephson-
coupled grains [39, 40, 41]. The anomalous hysteresis was observed only for
magnetic fields perpendicular to the planes, whereas in the parallel to the
planes direction, the MR remains negligible. This fact already points out to a
remarkable large anisotropic response of the superconducting phase(s) in
agreement with the hypothesis that these superconducting regions might be
embedded in some of the interfaces found inside some bulk graphite samples [7,
8]. The amplitude of the hysteresis in the MR reported in Ref. [38] vanishes
at temperatures $T\sim 10~{}$K, clearly below the temperature at which the
resistance shows a maximum, as it is the case for samples HOPG-1 in Fig. 2(a)
or sample L2A in Fig. 2(b).

It is clear that thermal fluctuations can prevent the establishment of a
coherent superconducting state in parts of the sample and therefore zero
resistance state is not so simple to be achieved if the superconducting
distribution is a mixture of superconducting patches at the interfaces and
these are embedded in a multigraphene semiconducting matrix. Moreover, we
should take also into account that the voltage electrodes are usually
connected at the top surface of the graphite samples picking the voltage
difference coming from a non-negligible normal conducting path.

One possibility to increase the sensitivity of the measured voltage to the
field hysteresis these regions produce is to make a constriction in the middle
of the two voltage electrodes, see inset in Fig. 3(a). In this case, we expect
a locally narrower distribution of superconducting and normal regions at the
constriction such that averaging effects should be less important.
Simultaneously, through the constriction the main part of the voltage drop
depends mostly on the region at the constriction, see Fig. 2(c) in Ref. [16].
Then, a higher sensitivity to the superconducting paths can be achieved in
case they remain at or near the constriction. This idea has been successfully
realized in [42] and its main results will be reviewed in this section.

Figure 3: (a) Resistance vs. temperature, without constrictions and at zero
applied field, for two graphite flakes of size (distance between voltage
electrodes $\times$ width $\times$ thickness) for sample 1 (2): $13\times
16\times 0.015~{}(2.6\times 6\times 0.040)$ $\mu$m3. The observed temperature
dependence remains for all constrictions widths. The inset shows a scanning
electron microscope picture of sample 1 with a constriction width of 4.3
$\mu$m between the two voltage electrodes. The scale bar is 5$~{}\mu$m. (b)
Magnetoresistance (MR) vs. applied magnetic field for sample 1 with a
$4~{}\mu$m constriction width and at 2 K. The input current was $1~{}\mu$A.
Note the clear hysteresis in the MR when the field is swept from $|H_{\rm
max}|=1000~{}$Oe. The inset shows the difference $\Delta$MR between the curve
obtained starting from $H_{\rm max}=+1000~{}$Oe and the return curve measured
from $H_{\rm min}=-1000~{}$Oe. (c) The absolute difference between the two MR
curves of the hysteresis loop obtained at a fixed magnetic field of $16.6$ Oe
for sample 1 without constriction $(\star)$ and for two different constriction
widths. The figure also shows the corresponding data for another graphite
sample without constrictions $(\blacksquare)$ from [38]. (d) Magnetoresistance
measured from a starting maximum field of 1.4 kOe at 10 K for sample 2 with a
constriction width of $3~{}\mu$m. Some of the figures and the data were taken
from [42].

Let us take two slightly different samples, 1 and 2, with $R(T)-$curves as
shown in Fig. 3(a). The aim of the experiment is to study the hysteresis in
the MR those samples might show below the temperature at which a maximum in
the resistance is measured, in case that maximum is related to the Josephson
coupling between superconducting regions. Figure 3(b) shows one example of the
anomalous hysteresis loop in the MR. The going down curve (from high, positive
to low, negative fields, red arrow), for example, runs below the going up
curve (green arrow) in the same quadrant as the field sweep was started,
showing a minimum at positive fields of the order of 20 Oe, see also similar
curves in Ref. [38]. To present the anomalous behavior clearly, the inset in
Fig. 3(b) shows the difference between the two curves. This difference is in
clear contrast to the usual hysteresis in superconductors as well as
ferromagnets [39, 38], where the minimum (or maximum) in the MR is observed in
the opposite field quadrant, and the increasing field resistance curve is
usually below the decreasing field one.

