Why mercury is a superconductor

Despite being the oldest known superconductor, solid mercury is mysteriously absent from all current computational databases of superconductors. In this Research Letter, we present a critical study of its superconducting properties based on state-of-the-art superconducting density functional theory. Our calculations reveal numerous anomalies in electronic and lattice properties, which can mostly be handled, with due care, by modern ab initio techniques. In particular, we highlight an anomalous role of spin-orbit coupling in the dynamical stability and of semicore $d$ levels in the effective Coulomb interaction and, ultimately, the critical temperature.

Figure 1

Top: Electronic band structure and density of states (DOS) of $\alpha$-Hg, with (solid curve) and without (dashed curve) spin-orbit coupling. Bottom: From left to right, 3D plot of the Fermi surface from fully relativistic calculations; 2D cuts along the BZ boundary are compared with the corresponding experimental cuts from Ref. [32].

Figure 2

Left panels: Phonon dispersions of $\alpha$-Hg along selected high-symmetry lines; solid and dashed curves indicate DFT-GGA calculations with and without SOC. For comparison the experimental measurements from Ref. [9] are reported as open black circles. Rightmost panel: Calculated Éliashberg function ${\alpha }^{2}F\left(\omega \right)$ (dark blue; scale at bottom) and frequency-dependent electron-phonon coupling function $\lambda \left(\omega \right)$ (light blue; scale at top); experimental tunneling spectra from Ref. [11] are shown in red. PR, Physical Review.

Figure 3

Comparison between theoretical (light blue circles) and experimental gap [10] (red squares) plotted as a function of temperature. The blue solid circles are obtained with a 1.25 linear scaling of the electronic spectrum, as described in the text.

Figure 4

Top: Two-dimensional plot of the Coulomb potential as a function of the energy with respect to the Fermi level. The color scale expresses the intensity of $V(\varepsilon ,{\varepsilon }^{\prime })$ in rydbergs. Bottom: Linearly scaled GGA DOS with $f=1.25$ (see text) compared with the x-ray experiments from Ref. [69]. JESRP, Journal of Electron Spectroscopy and Related Phenomena.