Muon spin rotation study of the magnetic penetration depth in the intercalated graphite superconductor CaC6
D. Di Castro, A. Kanigel, A. Maisuradze, A. Keren, P. Postorino, D. Rosenmann, U. Welp, G. Karapetrov, H. Claus, D. G. Hinks, A. Amato, J. C. Campuzano
We report temperature- and magnetic field-dependent bulk muon spin rotation measurements in a c-axis oriented superconductor CaC6 in the mixed state. Using both a simple second moment analysis and the more precise analytical Ginzburg-Landau model, we obtained a field independent in-plane magnetic penetration depth λab (0) = 72(3) nm. The temperature dependencies of the normalized muon spin relaxation rate and of the normalized superfluid density result to be identical, and both are well represented by the clean limit BCS model with 2Δ/kB Tc = 3.6(1), suggesting that CaC6 is a fully gapped BCS superconductor in the clean limit regime.
We show that different non-conventional superconductors have one fundamental feature in common: pair eigenstates of the Hamiltonian are repulsion-free, the W=0 pairs. In extended Hubbard models, pairing can occur for resonable parameter values. For $(N,N)$ nanotubes the binding energy of the pair depends strongly on the filling and decreases towards a reduced but nonzero value for the graphite sheet $N \to \infty$.
Terahertz reflectance spectra of the Ca-intercalated graphite CaC6 reveal a superconducting gap below 11K. The gap signature lacks a sharp onset to full reflectivity at 2Delta, but rather shows a distribution of gap values consistent with an anisotropic gap. The experimental data were successfully fitted to the gap distribution obtained from density functional calculations by Sanna et al. (Phys.Rev. B75, 020511, 2007). The temperature dependence of the superconducting gap is characteristic for a BCS type superconductor.
We report measurements of the in-plane electrical resistivity $ρ$ and the thermal conductivity $κ$ of the intercalated graphite superconductor C$_6$Yb to temperatures as low as $T_c$/100. When a field is applied along the c-axis, the residual electronic linear term $κ_0/T$ evolves in an exponential manner for $H_{c1} < H < H_{c2}$. This activated behaviour establishes the order parameter as unambiguously s-wave, and rules out the possibility of multi-gap or unconventional superconductivity in this system.
The superconducting state of Ca-intercalated graphite CaC6 has been investigated by specific heat measurements. The characteristic anomaly at the superconducting transition (Tc = 11.4 K) indicates clearly the bulk nature of the superconductivity. The temperature and magnetic field dependence of the electronic specific heat are consistent with a fully-gapped superconducting order parameter. The estimated electron-phonon coupling constant is lambda = 0.60 - 0.74 suggesting that the relatively high Tc of CaC6 can be explained within the weak-coupling BCS approach.
In this letter we report the discovery of superconductivity in the isostructural graphite intercalation compounds C6Yb and C6Ca, with transition temperatures of 6.5K and 11.5K respectively. A structural characterisation of these compounds shows them to be hexagonal layered systems in the same class as other graphite intercalates. If we assume that all the outer s-electrons are transferred from the intercalant to the graphite sheets, then the charge transfer in these compounds is comparable to other superconducting graphite intercalants such as C8K 1,2 . However, the superconducting transition …
Muon spin rotation (muSR) experiments were performed on the intercalated graphite CaC6 in the normal and superconducting state down to 20 mK. In addition, AC magnetization measurements were carried out resulting in an anisotropic upper critical field Hc2, from which the coherence lengths xi_ab(0)=36.3(1.5) nm and xi_c(0)=4.3(7) nm were estimated. The anisotropy parameter gamma_H= H_c2_ab/H_c2_c increases monotonically with decreasing temperature. A single isotropic s-wave description of superconductivity cannot account for this behaviour. From magnetic field dependent muSR experiments the abso…
The pressure effect on the superconducting transition temperature ($T_c$) of the newly-discovered Ca-intercalated graphite compound CaC$_6$ has been investigated up to $\sim$ 16 kbar. $T_c$ is found to increase under pressure with a large relative ratio $Δ$$T_c$/$T_c$ of $\approx$ +0.4 %/kbar. Using first-principles calculations, we show that the large and positive effect of pressure on $T_c$ can be explained in the scope of electron-phonon theory due to the presence of a soft phonon branch associated to in-plane vibrations of Ca atoms. Implications of the present findings on the current debat…
In this letter, we report the discovery of superconductivity in Li3Ca2C6. Several graphite intercalation compounds (GICs) with electron donors, are well known as superconductors. It is probably not astonishing, since it is generally admitted that low dimensionality promotes high superconducting transition temperatures. Superconductivity is lacking in pristine graphite, but after charging the graphene planes by intercalation, its electronic properties change considerably and superconducting behaviour can appear. Li3Ca2C6 is a ternary GIC, for which the intercalated sheets are very thick and pol…
