Session J8: Focus Session: Novel Superconductors IV: Intercalated graphites and related

Superconductivity in alkaline earth-intercalated graphites: CaC$_6$ and SrC$_6$

The recent discovery of superconductivity in alkaline earth-intercalated graphites CaC$_6$ ($T_c$ = 11.5 K) with substantially higher $T_c$'s than the previously known, has renewed the interest in the graphite intercalated compounds and stimulated a debate about the relevant pairing mechanisms. We have investigated the superconducting properties of high-quality CaC$_6$ samples, using specific heat ($C_P$) and magnetization measurements. For CaC$_6$, the exponential temperature dependence of the electronic $C_P$ and its linear dependence on the magnetic fields provide evidence for a fully-gapped, intermediate-coupled, and phonon-mediated superconductor without essential contributions from alternative paring mechanisms. However, the $C_P$ anomaly at $T_c$ is found to be much smaller than expected from theory, indicating a possible anisotropy in the superconducting gap. Consistently, the anisotropy of the upper critical field $H_{c2}^{\parallel}$/$H_{c2}^{\perp}$ is also larger than expected from the Fermi velocities, and shows significant temperature dependence below $T_c$. Recently, we also discovered the superconductivity in SrC$_6$ at $T_c$ = 1.65(6) K as well as the absence of superconductivity in BaC$_6$ down to 0.3 K. Similar to CaC$_6$, the $C_P$ anomaly of SrC$_6$ is somewhat lower than that theory predicted, but the discrepancy is much reduced. The anisotropy of $H_{c2}$ for SrC$_6$ is also found to be much smaller than that of CaC$_6$, indicating a reduced superconducting gap anisotropy. Finally, we will discuss the significantly lower $T_c$ of SrC$_6$ than CaC$_6$ as well as their positive pressure dependence in terms of the \textit{e-ph} coupling with the in-plane intercalant and the out-of-plane C phonon modes, based on \textit{ab-initio} calculations. Implications of the present findings on the superconducting mechanisms in alkaline-earth as well as alkali- intercalated graphites will also be given.   

Bulk evidence for single-gap s-wave superconductivity in the intercalated graphite superconductor C$_6$Yb

We report measurements of the in-plane electrical resistivity $\rho$ and thermal conductivity $\kappa$ of the intercalated graphite superconductor C$_6$Yb to temperatures as low as $T_c$/100. When a magnetic field is applied along the c-axis, the part of $\kappa$ associated with fermionic quasiparticles increases exponentially for $H_{c1} [Preview Abstract]

Superconductivity in Alkali-Earth intercalated graphite.

It has long been known that Graphite intercalated compounds (GICs) can display a superconducting behavior at low temperature. However, until the discovery of YbC$_6$ and CaC$_6$, the critical temperatures achieved were typically inferior to 5 Kelvin. Using density functional theory we study superconductivity in AC$_6$ with A=Mg,Ca,Sr,Ba. We find that at zero pressure Ca, Ba and Sr intercalated graphite are superconducting with critical temperatures (T$_c$) 11.5, 0.2 K and 3.0 K, respectively. We study the pressure dependence of T$_c$. 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 is much smaller than what shown in several recent experiments. Thus we suggest that in CaC$_6$ stacking faults or a continous phase transformation,such as an increase in staging could occur at finite pressure. Finally we argue that, although MgC$_6$ is unstable, the synthesis of intercalated systems of the kind Mg$_x$Ca$_{1-x}$C$_y$ could lead to higher critical temperatures. \newline \newline [1] M. Calandra and F. Mauri, Phys. Rev. Lett. {\bf 95}, 237002 (2005) \newline [2] M. Calandra and F. Mauri Phys. Rev. B 74, 094507 (2006)   

Far-infrared signature of a superconducting gap in intercalated graphite CaC$_{6}$.

CaC$_{6}$ is exceptional in the series of intercalated graphite compounds because of its high superconducting transition temperature, $T_{c}$=11.5K. The superconducting gap, 2$\Delta $=25.6 $\pm $ 3.2cm$^{-1}$, measured by scanning tunneling spectroscopy (N. Bergeal et al., PRL \textbf{97}, 077003 (2006)), is consistent with the weak-coupling BCS type superconductivity. The superconducting gap can be directly probed also by far-infrared spectroscopy. We studied the reflectance $R$ of CaC$_{6}$ between 4 and 100cm$^{-1}$ from 3K to 15K. We see the signature of the superconducting gap in the reflectance ratio of superconducting state $R_{s}$ to the normal state $R_{n }$and can follow its temperature dependence. The appearance of the gap signature in $R_{s}/R_{n}$ tells us that CaC$_{6}$ is in the dirty limit. Different models, including an anisotropic gap and a multi-gap scenario, will be discussed to fit the optical data.   

A First-Principles Insight into the Superconductivity of Graphite Intercalation Compounds

Experimental evidences have estabilished that the recently discovered superconductivity in graphite-intercalation compounds (GICs) CaC$_6$ and YbC$_6$ is due to electron-phonon ($e-ph$) coupling. First-principles calculations predict for CaC$_6$ an intermediate $e-ph$ coupling ($\lambda \sim 0.83$), resulting from intercalant in-plane ($I_{xy}$) and carbon out-of-plane ($C_z$) vibrations. Whereas the softening of the $I_{xy}$ modes explains increase of T$_c$ with pressure [1], the presence of the $C_z$ peak is due to an interaction which is ``dormant'' in pure graphite. A simple analysis of the band structure of the GICs also permits to rule out the possibility of plasmon-meadiated superconductivity[1]. \newline \newline [1] J. S. Kim, L. Boeri, R. K. Kremer, and F. S. Razavi Phys. Rev B, in press and Phys. Rev. Lett. 96, 217002 (2006).   

