Structural phase transition and superconductivity of ytterbium under high pressure

Recent advances in theory and experiment declare the rare-earth (RE) hydrogen-rich compound $\mathrm{La}{\mathrm{H}}_{10}$ is a near room-temperature superconductor under high pressure. To understand the underlying mechanism of superconductivity and explore the crucial role of lanthanides in forming the RE-based polyhydrides, we here perform a theoretical study on the structural phase transition and superconductivity of late lanthanide ytterbium (Yb) metal under high pressure up to 240 GPa. Two alternative structures, $R\overline{3}m$ and $I4/mmm$ phases, of Yb are presented. Most interestingly, the $P{6}_3/mmc$ phase of Yb is serendipitously discovered to be a superior superconductor with a critical temperature value of 19.5 K at 160 GPa, which is higher than other known RE elemental superconductors. The present findings establish an alternative structural phase transition sequence of Yb, which offers insights for further understanding the vital physics mechanisms of a lanthanide-based superconductor.

Figure 1

Calculated enthalpies per atom of various phases of Yb under different pressures. (a) Enthalpy-pressure curves from ambient pressure to 20 GPa. (b) Enthalpy-pressure curves from 20 to 100 GPa. (c)–(f) Crystal structures of $R\overline{3}m$, $Im\overline{3}m$, $I4/mmm$, and $P{6}_3/mmc$ phases of Yb, respectively.

Figure 2

Calculated phonon dispersion curves of Yb under different pressures. (a) $R\overline{3}m$ at ambient pressure, (b) $Im\overline{3}m$ at 5 GPa, (c) $I4/mmm$ at 20 GPa, and (d) $P{6}_3/mmc$ at 50 GPa.

Figure 3

(a) Calculated band structures of the $R\overline{3}m$ phase of Yb at ambient pressure. The red dashed line indicates that the VBM along the $\mathrm{\Gamma }$-T high-symmetry path is slightly higher than the CBM at the H point. (b) Calculated PDOS of the $R\overline{3}m$ phase at ambient pressure. (c) Calculated band structures of the $R\overline{3}m$ phase at 2 GPa. The red dashed line indicates that the VBM along the $\mathrm{\Gamma }$-T high-symmetry path is slightly higher than the CBM at the H point. (d) Calculated PDOS of the $R\overline{3}m$ phase at 2 GPa.

Figure 4

Calculated partial-wave electron density of states of Yb under different pressures. (a) $Im\overline{3}m$ at 5 GPa, (b) $I4/mmm$ at 20 GPa, (c) $P{6}_3/mmc$ at 50 GPa, and (d) $P{6}_3/mmc$ at 140 GPa. The position indicated by the dashed line is the Fermi level, and the Van Hove singularities (red circles) appear in all phases.

Figure 5

Calculated $N_{E_F}$, $N_{n{E}_F-d}$, EPC parameter $\lambda$, ${\omega }_{log}$, and $T_c$ of Yb under different pressures. (a) $N_{E_F}$, (b) $N_{n{E}_F-d}$, (c) EPC parameter $\lambda$, (d) ${\omega }_{log}$, and (e) $T_c$. $N_{E_F}$ and $N_{n{E}_F-d}$ are the TDOS per unit volume and the average PDOS of $d$ orbitals per unit volume, respectively. The units are state$/\mathrm{eV}/{\mathring{\mathrm{A}}}^3$.

Figure 6

(a) Calculated phonon dispersion curves, phonon density of states (PHDOS), Eliashberg function ${\alpha }^{2}F\left(\omega \right)$, and EPC parameter $\lambda$ of the $P{6}_3/mmc$ phase of Yb under 160 GPa. The relative intensities of the EPC parameters ${\lambda }_{qv}$ are represented by the purple circles. (b) Vibration patterns of $E_{2g}^1$ phonon modes at the $\mathrm{\Gamma }$ point. (c) The influences of $E_{2g}^1$ phonon modes on the band structures. The greatest influences are circled by the green circles. (d) Vibration patterns of $B_{2g}$ phonon modes at the $\mathrm{\Gamma }$ point. The orange circle indicates the upward vibration direction. (e) The influences of $B_{2g}$ phonon modes on the band structures.

Figure 7

Calculated orbital-resolved band structures corresponding to different orbitals of the $P{6}_3/mmc$ phase of Yb under 160 GPa. (a) $d_{x^2-y^2}$, (b) $d_{z^2}$, (c) $d_{yz}$, and (d) $d_{xz}$ orbitals. The thicknesses of curves represent the weight of orbitals in the corresponding band structures.