Understanding of the Temperature--Pressure Phase Diagram of $\beta$-Pyrochlore Oxides: A Role of Anhamonicity on Superconductivity

We develop a physical understanding for how anhamonicity of lattice vibration affects transition temperature, $T_{\text{c}}$, of superconductivity mediated by phonons, via specific heat measurements on $\beta$-pyrochlore oxide superconductors under high pressure and in magnetic fields. We find that $T_{\text{c}}$ demonstrates unimodal dependence on pressure, where $T_{\text{c}}$ increases more than three times by pressure. On the other hand, an electron--phonon coupling constant, $\lambda$, is monotonically enhanced as pressure is applied, leading to the enhancement of effective mass of conduction electrons. From the analysis based on the McMillan equation, moreover, an average phonon frequency, $\omega_{\text{log}}$, is found to reflect a downward trend on all the pressure regions, which is consistent with the results of the previous inelastic neutron scattering and specific heat measurements. The downward trend of $\omega_{\text{log}}$ means that the application of pressure enhances a magnitude of anhamonicity, contrary to a common sense of pressure effects. On the basis of all the results, we indicate that the unimodal pressure variation in $T_{\text{c}}$ is attributed to two competing effects, that is, the enhancement of $\lambda$ and the simultaneous suppression of $\omega_{\text{log}}$ caused by the pressure evolution of anhamonicity.