Figure 3(c) shows the temperature dependence of the difference in the MR
between the decreasing and increasing field curves at a fixed magnetic field
for sample 1, without and with two constrictions. The results show that the
smaller the constriction width, the higher the temperature at which the
anomalous hysteresis is observed, decreasing below the sensitivity limit at
$T>50$ K for a constriction width of $4~{}\mu$m, whereas the maximum in the
$R(T)$ curve is at $\sim 70~{}$K, see Fig. 3(a). The absence of any hysteresis
in the MR for sample 2 with a constriction width of $3~{}\mu$m and at
$T=10~{}$K indicates that the hysteresis does not come from some artifact due
to the used focused ion beam method [42, 43] or due to an artifact in the
measurement of the real field applied to the sample. As expected from the
$R(T)$ curve, see Fig. 3(a), sample 2 shows the anomalous hysteresis in the MR
at lower temperatures than sample 1 [42].

Summarizing this section, the observation of the anomalous hysteresis in the
MR – together with the MIT and the relatively large MR at temperatures below
the maximum in $R(T)$ – provides already striking hints that granular
superconductivity is at work in some regions of these samples. The increase in
the temperature region where the hysteresis is observed, decreasing the
constriction width, demonstrates the problem of current averaging and voltage
sensitivity limits usual experiments with large samples have.

Figure 4: (a) Scanning Electron Microscopy (SEM) image of a lamella of 300 nm
thickness on a Si/SiN substrate where the yellowish colored areas are the
electrodes. A four-point configuration has been prepared with the outer
electrodes used to apply current and the inner ones to measure the voltage
drop. The $c-$axis runs parallel to the substrate surface and normal to the
current direction. (b) Transmission Electron Microscopy (TEM) image of a HOPG
lamella. The different brightness corresponds to a different orientation
within the $a-b$ plane of the crystalline regions with thickness $>30$ nm. (c)
Voltage vs. temperature at different input currents for a lamella of $\sim
800$ nm thickness and with Van der Pauw contact configuration. (d) Current-
Voltage characteristics at different temperatures for a lamella of
$\sim~{}300$ nm thickness in reduced coordinates, where $R$ is the normal
state resistance, $I$ the input current, and $I_{c}$ the critical Josephson
current. The continuous curves are fitted to the model proposed in Ref. [44]
with $I_{c}(T)$ as the only free parameter. Figures taken from [45].

##  4 Direct evidence for Josephson behavior in the transport properties of
graphite: Measurements in TEM lamellae

If the embedded interfaces (or some other quasi two dimensional regions)
inside the measured graphite samples have superconducting properties, the best
way to check them would be contacting electrodes as near as possible to those
interfaces or interface regions and study the behavior as a function of any
useful parameter one can take to influence their response. It should be clear
that one cannot simply open the graphite sample at the interface and put
voltage electrodes at the open surfaces of the interface, simply because it
will not remain anymore. A tentative approach to put the contacts as near as
possible to an interface has been done in Ref. [46]. Indeed, the observed
behavior at low temperatures and as a function of magnetic field appeared to
be superconducting-like.

A better and appealing evidence for the superconducting behavior embedded in
some graphite ordered samples can be obtained by trying to locate the voltage
electrodes directly at the inner edges of the interfaces. The work in Ref.
[45] prepared TEM lamellae from bulk HOPG samples and using lithography and
focused ion beam techniques, current and voltages electrodes at different
positions of the samples were prepared. In this way, one tries to contact
several of those interface edges simultaneously, as shown in Fig. 4(a). We
note, however, that a thin surface layer of disordered graphite exists due to
the Ga+ ion irradiation used to cut the lamella from the bulk HOPG sample.
This layer has a much larger resistance than the one of the graphene layers or
of the interfaces [43] and therefore the input current goes through the lowest
resistance path as well as the voltage electrodes pick up the response of the
graphite sample with its interfaces. One can see this comparing first the
$R(T)$ curves obtained at large enough currents in the lamellae (Fig. 4(c))
with those of graphite samples with top electrodes (Fig. 2). The fact that a
zero resistance state (minimum voltage noise $\pm$ 5 nV upon sample) is
obtained at low currents with $I-V$ characteristic curves that resemble the
one expects for Josephson coupled grains leaves little doubt about the origin
of the obtained signals. In the TEM picture of Fig. 4(b), one can see the
graphite single crystalline regions (different gray colors) oriented
differently between them about the common $c-$axis and having well defined two
dimensional interfaces, as high resolution TEM studies revealed [47].

