Evidence of Josephson-coupled superconducting regions at the interfaces of Highly Oriented Pyrolytic Graphite

Transport properties of a few hundreds of nanometers thick (in the graphene plane direction) lamellae of highly oriented pyrolytic graphite (HOPG) have been investigated. Current-Voltage characteristics as well as the temperature dependence of the voltage at different fixed input currents provide evidence for Josephson-coupled superconducting regions embedded in the internal two-dimensional interfaces, reaching zero resistance at low enough temperatures. The overall behavior indicates the existence of superconducting regions with critical temperatures above 100 K at the internal interfaces of oriented pyrolytic graphite.

Transport properties of a few hundreds of nanometers thick (in the graphene plane direction) lamellae of highly oriented pyrolytic graphite (HOPG) have been investigated. Current-Voltage characteristics as well as the temperature dependence of the voltage at different fixed input currents provide evidence for Josephson-coupled superconducting regions embedded in the internal twodimensional interfaces, reaching zero resistance at low enough temperatures. The overall behavior indicates the existence of superconducting regions with critical temperatures above 100 K at the internal interfaces of oriented pyrolytic graphite.
PACS numbers: 74. 10.+v,74.45.+c,74.78.Na Superconductivity in doped graphite goes back to 1965 when it was first observed in the potassium intercalated graphite C 8 K [1]. Since then a considerable amount of studies reported this phenomenon, reaching critical temperatures T c ∼ 10 K in intercalated graphite [2,3] and above 30 K -though not percolative -in some HOPG samples [4] as well as in doped graphite [5][6][7][8]. 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 [9] or d−wave high-T c superconductivity [10] based also on resonance valence bonds [11], or at the graphite surface region due to a topologically protected flat band [12]. Following a BCS approach in two dimensions (with anisotropy) critical temperatures T c ∼ 60 K have been estimated if the density of conduction electrons per graphene plane increases to n ∼ 10 14 cm −2 , a density that might be induced by defects and/or hydrogen ad-atoms [13] or by Li deposition [14]. Further predictions for superconductivity in graphene support the premise that n > 10 13 cm −2 in order to reach T c > 1 K [15,16].
The possibility of high-temperature superconductivity at surfaces and interfaces has attracted the attention of the low-temperature physics community also since the 60's [17]. Recently, superconductivity has been found at the interfaces between oxide insulators [18] as well as between metallic and insulating copper oxides with T c 50 K [19]. In case of doped semiconductors the example of Bi is of interest; interfaces in Bibicrystals of inclination type show superconductivity up to 21 K, although Bi bulk is not a superconductor [20]. These two independently obtained indications, the possible existence of high-temperature superconductivity in graphite/graphene and the special role of interfaces [21,22] stimulated us to pursue the study of the transport properties of a bundle of internal interfaces in bulk HOPG samples.
Transmission electron microscope (TEM) studies on HOPG samples revealed single crystalline regions of Bernal graphite of thickness in the c−axis direction between 30 nm and ∼ 150 nm [21]. As example, we show in Fig. 1(b) a typical TEM picture of the HOPG samples studied in this work. The different gray colors shown in Fig. 1(b) indicate sightly different angle misalignments about the c-axis between each other and the existence of very well defined two-dimensional interfaces between them. We note that rotations up to 30 • between the graphene layers from neighboring graphite regions has been seen by high resolution TEM in few layers graphene sheets [23]. The electrical response of those interfaces is the aim of our experimental study.
Thin TEM lamellae have been prepared from a HOPG (ZYA grade, 0.3 • rocking curve) bulk sample using a dual beam microscope (FEI Nanolab XT200). To avoid contamination and structural disorder the lamellae were cut after depositing a protective layer of 300 nm of tungsten carbide using the electron gun (EBID) on top of the HOPG surface. The Ga + ion beam was used to cut the lamellae of thickness between ∼ 300 and 800 nm in the a-b graphene plane direction and lengths up to ∼ 17 µm. After transferring the lamellae to an insulating Si/SiN substrate, electron beam lithography followed by thermal evaporation of Pt/Au was used to make the four electrical contacts allowing us the measurement of the voltage drop of several interfaces in parallel to the graphene planes along a length ∼ 2 . . . ∼ 8 µm. More than ten lamellae were studied. Although we found qualitatively similar behavior, the main difference in their characteristic transport properties depends on the used thickness, i.e. the observed Josephson-like I − V characteristics and the granular superconductivity behavior are observed at lower temperatures or even vanish the smaller the thickness (in the a, b plane) of the lamella. In this paper we present and discuss the results of four of them (L1-L4) with thickness (∼ 500nm, ∼ 800nm, ∼ 300nm, ∼ 800nm), respectively. Four probe electrode configuration as shown in Fig. 1(a), and also the van der Pauw configuration (contacts at lamella edges) were used to measure the tem- perature (T ) dependence of the voltage (V ) at constant input current (I) and the I − V characteristic curves. Figure 2 shows the T -dependence of the measured voltage at I = 1 nA (L1,L3) and 100 nA (L2,L4). A clear drop in the measured voltage is observed, upon sample at different "critical" temperatures T c between ∼ 15 K to ∼ 150 K. This T c reflects the temperature above which the Josephson coupling between superconducting patches at some of the interfaces vanishes. At low enough temperatures and currents zero resistance states were reached for L1, L3 and L4. Negative saturation voltages (L2) instead of zero are obtained for the van der Pauw configuration, which can be quantitatively explained using a simple Wheatstone bridge circuit and assuming two Josephson junctions with different T c 's as explained below.
The observed T −dependence in Fig. 2 is determined mainly by the contribution of the internal interfaces, since the graphene layers within the crystalline regions show a semiconducting narrow-band-gap behavior [24]. If the voltage drop is related to some kind of granular superconductivity we expect that its temperature dependence is sensitively influenced by the applied current. Figures 3  (a) to (c) show clearly that the higher the input current the lower the transition temperature, revealing a semiconducting-like behavior at higher I and T . The observed behavior is compatible with the existence of granular superconductivity (see, e.g., Ref. 25) embedded in some of the internal interfaces.
Further support to this claim is obtained from the I − V characteristics curves. Samples L1 (Fig. 3(d)) and L3 (Fig. 3(f)) show typical Josephson behavior. In the case of L2 (Fig. 3(e)) the curves were obtained with the van der Pauw configuration and a current and voltage paths that catch the answer of more than one Josephson junction in that sample. Taking into account the used current distribution in this case and assuming two Josephson junctions with different T c 's the rather exotic I − V curves can be quantitatively understood using the model of Ambegaokar and Halperin [26] where the influence of thermal fluctuations on the dc Josephson effect in a junction of small capacitance are taking into account, see Fig. 4(a). The same model can be successfully used to fit the I − V characteristics for sample L3 assuming only one Josephson junction, see 4(b). In the case of sample L1, a sharp jump in the current appears at the corresponding critical Josephson current I c where also a small hysteresis is observed, see Fig. 3