We report the discovery of superconductivity below 1.65(6) K in Sr-intercalated graphite SrC6, by susceptibility and specific heat (Cp) measurements. In comparison with CaC6, we found that the anisotropy of the upper critical fields for SrC6 is much reduced. The Cp anomaly at Tc is smaller than the BCS prediction indicating an anisotropic superconducting gap for SrC6 similar to CaC6. The significantly lower Tc of SrC6 as compared to CaC6 can be understood in terms of "negative" pressure effects, which decreases the electron-phonon coupling for both in-plane intercalant and the out-of-plane C p…
The occurrence of non-adiabatic effects in the vibrational properties of metals have been predicted since the 60's, but hardly confirmed experimentally. We report the first fully \emph{ab initio} calculations of non-adiabatic frequencies of a number of layer and conventional metals. We suggest that non-adiabatic effects can be a feature of the vibrational Raman spectra of any bulk metal, and show that they are spectacularly large (up to 30% of the phonon frequencies) in the case of layer metals, such as superconducting $MgB_2$, $CaC_6$ and other graphite intercalated compounds. We develop a fr…
Superconductivity at 22.3 K in Compressed Sodium-intercalated Graphite
Center for High Pressure Science, State Key Laboratory of Metastable Materials Science and Technology, Yanshan University（燕山大学亚稳材料科学与国家重点实验室高压科学中心）；Hebei Key Laboratory of Microstructural Material Physics, School of Science, Yanshan University（燕山大学理学院河北省微观结构材料物理重点实验室）；Key Laboratory of Weak-Light Nonlinear Photonics, School of Physics, Nankai University（南开大学物理学院弱光非线性光子学重点实验室）
Using density functional theory we investigate the occurrence of superconductivity in AC$_6$ with A=Mg,Ca,Sr,Ba. We predict that at zero pressure, Ba and Sr should be superconducting with critical temperatures (T$_c$) 0.2 K and 3.0 K, respectively. We study the pressure dependence of T$_c$ assuming the same symmetry for the crystal structures at zero and finite pressures. We find that the SrC$_6$ and BaC$_6$ critical temperatures should be substantially enhanced by pressure. On the contrary, for CaC$_6$ we find that in the 0 to 5 GPa region, T$_c$ weakly increases with pressure. The increase i…
We report anisotropy of the upper critical field (Bc2) of an intercalated graphite superconductor YbC6 (Tc = 6.5 K) determined from angular dependent magnetoresistance measurements. Though the perpendicular coherence length is much longer than interlayer spacing, measured angular dependences of Bc2 are well fitted by the Lawrence-Doniach model or the Tinkham model, which are known to be applicable to quasi two-dimensional materials or thin films, rather than the effective mass model. This observation is similar to the measurements for the other intercalated graphite superconductor, CaC6, by Jo…
First-principles calculations of the electronic structure and vibrational modes, in a system of graphene bilayers and trilayers intercalated with alkaline earth atoms, are resented. It is found that, in similarity to the case of superconducting graphite intercalation compounds, the Fermi level is crossed by an s-band derived from the intercalant states, as well as graphitic pi-bands. The electron-phonon coupling parameter is found to be 0.60 and 0.80, respectively, in calcium intercalated graphene bilayers and trilayers. In superconducting CaC6 graphite intercalation compound, the calculated v…
Sulfur intercalated graphite composites with diamagnetic transitions at 6.7 K and 37 K are prepared. The magnetization hysteresis loops (MHL), Xray diffraction patterns, and resistance were measured. From the MHL, a slight superconducting like penetration process is observed at 15 K in low field region. The XRD shows no big difference from the mixture of graphite and sulfur indicating that the volume of the superconducting phase (if any) is very small. The temperature dependence of resistance shows a typical semiconducting behavior with a saturation in low temperature region. This saturation i…
Recently deiscovered superconductivity in YbC$_6$ and CaC$_6$ at temperatures substantially higher than previously known for intercalated graphites, raised several new questions: (1) Is the mechanism considerably different from the previously known intercalated graphites? (2) If superconductivity is conventional, what are the relevant phonons? (3) Given extreme similarity between YbC$_6$ and CaCa$_6$, why their critical temperatures are so different? We address these questions on the basis of first-principles calculations and conclude that coupling with intercalant phonons is likely to be the …
We present muon spin rotation measurements on superconducting Cu intercalated Bi$_2$Se$_3$, which was suggested as a realization of a topological superconductor. We observe a clear evidence of the superconducting transition below 4 K, where the width of magnetic field distribution increases as the temperature is decreased. The measured broadening at mK temperatures suggests a large London penetration depth in the $ab$ plane ($λ_{\mathrm{eff}}\sim 1.6$ $\mathrmμ$m). We show that the temperature dependence of this broadening follows the BCS prediction, but could be consistent with several gap sy…