Figure 4(c) shows the voltage vs. temperature measured in a TEM lamella of
oriented graphite [45] at different input DC currents, from 100 nA to
10$~{}\mu$A. The clear sharp transition, observed at $\sim 150$ K at the
lowest current, shifts to lower temperatures increasing the input DC current.
For the largest input currents, the temperature dependence of the resistance
of the contacted lamella shows a maximum or follows the intrinsic
semiconducting behavior of the graphene layers. This behavior already suggests
the existence of high temperature granular superconductivity at some parts of
the sample. The study reported in Ref. [45] shows that the transition
temperature depends on the prepared sample. This indicates a sample dependent
distribution of the superconducting regions and/or some influence of the
preparation process or sample size on the superconductivity [47]. We also note
that the observed sharp decrease in the measured voltage does not necessarily
indicate the critical temperature of the superconducting regions but the
temperature below which a percolative granular system shows negligible
resistance due to the Josephson coupling at the used input current.

Current-voltage characteristic curves at different temperatures and in
different lamellae obtained from different HOPG samples have been studied in
Ref. [45]. An example of this $I-V$ curves at three temperatures is shown in
Fig. 4(d) obtained for a different lamella. The curves follow the expected
dependence for a Josephson junction [44] with a temperature dependent critical
current, the only free parameter in the fit.

Further evidence that speaks for a superconducting origin of the $I-V$ curves
is given by the expected detrimental effect of a magnetic field on the
superconducting state. This effect can be due to an orbital depairing effect
or due to the alignment of the electron spins at much higher fields, in case
of singlet coupling. The effect of a magnetic field applied normal and
parallel to the interfaces has been studied in detail for thick and thin
lamellae in Ref. [45]. Upon sample size (thickness, i.e., width of the
graphene planes inside the lamella) the observed effects are from the usual
vanishing of the zero resistance state or no effect at all for thin lamellae.
A magnetic field of a few kOe applied normal to the interfaces is enough to
destroy the Josephson coupling at low temperatures, an effect compatible with
the MIT observed in several graphite samples, see section II. Whereas a field
applied parallel to them does not influence the $I-V$ curves at all, a fact
that speaks for the two dimensionality of the superconducting regions.

Nevertheless, the influence of a magnetic field in HOPG samples with
interfaces is not as “simple” as in conventional superconductors. For high
fields applied normal to the interfaces, the $I-V$ curves show a recovery to
the zero resistance state. The observed reentrance appears to be related to
the magnetic-field driven reentrance observed at low temperatures in the
longitudinal resistance at high enough magnetic fields [48]. This interesting
behavior as well as the insensitivity of the $I-V$ curves to magnetic fields
in very thin lamellae [45] deserve further studies.

We would like to note here that the possible effects of a magnetic field on
the superconducting state of quasi two-dimensional superconductors, or in case
the coupling does not correspond to a singlet state, are not that clear as in
conventional superconductors. For example, results in two different two-
dimensional superconductors, including one produced at the interfaces between
non superconducting regions [49], show that superconductivity can even be
enhanced by a parallel magnetic field. In case the pairing is $p-$type [50],
the influence of a magnetic field is expected to be qualitatively different
from the conventional, singlet coupling behavior [51, 52] with even an
enhancement of the superconducting state at intermediate fields. In case the
London penetration depth is much larger than the size of the superconducting
regions at the interfaces of our lamellae or if the superconducting coherence
length is of the order or larger than the thickness of the lamella, the
influence of a magnetic field should be less detrimental.

