The superconducting properties of two beta-pyrochlore oxides, CsOs2O6 and RbOs2O6, are studied by thermodynamic and transport measurements using high-quality single crystals. It is shown that the character of superconductivity changes systematically from weak coupling for CsOs2O6 to moderately strong coupling for RbOs2O6, and finally to extremely strong coupling with BCS-type superconductivity for KOs2O6, with increasing Tc. Strong-coupling correction analyses of the superconducting properties reveal that a low-energy rattling mode of the alkali metal ions is responsible for the mechanism of the superconductivity in each compound. The large enhancement of Tc from Cs to K is attributed to the increase in the electron-rattler coupling with decreasing characteristic energy of the rattling and with increasing anharmonicity. The existence of weak anisotropy in the superconducting gap or in the electron-rattler interactions is found for the Cs and Rb compounds.
Rattling-induced superconductivity in the beta-pyrochlore oxide RbOs2O6 is investigated under high pressures up to 6 GPa. Resistivity measurements in a high-quality single crystal show that the superconducting transition temperature Tc increases gradually from 6.3 K at ambient pressure to 8.8 K at 3.5 GPa, surprisingly remains almost constant at 8.8 \pm 0.1 K in a wide pressure range between 3.5 (Po) and 4.8 GPa, and suddenly drops to 6.3 K at Ps = 4.9 GPa, followed by a gradual decrease with further pressure increase. Two anomalies in the temperature dependence of the normal-state resistivity…
We report nuclear magnetic resonance studies on the beta-pyrochlore oxide superconductor KOs2O6. The nuclear relaxation at the K sites is entirely caused by fluctuations of electric field gradient, which we ascribe to highly anharmonic low frequency oscillation (rattling) of K ions. A phenomenological analysis shows a crossover from overdamped to underdamped behavior of the rattling phonons with decreasing temperature and its sudden sharpening below the superconducting transition temperature Tc. Absence of the Hebel-Slichter peak in the relaxation rate at the O sites below Tc also indicates st…
We calculate the temperature dependence of NMR relaxation rate and electrical resistivity for coupling to a local, strongly anharmonic phonon mode. We argue that the two-phonon Raman process is dominating NMR relaxation. Due to the strong anharmonicity of the phonon an unusual temperature dependence is found having a low temperature peak and becoming constant towards higher temperatures. The electrical resistivity is found to vary like T^2 at low temperatures and following a sqrt{T} behavior at high temperatures. Both results are in qualitative agreement with recent observations on beta-pyroch…
Microwave penetration depth $λ$ and surface resistance at 27 GHz are measured in high quality crystals of KOs$_2$O$_6$. Firm evidence for fully-gapped superconductivity is provided from $λ(T)$. Below the second transition at $T_{\rm p}\sim 8$ K, the superfluid density shows a step-like change with a suppression of effective critical temperature $T_{\rm c}$. Concurrently, the extracted quasiparticle scattering time shows a steep enhancement, indicating a strong coupling between the anomalous rattling motion of K ions and quasiparticles. The results imply that the rattling phonons help to enhanc…
Rattling-induced superconductivity in the β-pyrochlore oxide KOs2O6 is investigated under high pressure up to 5 GPa. Resistivity measurements in a high-quality single crystal reveal a gradual decrease in the superconducting transition temperature Tc from 9.7 K at 1.0 GPa to 6.5 K at 3.5 GPa, followed by a sudden drop to 3.3 K at 3.6 GPa. Powder X-ray diffraction experiments show a structural transition from cubic to monoclinic or triclinic at a similar pressure. The sudden drop in Tc is ascribed to this structural tran-sition, by which an enhancement in Tc due to a strong electron-rattler inte…
In order to clarify that the Cooper pair in $β$-pyrochlore oxides is mediated by anharmonic oscillation of guest atom, i.e., rattling, we propose an experiment to detect anomalous isotope effect. In the formula of $T_{\rm c} \propto M^{-η}$, where $T_{\rm c}$ is superconducting transition temperature and $M$ denotes mass of the oscillator, it is found that the exponent $η$ is increased with the increase of anharmonicity of a potential for the guest atom. We predict that $η$ becomes larger than 1/2 in rattling-induced superconductor, in sharp contrast to $η=1/2$ for weak-coupling superconductiv…
Chemical trends of fundamental superconducting parameters and normal-state properties are described for a family of pyrochlore oxide superconductors. Particularly, the change of Tc from 1.0 K for alpha-pyrochlore Cd2Re2O7 to 3.3 K (A = Cs), 6.3 K (Rb), and 9.6 K (K) for beta-pyrochlore AOs2O6 is discussed on the basis of the conventional BCS scheme. Enhanced Tc and anomalous features observed for KOs2O6 are ascribed to low-energy phonons probably coming from the rattling of the K cations.
