Lattice Dynamics and Superconductivity in Cerium at High Pressure

We have measured phonon dispersion relations of the high-pressure phase cerium-$oC4$ (${\alpha }^{\prime }$ phase with the $\alpha$-uranium crystal structure) at 6.5 GPa by using inelastic x-ray scattering. Pronounced phonon anomalies are observed, which are remarkably similar to those of $\alpha \mathrm{\text{−}}\mathrm{U}$. First-principles electronic structure calculations reproduce the anomalies and allow us to identify strong electron-phonon coupling as their origin. At the low-pressure end of its stability range, Ce-$oC4$ is on the verge of a lattice-dynamical instability and possibly a charge density wave. The superconducting transition temperatures of the fcc, $oC4$, and $mC4$ phases of Ce have been calculated, and the superconductivity observed experimentally by Wittig and Probst is attributed to the $oC4$ phase.

Figure 1

(a) Crystal structure and (b) Brillouin zone of Ce-$oC4$ ($\alpha \mathrm{\text{−}}\mathrm{U}$ type). Cell boundaries are indicated by black lines, and the near-neighbor contacts are highlighted in (a).

Figure 2

Selected IXS spectra of Ce-$oC4$ at 6.5 GPa for different momentum transfers $\mathbf{q}$. When $\mathbf{q}$ is reduced to the first Brillouin zone, (2.5 0 1) corresponds to $(\frac{1}{2}00)$, i.e., halfway along the $\Gamma \mathrm{\text{−}}Y$ line. The spectra in the right panel are collected with momentum transfers all corresponding to the $Y$ point (100) but with emphasis on different phonon branches. The spectra are offset vertically for clarity.

Figure 3

(a) Experimental phonon dispersion relations for Ce-$oC4$ at 6.5 GPa. The symbols distinguish $\mathbf{q}$ scans with different momentum offsets relative to the center of the Brillouin zone: ▴ (151)–(051)–(041)–$(04\frac{1}{2})$; ● (201)–(301); ▪ (200)–(300); ◆ (061)–$(\overline{1}61)$; ▸ (210)–(220); ◂ (210)–(200); ▾ (201)–$(20\frac{1}{2})$. The experimental uncertainties of the phonon energies correspond approximately to the symbol size. The lines are guides to the eye, and the branches are labeled as in Ref. 21. (b) Calculated phonon energies (solid lines) and IXS results (symbols). Selected results of the calculations at 4 and 2 GPa are indicated by dashed lines. (c) Mode-specific electron-phonon coupling strength ${\lambda }_{\mathbf{q}\nu }$ for the ${\Sigma }_4$ and ${\Sigma }_1$ branches. (d) Fermi-surface nesting function $\xi (\mathbf{q})$. (e) Bare static susceptibility ${\chi }_0(\mathbf{q})$.

Figure 4

Calculated Fermi surface of Ce-$oC4$ at 6.5 GPa. Colors represent the $f$ character of the electronic states at the Fermi level, according to the angular decomposition of the wave functions in the atomic spheres. Thick gray lines show the edges of the Brillouin zone, while the black lines mark the Wigner-Seitz cell corresponding to the conventional crystallographic unit cell.