Through these studies, and taking into account that in samples without these
interfaces no signature of superconducting or metallic-like behavior has been
observed (see also section V) it is appealing to suggest that
superconductivity is somewhere hidden at some of those interfaces or interface
regions. It should be also clear that not all those interfaces have
superconducting regions with similar critical parameters. Those interfaces are
formed during the preparation of the HOPG samples based on treatments at very
high temperatures ($T>3400^{\circ}$C) and high pressures ($P\sim$10 kg/cm3)
and in a non-systematic way [8]. Actually, they are not at all an aim of the
production but actually the opposite, they should be avoided in order to
enhance the crystal perfection of the bulk HOPG material. It is even possible
that, upon the procedure used to control the structure and texture of the
graphite sample, the near surface region, for example, can have a different
degree of graphitization as inside the bulk HOPG sample [8]. This means that
one may obtain different results from different parts of the same HOPG sample.
Therefore, disconcerting situations and an apparent lack of reproducibility
are preprogrammed in case the research studies are done without taking care of
the internal microstructure of the studied samples.

##  5 Magnetization measurements

In this section, we present and discuss magnetization measurements done in
bulk HOPG samples with and without embedded interfaces and in water treated
graphite powders. One of the main problems in interpreting magnetization data
for fields applied parallel to the $c-$axis of the graphite structure, i.e.,
normal to the graphene layers and interfaces, is the need of subtraction of a
large diamagnetic background. Due to the small amplitude of the
superconducting-like signals in the studied samples, the subtraction of this
linear in field background is not so simple, because it is not known with
enough certainty to obtain the true field hysteresis after its subtraction.
That means that we always have a certain arbitrariness in the shape of the
obtained field hysteresis, a situation that will improve with the increase of
the amount of material responsible for those superconducting-like signals. The
small SQUID signals of interest imply that one should take additional efforts
to minimize or rule out possible SQUID artifacts [53, 54, 55]. Therefore,
systematic studies of samples of different or equal geometry and magnetic
background, with and without interfaces, are necessary.

Taking into account: the overall shape of the hysteresis, the slope of the
virgin curve at low fields where the subtraction does not affect too much, and
the overall experience with ferromagnetic graphite [22, 56], one can rely to a
certain extent on the obtained hysteresis shape. Certainly, not only the field
hysteresis but also other evidence one gets from magnetization measurements
as, e.g., the remanence at zero field as a function of the maximal field
applied (see for example measurements for YBa2Cu3O7 in Ref. [57]) and the
hysteresis in temperature dependent measurements helps to convince oneself
about the existence of some kind of granular superconductivity. The hysteresis
between the field cooled (FC) and zero-field cooled (ZFC) curves can help to
discern between a superconducting or ferromagnetic-like behavior. The most
obvious evidence that speaks against a simple ferromagnetic order of the
hysteresis observed as a function of temperature and field is the two
dimensionality of the obtained hysteretic signals [29], i.e., the
superconducting-like signals are mainly measured for fields normal to the
interfaces. This fact is not compatible with any kind of magnetic order
including shape or magneto crystalline anisotropy, whatever large they might
be. We note that the ferromagnetic response of graphite due to DIM is mostly
measured for fields parallel to the graphene layers, parallel to the main area
of the samples [22].

###  5.1 Bulk graphite samples

Figure 5: (a) Magnetization of two HOPG bulk samples (HOPG-1 and HOPG-2) after
subtraction of a diamagnetic background and of water treated graphite powder
(WTGP, right $y-$axis) at 300 K. The HOPG-2 sample shows no hysteresis in
contrast to the other two samples. (b) Temperature dependence of the
difference between FC and ZFC magnetic moments of the HOPG-1 sample before
(b.a.) and after (a.a.) warming the sample up to $\simeq 600~{}$K, at two
constant applied fields, 0.5 T (left $y-$axis) and 4 T (right $y$-axis). The
field was applied always normal to the interfaces or graphene planes of the
samples. Data taken from [29].