(d).
Considering the I − V results from all samples and configurations we obtain I c (T ) shown in Fig. 5 in normalized units. The overall behavior is compatible with the temperature dependence expected for Josephsonjunctions where the normal barrier is given by ballistic graphene [27], the continuous line in Fig. 5. One may ask whether a Josephson coupling is possible through graphene layers and at large distances. Indeed, the work in Ref. 28 showed experimentally that the Josephson effect is possible between superconducting electrodes separated by hundreds of nanometers long graphene path. Therefore, the assumption of the existence of superconducting regions Josephson coupled through graphene-like semiconducting paths at the observed interfaces appears reasonable. Because these superconducting regions at the interfaces are not homogeneously distributed in the used samples, upon the junctions' distribution, a noisy or "jumpy" behavior of the voltage is expected at low  enough temperatures and currents due to phase and current path fluctuations. We have observed this behavior in samples L1, see Fig. 3(a), and L2, see inset in Fig. 6(a). This noisy behavior is intrinsic of the samples and can be suppressed by applying a magnetic field normal to the graphene planes, see inset in Fig. 6(a), or increasing I. shielding currents, or at much higher fields due to the alignment of the electron spins, in case of singlet coupling. However, 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. For example, recently published experimental results [29] in two different two-dimensional superconductors, including one produced at the interfaces between non superconducting regions, show that superconductivity can be even enhanced by a parallel magnetic field. In case the pairing is p−type [9] the influence of a magnetic field is expected to be qualitatively different from the conventional behavior [30,31] with even an enhancement of the superconducting state at intermediate fields, in case the orbital diamagnetism can be neglected or for parallel field con-figuration. On the other hand, even for applied fields normal to the planes we expect much less influence of the orbital effect in case the London penetration depth is much larger than the size of the superconducting regions at the interfaces of our lamellae. If the superconducting coherence length is of the order or larger than the thickness of the lamella then we expect a superconducting (granular) behavior at lower T but a magnetic field may be less detrimental. We have studied the effects of magnetic fields applied parallel and normal to the interfaces on the transport characteristics in all measured lamellae. Upon sample the observed effects are from an usual detrimental, no effect at all or in some cases even a partial recovery of the superconducting state. Figure 6 shows the I − V characteristics of the samples L4 (a) and L3 (b). For the relatively thick lamella L4 the magnetic field of 1 T applied normal to the interface planes vanishes the zero resistance state observed at zero field and at 50 K. At higher fields, however, the I − V curves show a recovery to the zero resistance state. A field applied parallel to the interface planes does not affect the curves. Recent studies on possible superconductivity triggered by a large enough electric field applied on multigraphene samples revealed also a kind of reentrance above a certain magnetic field applied normal to the graphene layers [32]. For the thinnest sample L3, however, a magnetic field applied in both directions has little or no effect on the I − V characteristics or V (T ) up to 8 T, see Fig. 6(b) and its inset.
In conclusion, the transport characteristics of thin lamellae with tens of 2D interfaces between crystalline graphite regions reveal Josephson-like behavior with zero resistance states at low enough temperatures and input currents. Our results finally clarify that the origin for the metallic-like behavior as well as the giant magnetic field induced metal-insulator (MIT) transition measured in HOPG in the past [33][34][35] is related to the superconducting properties of internal interfaces and it is not intrinsic of the graphite structure. The existence of very high temperature superconductivity embedded at these interfaces is supported by recently done magnetization measurements [36]. This work is supported by the Deutsche Forschungsgemeinschaft under contract DFG ES 86/16-1. A.B. was supported by ESF-Nano under the Graduate School of Natural Sciences "BuildMona".