Session P8: Focus Session: Novel Superconductors:Miscellaneous Materials

Recent progress in applications of the superconducting density functional theory

One of the great challenges of condensed-matter theory is the prediction of material specific properties of superconductors (SC) such as the critical temperature $T_c$ or the gap at zero temperature. Recently, based on a seminal work by Oliveira, Gross and Kohn(1), an extention of density functional theory to the superconducting state (SCDFT) was introduced and applied to elemental superconductors (2). Later work showed how the method is able to describe the properties of real materials ranging from weak to strong coupling. Unique feature of the method is the ab-initio inclusion of the Coulomb interaction which, recently combined with a fully anisotropic treatment of the electron-phonon coupling, allows for a detailed description of the most important material specific properties, including the relevance of multiple gaps, in good agreement with the available experiments. \\ The discovery of novel electron-phonon SC provided new challenges to the method. We will report on the most recent applications, including MgB$_2$, alkali metals under pressure, Ca intercalated graphite and other new and traditional SC. The subtle interplay between e-ph mediated attraction and Coulomb repulsion, normally hidden by the use of the pseudopotential $\mu^*$, will show its material-specific importance in the resulting $T_c$. (1) L. N. Oliveira, E. K. U. Gross, and W. Kohn, Phys. Rev. Lett. 60, 2430 (1988) (2) Marques et al., Phys Rev. B 72, 024545 (2005); M. Lueders et al., $ibid$ 024546 (2005)   

First-Principles Investigation of Superconductivity in Transition Metal Carbides

We investigate the origin of superconductivity in the transition metal carbides TaC and HfC by a first-principles approach. The electronic structure is described within density functional theory in the local density approximation, and the lattice dynamical properties are determined through density functional perturbation theory. We calculate the average electron-phonon coupling strength through the isotropic approximation to the Migdal-Eliashberg theory, and the superconducting transition temperature through the McMillan formula. The calculated transition temperatures are found to be in excellent agreement with experiment. The relatively high transition temperature of TaC (10.3 K) is associated with a Kohn anomaly in the phonon dispersions, and arises from significant Fermi surface nesting. In contrast, the absence of nesting in HfC results in a limited phase-space availability for electron-phonon scattering. Correspondingly, HfC exhibits a negligible transition temperature ($<0.1$ K).   

Strong Electron-Phonon Coupling in Elemental Metals Under Pressure

The superconductivity of yttrium with T$_c$=20K at 115 GPa has been confirmed by strong electron-phonon coupling obtained using linear response methods. The increase of T$_c$ under pressure mainly comes from the increasingly strong coupling to the transverse modes at all high-symmetry zone boundary points X, K, and L. Evaluation of the electron-phonon spectral function shows a very strong increase with pressure of coupling strength in the 2-8 meV range, but with an accompanying steady increase in the 8-20 meV range.The superconductivity of Ca under pressure, however, is a challenge. While other elemental superconductors are usually close-packed, Ca is simple cubic (SC) at pressure between 30 GPa and 109 GPa, and its T$_c$ increases significantly in this pressure range, and goes to 23 K at 109 GPa (25 K at 161 GPa), making Ca the highest T$_c$ superconductor among elements. From linear response calculations we find the harmonic frequencies are unstable over a large portion of the zone for a wide range of pressure in the SC phase. We present calculational results and discuss possibilities, which include the likely stabilization of the SC structure by large anharmonic contributions to the lattice dynamics.   

Calculations of Superconducting Properties in Yttrium and Calcium under High Pressure

We have used first-principles electronic structure calculations to generate the bulk modulus as a function of volume as well as the densities of states and scattering phase shifts at the Fermi level. These quantities were used in conjunction with the rigid-muffin-tin theory of Gaspari and Gyorffy and the McMillan theory to determine the electron-phonon coupling and the superconducting transition temperature for Yttrium and Calcium under high pressures. Our results provide a good interpretation of the measured increase of $T_{c}$ in these metals.   

Assessment of the importance of correlation effects in Li$_x$NbO$_2$

About 15 years ago Geselbract {et al.} reported superconductivity with $T_c$=5K for $x \approx$0.5 in Li$_x$NbO$_2$. The critical temperature does not show significant change in the range 0.45 $ [Preview Abstract]

Nearly-free electron superconductor Ag$_5$Pb$_2$O$_6$

Superconductivity in the silver lead oxide Ag$_5$Pb$_2$O$_6$ has been discovered below 52~mK [1,2]. Although its $T_c$ is one of the lowest among the known oxide superconductors, this oxide is interesting from the viewpoint that it is the first superconductor with a nearly-free-electron Fermi surface. This fact is revealed by our quantum oscillation study [3] as well as recent band-calculation studies, which concluded that the system possesses one near-spherical Fermi surface with a small electron- mass enhancement. We will present its type-I superconducting properties, as well as the properties of the normal state where the resistivity varies nearly as $T^2$ up to room temperature [1]. \newline [1] S. Yonezawa and Y. Maeno, Phys.~Rev.~B 70, 184523 (2004). [2] S. Yonezawa and Y. Maeno, Phys.~Rev.~B 72, 180504(R) (2005). [3] M. Sutherland et al., Phys.~Rev.~Lett. 96, 097008 (2006).   

Electron-phonon interaction in the polymeric superconductor, polysulfur nitride, (SN)$_{x}$.