Figure 5(a) shows the field hysteresis, after subtraction of the corresponding
diamagnetic linear background, at 300 K of two bulk HOPG samples, HOPG-1 and
HOPG-2 and a water treated graphite powder (WTGP) (right $y-$axis). A TEM
characterization of the internal microstructure of the HOPG-1 sample shows
clear evidence for well defined interfaces running parallel to the graphene
layers, in contrast to the HOPG-2 sample [29], see Fig. 1(b). These results
clearly indicate that the origin of the hysteresis is related to the existence
of the interfaces in the HOPG-1 sample. The absence of the hysteresis in the
HOPG-2 sample, which has a similar diamagnetic background and overall geometry
as the HOPG-1 sample, also indicates that the hysteresis is not due to an
obvious SQUID artifact or an artifact in the background subtraction. The field
hysteresis is similar to that of WTGP. The narrowing of the hysteresis
observed at high fields is expected for granular superconductors [60, 61, 62,
58]. From the hysteresis, as well as measuring the remanent magnetic moment as
a function of the applied field [29], one obtains the characteristic Josephson
critical fields $h_{c1}^{J}(T)$ and $h_{c2}^{J}(T)$ with values similar to the
WTGP [58] and a similar ratio $h_{c2}^{J}(T)/h_{c1}^{J}(T)\sim 3$ [29].

Figure 5(b) shows the magnetic moment hysteresis in temperature (FC minus the
ZFC curve) for the HOPG-1 sample as received (b.a.) and after sweeping the
temperature up to 500 K (a.a.) [29], at two applied fields. We would like to
stress the following features: The hysteresis for the as-received sample
starts from the turning point (390 K) and it is positive. The hysteresis in
temperature at both applied fields are qualitatively similar, showing a
crossing to negative values at low temperatures. Larger ZFC values (smaller in
absolute value) than FC ones in the magnetic moment are usually not observed,
neither in superconductors nor in ferromagnets and it does appear to be a
SQUID artifact [29]. This negative hysteresis in temperature would suggest
that the superconducting properties can be enhanced to some extent under a
magnetic field, an effect that might be related to the reentrance we have
shortly mentioned in section IV. A slight annealing of the HOPG-1 sample of
less than one hour at $\sim 500$ K changes drastically the observed hysteresis
for both fields (open symbols in Fig. 5(b)). The hysteresis appears to be
shifted to lower temperatures but with negative values at high temperatures
and high fields. We note that annealing at similar temperatures for several
hours produced a decrease in the overall hysteresis observed in WTGP (see
supporting information of Ref. [58]). At the state of this research, it is
unclear whether pinning properties of vortices and/or of fluxons or the
existence of different superconducting phases play a main role in the
hysteresis that is observed for fields applied normal to the interfaces.

###  5.2 Water treated graphite powder

Figure 6: (a) Field hysteresis at 5 K for a maximum applied field of 40 mT for
the water treated graphite powder (S1), the same powder but after pressing it
in a pellet with a pressure of $18\pm 5$ MPa (S2) and after pressing it again
with a pressure of $60\pm 20$ MPa (S3). The corresponding diamagnetic linear
backgrounds were subtracted from the measured data. (b) Difference between the
FC and ZFC curve at different applied fields for a water treated graphite
powder. Data taken from Ref. [58].

The work of Ref. [58] reports on the magnetic response of WTGPs. The main
message of that work is that the WTGP shows a hysteretic behavior in field and
temperature compatible with granular superconductivity. As an example, we show
in Fig. 6(a) the field hysteresis at 5 K of a WTGP (S1, lose powder without
applying significant pressure) and the same WTGP but after pressing it into a
pellet with two different pressures (S2,S3). After the diamagnetic background
subtraction, the field hysteresis is similar to that obtained for bulk HOPG
sample with interfaces, see Fig. 5(a) for similar data but at 300 K. The fact
that the hysteresis vanishes after applying pressure to the powder rules out
simple SQUID artifacts (the diamagnet background does not diminish after
making a pellet from the graphite powder, but the contrary) and also it rules
out that the hysteresis is due to a ferromagnetic response due to impurities.