We report muon spin relaxation ($μ$SR) and magnetization measurements, together with synthesis and characterization, of the Li-intercalated layered superconductors Li$_{x}$HfNCl and Li$_{x}$ZrNCl with/without co-intercalation of THF (tetrahydrofuran) or PC (propylene carbonate). The 3-dimensional (3-d) superfluid density $n_{s}/m^{*}$ (superconducting carrier density / effective mass), as well as the two dimensional superfluid density $n_{s2d}/m^{*}_{ab}$ (2-dimensional (2-d) area density of superconducting carriers / ab-plane effective mass), have been derived from the $μ$SR results of the ma…
Recent observation of proximity effect \cite{Morpurgo:2007} has ignited interest in superconductivity in graphene and its derivatives. We consider Ca-intercalated graphene bilayer and argue that it is a superconductor, and likely with a sizeable $T_{c}$. We find substantial and suggestive similarities between Ca-intercalated bilayer (C$_{6}$CaC$_{6}$), and CaC$_{6} $, an established superconductor with $T_{c}$ = 11.5 K. In particular, the nearly free electron band, proven to be instrumental for superconductivity in intercalated graphites, does cross the chemical potential in (C$_{6}$CaC$% _{6}…
Although not an intrinsic superconductor, it has been long--known that, when intercalated with certain dopants, graphite is capable of exhibiting superconductivity. Of the family of graphite--based materials which are known to superconduct, perhaps the most well--studied are the alkali metal--graphite intercalation compounds (GIC) and, of these, the most easily fabricated is the C${}_8$K system which exhibits a transition temperature $\bm{T_c\simeq 0.14} $K. By increasing the alkali metal concentration (through high pressure fabrication techniques), the transition temperature has been shown to…
It has been reported that graphite hosts room temperature superconductivity. Here we provide new results that confirm these claims on different samples of highly oriented pyrolytic graphite (HOPG) and commercial flexible graphite gaskets (FGG). After subtraction of the intrinsic graphite diamagnetism, magnetization measurements show convoluted ferromagnetism and superconducting-like hysteresis loops. The ferromagnetism is deconvoluted by fitting with a sigmoidal function and subtracting it from the data. The obtained superconducting-like hysteresis loops are followed to the highest available t…
We investigate the possibility of inducing superconductivity in a graphite layer by electronic correlation effects. We use a phenomenological microscopic Hamiltonian which includes nearest neighbor hopping and an interaction term which explicitly favors nearest neighbor spin-singlets through the well-known resonance valence bond (RVB) character of planar organic molecules. Treating this Hamiltonian in mean-field theory, allowing for bond-dependent variation of the RVB order parameter, we show that both s- and d-wave superconducting states are possible. The d-wave solution belongs to a two-dime…
We report the low-temperature electronic and magnetic properties of the alkali metal-organic solvent intercalated iron selenide superconductor Lix(C5H5N)yFe2-zSe using muon-spin-spectroscopy measurements. The zero-field \muSR results indicate that nearly half of the sample is magnetically ordered and there is a spatial phase separation between the superconducting and the magnetic fraction. The transverse-field \muSR results show that the temperature dependence of the penetration depth λ(T) in the mixed state of Lix(C5H5N)yFe2-zSe can be explained using a two-gap s+s-wave model with gap values …
This study examines the potential of superconductivity in transition metal (TM) intercalated bilayer graphene through a systematic study of the electronic and magnetic properties. We determine the electronic structure for all first row TM elements in the stable honeycomb configuration between two layers of graphene using density functional theory (DFT). Through an analysis of the electron density, we assess the induction of the magnetic moment in each case, where a comparison of the ferromagnetic and antiferromagnetic configurations allow us to ascertain an estimated exchange coupling between …
We report a study of the temperature dependence of the surface resistance RS in the graphite intercalated compound (GIC) CaC6, where superconductivity at 11.5 K was recently discovered. Experiments are carried out using a copper dielectrically loaded cavity operating at 7 GHz in a "hot finger" configuration. Bulk CaC6 samples have been synthesized from highly oriented pyrolytic graphite. Microwave data allows to extract unique information on the quasiparticle density and on the nature of pairing in superconductors. The analysis of RS(T) confirms our recent experimental findings that CaC6 behav…