Strong electron-phonon coupling in the rare-earth carbide superconductor La$_2$C$_3$

Superconductivity in rare earth carbides has attracted interested again after the recent discovery of the 18 K superconductor Y$_2$C$_3$. Here, we present the crystal structure as well as the superconducting properties of the rare-earth sesquicarbides La$_2$C$_3$ ($T_c$ $\approx$ 13.4 K) gained from low-temperature neutron powder diffraction, specific heat and electrical resistivity measurements. From a detailed analysis of specific heat as well as the comparison with the full potential electronic structure calculations, a quantitative estimate of the electron-phonon coupling strength and the logarithmic average phonon frequency is made. The electron-phonon coupling constant found to be $\lambda_{ph}$ $\sim$ 1.35, and the low energy phonon modes are responsible for the superconductivity. These results suggest that La$_2$C$_3$ is in the strong coupling regime and the relevant phonon modes are the La-related modes rather than the C-C stretching modes. The upper critical fields($H_{c2}$) show a clear enhancement with respect to the Werthamer-Helfand-Hohenberg prediction and amount to $H_{c2}(0)$ $\sim$ 20 T confirming the strong electron-phonon coupling.   

The potential for mean-field $d$-wave superconductivity in graphite

We investigate the possibility of inducing superconductivity in a graphite layer by electronic correlation effects. We use a phenomenological microscopic Hamiltonian[1] 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 the 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 with the $d$-wave state having a significantly higher $T_c$ at finite doping. By using density functional theory we show that the doping induced from sulfur absorption on a graphite layer is enough to cause an electronically driven $d$-wave superconductivity at graphite-sulfur interfaces (see e.g. [2]). We will also briefly discuss applying our results in the case of the intercalated graphites as well as the validity of a mean-field approach. \newline [1] G. Baskaran PRB {\bf 65} 212505 (2002) \newline [2] S. Moehlecke {\it et al.} PRB {\bf 69} 134519 (2004)   

Possibility of superconductivity in high pressure phases of BC$_3$

Using an ab-initio pseudopotential-local-density-approximation, we study the possibility of a high-pressure transition of graphitic planar sp$^2$ bonded BC$_3$ into an sp$^3$ bonded covalent network. Energy barriers are examined for the predicted transition to the sp$^3$ phase and for the observed onset of phase separation in BC$_3$ under high pressure, high temperature conditions [V. L. Solozhenko \textit{et al.}, Appl. Phys. Lett. \textbf{85}, 1508 (2004)]. The sp$^3$ phase of BC$_3 $ is predicted to be metallic and superconducting and is similar to 25\% boron-doped diamond without boron clusters. Calculations of phonon frequencies and electron-phonon coupling allow for an estimate of the superconducting transition temperature.   

Probing electronic structure and electron-phonon interaction in borides using optical spectroscopy

We report optical properties of high-quality single crystals of boron type superconductor ZrB$_{12}$ (T$_{c}$=6 K) in the normal state from 20 to 300 K. The optical conductivity was measured from (6 meV-4 eV) by a combination of reflectivity and ellipsometry. The Drude plasma frequency and interband optical conductivity calculated by self-consistent full-potential LMTO method agree well with experiments. The $\alpha ^{2}$F($\omega )$ function extracted from optical spectra presents two peaks at 25 and 80 meV with partial coupling constants of 0.8 and 0.3 respectively. The low energy peak corresponds to the displacement mode of Zr inside B$_{24}$ cages, while the second one involves the rigid boron network. In addition to the usual narrowing of the Drude peak with cooling down, we observed an unexpected removal of about 10 {\%} of the Drude spectral weight which is partially transferred to the region of the lowest-energy interband transition ($\approx $ 1 eV). This effect may be caused by a delocalization of the metal ion from the centre of the B$_{24}$ cage. The discussion will refer to recent work on other boron rich compounds.   

Gapless Fermi Surfaces in anisotropic multiband superconductors in magnetic field.

We propose that a new state with a fully gapless Fermi surface appears in quasi-2D multiband superconductors in magnetic field applied parallel to the plane. It is characterized by a paramagnetic moment caused by a finite density of states on the open Fermi surface. We calculate thermodynamic and magnetic properties of the gapless state for both s-wave and d-wave cases, and discuss the details of the 1-st order metamagnetic phase transition that accompanies the appearance of the new phase in s-wave superconductors. We suggest possible experiments to detect this state both in the s-wave (2-H NbSe$_2$) and d-wave (CeCoIn$_5$) superconductors.   

Superconducting order parameter in NbSe$_{2}$ derived from the specific heat

To resolve the discrepancies on the superconducting order parameter of quasi-2D NbSe$_{2}$, the comprehensive specific heat measurements have been carried out.The thermodynamic consistence requires more than one energy scale of the order parameters The zero field data and the results of the mixed states respectively with $H$//$c$ and $H\bot c$ conclude: (1) $\Delta _{L}$=1.26 meV and $\Delta _{S}$=0.73 meV; (2) $N_{Se}$(0)/$ N$(0)=11{\%}$\sim $20{\%}; (3) $\Delta _{S}$ is 3-D and like on the Se derived Fermi surface. This present scenario largely removes the dispute over the order parameter existing in the previous literature. The alternative anisotropic$ s$-wave model is also discussed.