In early 1975, superconductivity at temperatures between 0.3 -- 0.4 K was discovered in the inorganic polymer, polysulfur nitride, (SN)$_{x}$. The compound itself was originally synthesized in the first decade of the 20$^{th}$ century, but its transport properties went largely undetermined until their investigation was sparked by the emergence of the low dimensional layered organic charge transfer salts in the decade of the 1980s. The issue of why the transition temperature of (SN)$_{x}$ is so low has not been adequately addressed computationally, especially in view of the realization of superconductivity at nearly 40 K in magnesium diboride, MgB$_{2}$, in 2001, a compound whose electronic structure is remarkably similar to (SN)$_{x}$, in that both are two-band, hole-electron semimetals with low-dimensional Fermi surface topologies. In this talk, we report our results on the calculation of the electron-phonon dispersion relation,$\alpha ^2F(\omega ),$ for (SN)$_{x}$ obtained from the application of recently available DFT algorithms capable of accurately treating screening of electron-phonon interactions in metals.   

Microscopic theories for Cubic and Tetrahedral Superconductors

We will examine the weak coupling theory for the unconventional superconducting states of cubic or tetrahedral superconductors for arbitrary order parameters and Fermi surfaces in zero applied magnetic fields. We will also look at multiple transitions where a higher symmetry is weakly broken to account for them. We will then perform a weak coupling theory where two representations of the symmetry group have accidentally nearly degenerate transition temperatures.   

Density of states, specific heat and nuclear spin-lattice relaxation rate in PrOs$_4$Sb$_{12}$

We present a theoretical study of the density of states, specific heat and nuclear spin-relaxation rate in the unconventional superconductor PrOs$_4$Sb$_{12}$. In this material, superconductivity is best described by a three component order parameter in the triplet channel. Instead of nodes, deep dips appear in the gap function producing power law temperature dependencies at higher temperatures and exponential suppression at low temperatures of the specific heat and the nuclear spin lattice relaxation rate. Various experimental observations will be discussed in this context.   

Multiband superconductivity and penetration depth in PrOs$_{4}$Sb$_{12}$

The penetration depth lambda in the filled-skutterudite heavy-fermion superconductor PrOs$_4$Sb$_{12}$ has been measured using transverse-field muon spin rotation. It is found to be temperature-independent at low temperatures, consistent with a nonzero gap for quasiparticle excitations. In contrast, zero-field radiofrequency inductive measurements yield a stronger temperature dependence of lambda, indicative of point nodes in the gap. A $\sim$10\% discrepancy is found at intermediate temperatures. This seems likely to be due to multiband superconductivity in this compound, recently found from thermal conductivity measurements. A sufficiently large difference between gaps would render the field distribution in the vortex controlled exclusively by the larger gap band, whereas all bands would participate in zero field.   

Fully gapped $s$-wave superconductivity in KOs$_2$O$_6$

The discovery of superconductivity in the $\beta$-pyrochlore oxides AOs$_2$O$_6$ (A=Cs, Rb, and K) has attracted so much attention, because the geometric spin frustration inherent to their pyrochlore crystal structures is supposed to give rise to unconventional superconductivity via magnetic spin fluctuations. Until now experimental results suggest, however, that CsOs$_2$O$_6$ ($T_c=3.3$ K) and RbOs$_2$O$_6$ ($T_c=6.3$ K) are fully gapped $s$-wave superconductors. On the other hand, the experimental data of KOs$_2$O$_6$ ($T_c=9.6$ K) show somewhat unusual behaviors, pointing out in some cases to unconventional superconductivity. In this talk we will discuss magnetic penetration depth data of single crystals of KOs$_2$O$_6$ down to 30 mK. The data clearly indicate that KOs$_2$O$_6$ is a fully single-gapped $s$-wave superconductor. This implies that all of the geometrically spin-frustrated compounds known until now respond as conventional superconductors, which would suggest that spin frustration does not lead to unconventional pairing as expected.   

Muon spin relaxation and hyperfine-enhanced $^{141}$Pr nuclear spin dynamics in (Pr,La)Os$\rm{_4}$Sb$\rm{_{12}}$ and Pr(Os,Ru)$\rm{_{4}}$Sb$\rm{_{12}}$

The longitudinal-field muon relaxation experiments have been carried out in the Pr,La)Os$\rm{_4}$Sb$\rm{_{12}}$ and Pr(Os,Ru)$\rm{_{4}}$Sb$\rm{_{12}}$ alloy systems. At low temperatures, the dynamic fluctuations are involved in muon relaxation in addition to the contribution from a distributions of static muon local fields. The temperature and concentration dependencies of the muon damping rate $\Lambda$ indicate that this dynamic contribution is due to $^{141}$Pr nuclear magnetism, which is enhanced by hyperfine coupling to the Pr$^{3+}$ Van Vleck susceptibility. Further evidence comes from the field dependence of $\Lambda$, which is in reasonable agreement with the modified model for muon spin relaxation by dipole-coupled nuclear spins.   

Andreev Spectroscopy Study of the Heavy-Fermion Superconductor PrOs$_{4}$Sb$_{12}$

The discovery of superconductivity in the heavy-fermion material PrOs$_{4}$Sb$_{12}$ has attracted widespread interest. In particular, there is evidence for multiple superconducting order parameters, at least one of which is believed to have nodes. We present Andreev spectroscopy data, down to 80 mK and up to 2.5 T, taken using ballistic point contacts made with Pt-Ir tips on single crystals of PrOs$_{4}$Sb$_{12}$. Pronounced zero-bias conductance peaks (ZBCP's) seen in the differential conductance spectra, show the existence of nodes in the order parameter. The magnetic field and temperature evolution of the spectra were studied to track how the pairing symmetry evolved, allowing us to map out the order parameter phase diagram. We observed that the ZBCP's vanished at a magnetic field, $H^{*}$, lower than the upper critical field, $H_{c2}$. This implies a field-driven change in the nodality of the order parameter at $H^{*}$, suggesting there are multiple superconducting phases with different pairing symmetries in PrOs$_{4}$Sb$_{12}$.