We study the influence of the rattling phonons on superconductivity in $β$-pyrochlore KOs$_{2}$O$_{6}$ compound based on the strong-coupling Eliashberg approach. In particular, analyzing the specific heat data we find that the rattling phonon frequency changes discontinuously at the critical temperature of the first order phase transition. Solving the strong-coupling Eliashberg equations with temperature dependent $α^{2}F(ω)$, we investigate the consequence of this first order phase transition for the anomalous temperature dependence of the superconducting gap. We discuss our results in contex…
We report the single-crystal X-ray analysis of the structure of the pyrochlore oxide superconductor KOs$_2$O$_6$. The structure was identified as the $β$-pyrochlore structure with space group $Fd\bar{3}m$ and lattice constant $a$ = 10.089(2)~Åat 300 K: the K atom is located at the 8$b$ site, not at the 16$d$ site as in conventional pyrochlore oxides. We found an anomalously large atomic displacement parameter $U_\mathrm{iso}$ = 0.0735(8)~Å$^2$ at 300 K for the K cation, which suggests that the K cation weakly bound to an oversized Os$_{12}$O$_{18}$ cage exhibits intensive rattling, as recently…
ß-pyrochore KOs2O6, which shows superconductivity below ~ 9.7K, has been converted into KxOs2O6 (x < 2/3 - 1/2) electrochemically to show spin glass-like behavior below ~ 6.1K. Room temperature sample surface potential versus charge transfer scan indicates that there are at least two two-phase regions for x between 1 and 0.5. Rattling model of superconductivity for the title compound has been examined using electrochemical potassium de-intercalation. The significant reduction of superconducting volume fraction due to minor potassium reduction suggests the importance of defect and phase coheren…
Using the Eliashberg theory of superconductivity we have examined several properties of a model in which electrons are coupled only to rattling phonon modes represented by a sharp peak in the electron-phonon coupling function. Our choice of parameters was guided by experiments on $β$-pyrochlore oxide superconductor KOs$_{2}$Os$_{6}$. We have calculated the temperature dependence of the superconducting gap edge, the quasiparticle decay rate, the NMR relaxation rate assuming that the coupling between the nuclear spins and the conduction electrons is via a contact hyperfine interaction which woul…
Another phase transition that is probably of first order is found in the beta-pyrochlore oxide superconductor KOs2O6 with a superconducting transition temperature Tc of 9.6 K. It takes place at Tp=7.5 K in the superconducting state in a zero magnetic field. By applying magnetic fields of up to 140 kOe, the Tc gradually decreased to 5.2 K, while Tp changed little, eventually breaking through the Hc2 line at approximately 65 kOe in the H-T diagram. Both the normal-state resistivity and Hc2 change slightly but significantly across the second phase transition. It is suggested that the transition i…
Superconducting and normal-state properties of the beta-pyrochlore oxide KOs2O6 are studied by means of thermodynamic and transport measurements. It is shown that the superconductivity is of conventional s-wave type and lies in the extremely strong-coupling regime. Specific heat and resistivity measurements reveal that there are characteristic low-energy phonons that give rise to unusual scattering of carriers due to strong electron-phonon interactions. The entity of the low-energy phonons is ascribed to the heavy rattling of the K ion confined in an oversized cage made of OsO6 octahedra. It i…
