<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>MoB</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> under pressure: Superconducting Mo enhanced by boron
Yundi Quan, Kwan-Woo Lee, Warren E. Pickett
Abstract
The discovery of the first high critical temperature $({T}_{c})$ transition metal diboride superconductor ${\mathrm{MgB}}_{2}$ structure $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{MoB}}_{2}$ under pressure with ${T}_{c}$ up to 32 K at 100 GPa provides new input into some unexplained aspects of electron-phonon coupling in intermetallic compounds. We establish that ${\mathrm{MoB}}_{2}$ is a phonon-mediated superconductor but has little in common with ${\mathrm{MgB}}_{2}$ (${T}_{c}=40\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ at zero pressure). ${\mathrm{MoB}}_{2}$ is a strongly metallic, three-dimensional, multi-Fermi-surface material, becoming of additional interest because it displays a frequency separation of Mo and B vibrations that mirrors that of metal superhydrides with ${T}_{c}$ approaching room temperature. This separation, which is unusual in intermetallic compounds, allows an analysis separately for Mo and B providing, among the other parameters essential for understanding phonon coupling, the matrix elements for scattering by the individual atoms. Strong coupling $({\ensuremath{\lambda}}_{\mathrm{Mo}}=1.48)$ is provided by Mo (total $\ensuremath{\lambda}=1.67$). A factor of 15 weaker coupling to each B atom is compensated by that coupling being to mean high-frequency modes around 85--90 meV (maximum of 140 meV), versus 18--20 meV for Mo. As a result, B enhances ${T}_{c}$ by 40% over the Mo-only value, to 33 K, corresponding to the experimental value. These results provide a guideline for designing higher-${T}_{c}$ materials from a cooperation of strong coupling from heavy atoms with weakly coupled light atoms. The new high-${T}_{c}$ paradigm discovered here highlights the need for studying and engineering larger ionic scattering matrix elements.