Superconducting characteristics such as the Meissner-Ochsenfeld state, screening supercurrents and hysteresis loops of type-II superconductors were observed from the temperature and magnetic field dependences of the magnetic moment, m(T, H), in graphite powders reacted with sulfur for temperatures below 9.0 K. The temperature dependence of the lower critical field Hc1(T) was determined and the zero-temperature penetration depth, lambda(0), was estimated (lambda (0) = 227 nm). The superconductivity was observed to be highly anisotropic and to coexist with a ferromagnetic state that has a Curie …
The calcium intercalated graphite (CaC$_{6}$) is considered to be a representative material of the graphite intercalated superconductors, which exhibits sizable anisotropy of the Fermi surface (FS). Herein, the influence of the FS anisotropy on the critical magnetic field ($H_{C}$) in CaC$_{6}$ superconductor is comprehensively analyzed within the Migdal-Eliashberg (M-E) formalism. To precisely account for the mentioned anisotropy effects, the analysis is conducted in the framework of the six-band approximation, hitherto not employed for calculations of the $H_{C}$ function in CaC$_{6}$ materi…
Superconducting properties were studied on high quality superconductors $Ba_{x}(NH_{3})Fe_{2}Se_{2}$ ($T_{c}$ = 39 K) and $Sr_{x}(NH_{3})Fe_{2}Se_{2}$ ($T_{c}$ = 44 K) prepared by intercalating Ba/Sr atoms into tetragonal $β$-FeSe by liquid ammonia. The elongated c-axis and almost unchanged a-axis of $Ba_{x}(NH_{3})Fe_{2}Se_{2}$, comparing with $β$-FeSe, suggested an unchanged intra-$Fe_{2}Se_{2}$-layer structure and the $T_{c}$ enhancement is due to a 3D to 2D-like Fermi surface transformation. The superconducting coherent lengths $ξ$(0), Ginzburg-Landau parameters $κ$ and penetration depths …
We study the effects of an external magnetic field on thensuperconducting phase diagram of a quasi-two-dimensional system of Dirac electrons at an arbitrary temperature. At zero temperature, there is a quantum phase transition connecting a normal and a superconducting phase, occurring at a critical line that corresponds to a magnetic field dependent critical coupling parameter, which should be observed in planar materials containing Dirac electrons, such as $Cu_xTiSe_2$. Moreover, the superconducting gap is obtained as a function of temperature, magnetic field and coupling parameter ($λ_{\rm R…
We study the graphite intercalated compound CaC$_6$ by means of Eliashberg theory, focusing on the anisotropy properties. An analysis of the electron-phonon coupling is performed, and we define a minimal 6-band anisotropy structure. Comparing with Superconducting Density Functional Theory (SCDFT) the condition under which Eliashberg theory is able to reproduce the SCDFT gap structure is determined, and we discuss the role of Coulomb interactions. The Engelsberg-Schrieffer polaron structure is computed by solving the Eliashberg equation on the Matsubara axis and analytically continuing it to th…
Superconductivity in intercalated graphite CaC6 and H under extreme pressure, in the framework of superconducting density functional theory, is discussed. A detailed analysis on how the electron-phonon and electron-electron interactions combine together to determine the superconducting gap and critical temperature of these systems is presented. In particular, we discuss the effect on the calculated Tc of the anisotropy of the electron-phonon interaction and of the different approximations for screening the Coulomb repulsion. These results contribute to the understanding of multigap and anisotr…
We present a joint experimental and theoretical study of the superconducting phase of the layered binary silicide BaSi2. Compared with the layered AlB2 structure of graphite or diboride-like superconductors, in the hexagonal structure of binary silicides the sp3 arrangement of silicon atoms leads to corrugated sheets. Through a high-pressure synthesis procedure we are able to modify the buckling of these sheets, obtaining the enhancement of the superconducting transition temperature from 4 K to 8.7 K when the silicon planes flatten out. By performing ab-initio calculations based on density fun…
We study the effects of an external magnetic field on the superconducting properties of a quasi-two-dimensional system of Dirac electrons at an arbitrary temperature. An explicit expression for the superconducting gap is obtained as a function of temperature, magnetic field and coupling parameter ($λ_{\rm R}$). From this, we extract the $B \times λ_{\rm R}$, $T\times λ_{\rm R}$ and $B \times T$ phase diagrams. The last one shows a linear decay of the critical field for small values thereof, which is similar to the behavior observed experimentally in the copper doped dichalcogenide $Cu_xTiSe_2$…
Recently, the niobium (Nb)-doped topological insulator Bi_2Se_3, in which the finite magnetic moments of the Nb atoms are intercalated in the van der Waals gap between the Bi_2Se_3 layers, has been shown to exhibit both superconductivity with T_c = 3 K and topological surface states. Here we report on muon spin rotation experiments probing the temperature-dependent of effective magnetic penetration depth Lambda_eff(T) in the layered topological superconductor candidate Nb_0.25Bi_2Se_3. The exponential temperature dependence of lambda_(eff)^(-2)(T) at low temperatures suggests a fully gapped su…