Figure 6(b) shows the difference in the magnetic moment between the ZFC and FC
curves, as in Fig. 5(b). The behavior of this difference as a function of the
applied field appears to be compatible with the one expected for granular
superconductors [58]. Note the following features: The hysteresis increases at
all $T$ for fields $\mu_{0}H\lesssim 50~{}$mT, showing a maximum near the
turning point of 300 K, similar to the HOPG-1 sample in the as-received state,
see Fig. 5(b). At fields 0.1 T $\lesssim\mu_{0}H\lesssim 0.2~{}$T the
difference decreases at all $T$ and remains rather field independent. At
higher fields, however, it increases showing a shift of the crossing point
(from negative to positive values) to higher $T$ . This behavior is at odds to
the one expected for ferromagnets, even for ferromagnetic nanoparticles [63]
as well as for superconductors with a pinning force that decreases with
applied field in the shown field range. From the results in [58], and using
basic concepts of vortex pinning, we would then conclude that if an upper
critical field exists, then it should be clearly larger than 7 T in the
temperature range of the figure.

In spite of some interesting differences between the behavior obtained for
bulk HOPG and WTGP, the similarities already suggest that the water treatment
helps to produce a certain amount of interfaces between graphite grains, being
the origin for the whole hysteresis. Thermal annealing as well as pressing the
WTGP are detrimental indicating that defects and/or hydrogen or oxygen at the
interfaces could play an important role in the observed phenomena.

##  6 Discussion

Superconductivity in carbon-based systems is a rather old, well recognized
fact. This phenomenon was probably first observed in the potassium
intercalated graphite $C_{8}K$ [64] back in 1965\. Since then, a considerable
amount of studies reported this phenomenon in carbon-based systems, reaching
critical temperatures $T_{c}\sim 10$ K in intercalated graphite [65, 66] and
above 30 K - though not percolative - in some HOPG samples [59] as well as in
doped graphite and amorphous carbon systems [67, 68, 69, 70]. Traces of
superconductivity at $T_{c}=65~{}$K have been recently reported in amorphous
carbon powder that contained a small amount of sulfur [71]. Superconductivity
was found also in carbon nanotubes with $T_{c}=0.55~{}$K [72] and 12 K [73] or
possibly even higher critical temperatures [74, 75]. Superconductivity with
$T_{c}\sim 4~{}$K in boron-doped diamond [76] and in diamond films with
$T_{c}\sim 7~{}$K [77] belong also to the recently published list of carbon-
based superconductors. We should note, however, that superconductivity at room
temperature in a disordered graphite powder has been already reported in 1974
[78], see also [79], a work that did not attract the necessary attention in
the community.

Whether quasi two dimensional interfaces play a role in the above mentioned
carbon-based superconductors, one can probably rule out only for the
intercalated graphite and doped diamond compounds, where the three dimensional
superconductivity is characterized by a relatively low critical temperature.
We may speculate that the traces of superconductivity found in doped amorphous
carbon, disordered or ordered graphite powders may be related to some
interfaces between well ordered graphite regions. The experience of the high
temperature superconducting oxides already suggests that two dimensionality is
advantageous to achieve higher critical temperatures.

Apart from the usual transport and magnetization measurements used to
characterize the superconducting state, there are scanning tunneling
spectroscopy (STS) results obtained on certain disordered regions of a HOPG
surface at $T=4.2~{}$K that revealed an apparent energy gap $\sim 100~{}$meV
[80]. Although the overall curves resemble a superconducting-like density of
states, the authors suggested that the gap originates from charging effects.
See further STS results and the discussion in [70].

Theoretical works that deal with superconductivity in graphite as well as in
graphene have been published in recent years. For example, $p$-type
superconductivity has been predicted to occur in inhomogeneous regions of the
graphite structure [50] or $d-$wave high-$T_{c}$ superconductivity [81] based
also on resonance valence bonds [82], or at the graphite surface region with
rhombohedral stacking due to a topologically protected flat band [83].