In order to clarify the mechanism of the enhancement of superconducting transition temperature $T_{\rm c}$ due to anharmonic local oscillation of a guest ion in a cage composed of host atoms, i.e., {\it rattling}, we analyze the anharmonic Holstein model by applying the Migdal-Eliashberg theory. From the evaluation of the normal-state electron-phonon coupling constant, it is found that the strong coupling state is developed, when the bottom of a potential for the guest ion becomes wide and flat. Then, $T_{\rm c}$ is enhanced with the increase of the anharmonicity in the potential, although $T_…
Pressure dependence of superconducting transition temperature $T_{\rm c}$ has been determined through the DC magnetic measurements under pressure up to $P$=10 GPa for $β$-pyrochlore oxides AOs$_2$O$_6$ with A=Cs ($T_{\rm c}$=3.3 K), Rb (6.3 K) and K (9.6 K). Both for A=Rb and Cs, $T_{\rm c}$ increases with increasing $P$ and shows a saturation at $T_{\rm cm}$$\sim$8.8 K, which is considered as the upper limit of $T_{\rm c}$ inherent in AOs$_2$O$_6$. In contrast, the $T_{\rm c}-P$ curve for KOs$_2$O$_6$ shows a sharp maximum of $\sim$10 K at $P$$\sim$0.5 GPa, and $T_{\rm c}$ is higher than $T_{…
Two beta-pyrochlore oxide superconductors, CsOs2O6 and RbOs2O6, are studied thermodynamically by measuring specific heat on polycrystalline samples. It is found that a Sommerfeld coefficient ? is nearly equal, 20 mJ/K2 mol Os, in the two oxides with different superconducting transition temperatures; Tc = 3.3 K and 6.3 K, respectively. This suggests that the density of states at the Fermi level is not a crucial parameter to determine the Tc of the beta-pyrochlore oxide superconductors, which is incompatible with the general expectation for a conventional BCS-type superconductor. Anomalous latti…
To assess electron correlation and electron-phonon coupling in the recently discovered beta-pyrochlores KOs2O6 and RbOs2O6, we have performed specific heat measurements in magnetic fields up to 14 T. We present data from high quality single crystalline KOs2O6, showing that KOs2O6 is a strong coupling superconductor with a coupling parameter lambda_ep \approx 1.0 to 1.6 (RbOs2O6: lambda_ep \approx 1). The estimated Sommerfeld coefficient of KOs2O6, gamma=76 to 110 mJ/(mol K^2), is twice that of RbOs2O6 [gamma=44 mJ/(mol K^2)]. Using strong-coupling corrections, we extract useful thermodynamic p…
Motivated by the discovery of superconductivity in beta-pyrochlore oxides, we study property of rattling motion coupled with conduction electrons. We derive the general expression of the Green's function of fully anharmonic lattice vibration within the accuracy of the second order perturbation of electron-ion interaction by introducing self-energy, vertex-correction, and normalization factor for each transition. Using the expression, we discuss the characteristic properties of the spectral function in the entire range from weakly anharmonic potential to double-well case, and calculate NMR rela…
We have applied ab initio molecular dynamics (MD) simulations to study metal-metal coupling on the alkali-metal sublattice in the β-pyrochlore osmates, AOs2O6 (A = K, Rb, Cs) at 300 K. We find that the alkali-metal atoms (rattlers) couple to each other more strongly than they couple to the cage atoms, and that, at 300 K, this coupling is strongest for Cs. We show that this coupling controls the dominant dynamics in the rattling of these atoms. We provide preliminary evidence that the rattlers couple to each other primarily through the T2g mode whereas their coupling to the cage modes occurs th…
