Electronic structure theory of H$_{3}$S: Plane-wave-like valence states, density-of-states peak and its guaranteed proximity to the Fermi level

TL;DR

The paper addresses why H$_{3}$S under high pressure exhibits a robust density-of-states peak at the Fermi level, a key driver of its high $T_{ m c}$. By dissecting first-principles Kohn–Sham wave functions, it reveals plane-wave–like valence states and derives a minimal nearly uniform plane-wave model with three (and optionally four) parameters that faithfully reproduce the band structure and the $E_{ m F}$-centered DOS peak. The authors connect this behavior to a Jones-zone activation mechanism, where Bragg-diffraction–induced hybridization of plane waves near a large zone edge lowers energy and generates 3D saddle points responsible for the DOS peak. This framework not only clarifies the origin of the peak but also provides a practical, first-principles–anchored approach to design band structure features near $E_{ m F}$ in compressed hydrides, with potential implications for enhancing $T_{ m c}$ in related systems.

Abstract

Superconductivity in sulfur superhydride H$_{3}$S under extreme pressures has been explained theoretically, but it requires a peaked concentration of the electronic density of states (DOS), which has been found in first-principles calculations. The mechanism of this peak formation, though vital for its high transition temperature, has however remained obscure. We address this problem through detailed analysis of the first-principles electronic wave functions. The valence wave functions are shown to be significantly plane-wave-like. From the Fourier-mode analysis of the self-consistent potential and atomic pseudopotentials, we extract the nearly uniform models that accurately reproduce the first-principles band structure with very few parameters. The DOS peak is shown to be the consequence of the hybridization of specific plane waves. Adjacency of Jones' large zone to the plane-wave spherical Fermi surface is posited to be the root cause of the multiple plane-wave hybridization, the DOS peak formation and its proximity to the Fermi level. The present theory resolves the minimal modeling problem of electronic states in H$_{3}$S, as well as establishes a mechanism that may help to boost the transition temperatures in pressure induced superconductors.

Figures (5)

• Figure 1: (a) Crystal structure of the high pressure phase of H$_{3}$S, visualized using VESTAMomma_JApplCrys2011. (b) The corresponding body centered cubic Brillouin zone. We indicate a point ${\rm q}=(2\pi/a)\times (2/3, 1/3, 0)$ for convenience. (c) Electronic band structures and density of states and (d) their close-up view. The maximum and minimum along $\Gamma$--${\rm q}$ have been found to be saddle points in the other directions Akashi_PRB2020Akashi_Bragg_PRR2024. The dashed line indicates the Fermi level.
• Figure 2: Plane wave components accumulated up to absolute wave number $|{\bf k}+{\bf G}|$ at selected points in the BZ. The band indexes are from lower to higher Kohn-Sham energy eigenvalues. Label "band 5" at "q" corresponds to the band that is responsible for the DOS peak.
• Figure 3: Plane-wave resolved spectral function $A({\bf k}+{\bf G};E_{\rm F})$ plotted in the region $({\bf k}+{\bf G})_{i}\geq 0 \ (i=x,y,z)$. The delta function $\delta$ in Eq. (\ref{['eq:spectral']}) was approximated to be Lorentzian with width=0.02 Hartree. We set the opacity of each point to be proportional to the function value. (a) Bird's eye view, (b) views from $(1 1 1)$ axis and (c) from $(0 0 1)$ axis.
• Figure 4: Band structure calculated from first principles compared with effective nearly uniform model results. The Fermi levels of the model results are determined to best fit the band concerning the DOS peak. (a) Comparison with the three-parameter model extracted from the first-principles potentials and (b) with the four-parameter model manually optimized to fit the first-principles band structure.
• Figure 5: Zones in ${\bf k}$-space. (a) BCC Brillouin zone. (b) Jones' large zone formed by (2 1 1) planes and its equivalents. The $\Gamma$-${\rm q}$ path [see Fig. \ref{['fig:H3S-band-dos']}] in the extended zone scheme is displayed. (c) Jones' zone overlaid by sphere with the same volume $V=9\times (2\pi/a)^3$.