For the graphite structure, the experimental evidence obtained in the last
years suggests that high temperature superconductivity exists at certain
interfaces or interface regions within the usual Bernal structure although the
structure of the superconducting regions remains unknown. One can further
speculate that due to the high carrier concentration that can be localized at
those interfaces, they should be predestined to play a role in triggering
superconductivity. Following a BCS approach in two dimensions (with
anisotropy), for example, a critical temperature $T_{c}\sim 60~{}$K has been
estimated if the density of conduction electrons per graphene plane increases
to $n\sim 10^{14}~{}$cm-2, a density that might be induced by defects and/or
hydrogen ad-atoms [84] at the interfaces, or by Li deposition [85]. Further
predictions for superconductivity in graphene support the premise that
$n>10^{13}~{}$cm-2 in order to reach $T_{c}>1~{}$K [86, 87]. On the other
hand, the possibility to have high temperature superconductivity at the
surface of or in the rhombohedral graphite phase [83, 21] – a phase that
sometimes is found in graphite samples [20, 19] – stimulates further careful
studies of these hidden interfaces. In the last years, superconductivity has
been found at the interfaces between oxide insulators [88] as well as between
metallic and insulating copper oxides with $T_{c}\gtrsim 50~{}$K[89]. Also,
interfaces in different Bi bicrystals show superconductivity up to 21 K,
although Bi bulk is not a superconductor [90, 91].

Finally, we think that some of the interfaces are also the origin for the
metallic-like behavior of graphite samples as well as for the quantum Hall
effect (QHE) found in some HOPG samples [48, 92]. Because the existence,
density as well as the intrinsic properties of these interfaces depend on
sample, we can now understand why the reproducibility of the QHE in bulk HOPG
samples is rather poor.

##  7 Conclusion

In this review, we have discussed the following experimental evidence:
Firstly, the temperature and magnetic field dependence of the electrical
resistance of bulk and thin films of graphite samples and its relation with
the existence of two dimensional interfaces.
Secondly, the Josephson behavior of the current-voltage curves with an
apparent zero resistance state at high temperatures in especially made TEM
lamellae.
Thirdly, the anomalous hysteresis in the magnetoresistance observed in
graphite thin samples as well as its enhancement restricting the current path
within the sample.
Finally, the overall magnetization of bulk graphite samples, with and without
interfaces, as well as water treated graphite powders.

All this experimental evidence as a whole indicates the existence of
superconductivity located at certain interfaces inside graphite samples.
Although we cannot rule out other interpretations for some of the observations
discussed in this work, the whole evidence suggests that superconductivity
should be the origin for all the phenomena discussed here. Clearly, the
situation is still highly unsatisfactory because several open questions
remain, namely, the characteristics of the superconducting phase(s), from the
structure to the main superconducting parameters, as “simple” as the critical
temperature and critical fields, the coherence and penetration lengths, etc.
It is clear that further studies are necessary in the future but the overall
work done until now shows us the way to go.

###### Acknowledgements.

The author acknowledges the support provided by the Deutsche
Forschungsgemeinschaft under contract DFG ES 86/16-1 and the ESF-Nano under
the Graduate School of Natural Sciences “BuildMona”. The results presented in
this review were part of the Ph.D. thesis of Heiko Kempa (section II), Srujana
Dusari (section III) and Ana Ballestar (section IV) as well as the master
thesis of Thomas Scheike (section V) done in the Division of Superconductivity
and Magnetism of the Institute for Experimental Physics II of the University
of Leipzig. The author thanks Dipl. Kris. Annette Setzer, Dr. José Barzola-
Quiquia and Dr. Winfried Böhlmann for their experimental assistance and
support. The permanent support as well as the discussions with Nicolás García
are gratefully acknowledged. Special thanks go to Yakov Kopelevich with whom
we started in the year 1999 and in a rather naive way the research of a new
and unexpected world behind graphite.

## Note added in proof

Since the submission of this manuscript, some new works related to the subject
of this review were published. Tight-binding simulations done in Ref. [93]
support the work done in Ref. [21] and found that surface superconductivity is
robust for ABC stacked multilayer graphene, even at very low pairing
potentials. Through the observation of persistent currents in a graphite
filled ring-shaped container immersed in alkanes, the author in Ref. [94]
claimed possible room temperature superconductivity. For completeness, we
include them in the reference list.

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