Interplay of Superconductivity and Rattling Phenomena in $\beta$-Pyrochlore ${\mathrm{KOs}}_2{\mathrm{O}}_6$ Studied by Photoemission Spectroscopy

The electronic structure near the Fermi level ($E_F$) of the $\beta$-pyrochlore superconductor ${\mathrm{KOs}}_2{\mathrm{O}}_6$ is studied using laser-excited ultrahigh-resolution photoemission spectroscopy. The superconducting gap clearly opens across the superconducting transition ($T_c=9.6\mathrm{K}$), with the strong electron-phonon coupling value of $2\Delta (0)/k_B{T}_c\ge 4.56$. A fitting analysis identifies clear anomalies at $T_p=7.5\mathrm{K}$ in the temperature dependencies of the superconducting gap size and the quasiparticle relaxation lifetime. These anomalies and the fine spectral structures arising from phonons suggest that the existence of the rattling behavior of K ions significantly affects the superconductivity in ${\mathrm{KOs}}_2{\mathrm{O}}_6$.

Figure 1

(a) Superconducting gap and fine electronic structures near $E_F$ are shown in an enlarged energy scale. The red solid curve represents the $s$-wave fitting function with $\Delta =1.63$ and $\Gamma =0.003\mathrm{meV}$. Black arrows indicate peaks centered around 3.7 and 10 meV. Inset shows the fine structures in an enlarged energy scale. The red broken curve represents the fitting function. The peak at 3.7 meV and the dip at 4.5 meV are indicated as $P$ and $D$ with arrows, respectively. (b) Temperature dependence of PES spectra observed in ${\mathrm{KOs}}_2{\mathrm{O}}_6$.

Figure 2

PES spectra and the fitting curves for ${\mathrm{KOs}}_2{\mathrm{O}}_6$ superconducting state. Black circles are spectra at (a) 4.7, (b) 6.6, and (c) 8.3 K. Error bars on the photoemission spectra are superimposed taking into account the total accumulated intensity of each spectrum. The blue, green, and pink curves represent the $s$-wave fitting functions with $\Gamma =0.003$, 0.10, and 0.52 meV, which are the values for the best fitting at respective temperatures.

Figure 3

(a) Temperature dependence of $\Gamma (T)$ for ${\mathrm{KOs}}_2{\mathrm{O}}_6$. The black broken curves are the guides for eyes. The gray and black solid curves represent the BCS curves with $2\Delta (0)/k_B{T}_c=3.52$ (theoretical value for weak-coupling limit) and $2\Delta (0)k_B{T}_c=4.56$, respectively. The value of $2\Delta (0)k_B{T}_c=4.56$ was estimated by fixing $T_c$ and the $\Delta (3.5\mathrm{K})$, which should indicate the lower limit of the reduced gap. The error bar of the temperature is within $\pm 0.25\mathrm{K}$, corresponding to the marker size. (b) $T$-dependence of $\Gamma (T)$ for ${\mathrm{KOs}}_2{\mathrm{O}}_6$. $\Gamma (T)$ for Nb and Pb are also plotted for comparison.