[Paper Review] Comparative study of high-Tc superconductivity in H3S and H3P

Hyungju Oh, Sinisa Coh+1 more|arXiv (Cornell University)|Jun 30, 2016

Quantum, superfluid, helium dynamics3 citations

TL;DR

This study compares high-Tc superconductivity in H3S and H3P under the same body-centered cubic structure and lattice parameter (3 Å), revealing that despite stronger electron-phonon coupling (λ = 1.66) in H3P, its superconducting transition temperature (Tc ≈ 76 K) is significantly lower than in H3S (Tc ≈ 166 K) due to softening of low-frequency H–P bond-bending modes and reduced phonon frequency weighting (ωln = 610 K vs. 1580 K), highlighting the critical role of phonon mode energy distribution over coupling strength alone.

ABSTRACT

We report on a comparative study of the electronic structure, phonon spectra, and superconducting properties for recently discovered superconducting hydrides, H3S and H3P. While the electronic structures of these two materials are similar, there are notable changes in the phonon spectra and electron-phonon coupling. The low-frequency bond-bending modes are softened in H3P and their coupling to the electrons at the Fermi surface is enhanced relative to H3S. Nevertheless, coupling to the high-frequency modes is reduced so the resulting calculated superconducting transition temperature is reduced from ~166 K in H3S to ~76 K in H3P.

Motivation & Objective

• To understand why H3P exhibits a lower Tc than H3S despite similar electronic structures.
• To investigate how changes in atomic mass and bonding (S → P) affect phonon spectra and electron-phonon coupling.
• To determine the origin of the reduced Tc in H3P relative to H3S, despite stronger overall electron-phonon coupling.
• To evaluate the role of phonon mode frequencies and their distribution in determining Tc in hydride superconductors.

Proposed method

• Ab initio calculations using norm-conserving pseudopotentials and the PBE functional in SIESTA and Quantum-ESPRESSO codes.
• Phonon frequencies and electron-phonon coupling (EPC) calculated via density-functional perturbation theory.
• Eliashberg spectral functions α²F(ω) and mode-resolved coupling strengths λqν computed using Wannier90 and EPW packages.
• EPC-weighted average phonon frequency ωln calculated using the formula ωln = exp{ (2/λ) ∫ (α²F(ω)/ω) lnω dω } to assess effective phonon energy.
• Tc estimated using the McMillan equation with μ* = 0.1 and validated with the Kresin–Barbee–Cohen model for large λ.
• A 16×16×16 k-point mesh was used for electronic structure, and interpolation via maximally localized Wannier functions enabled fine-grid EPC calculations.

Experimental results

Research questions

• RQ1 Why does H3P exhibit a lower superconducting transition temperature than H3S despite having a higher electron-phonon coupling strength?
• RQ2 How does the softening of low-frequency bond-bending modes in H3P affect its electron-phonon coupling and Tc compared to H3S?
• RQ3 To what extent do differences in phonon mode frequencies, rather than coupling strength, determine the Tc in these hydrides?
• RQ4 How does the distribution of phonon modes across the Brillouin zone influence the Eliashberg spectral function and superconducting properties?

Key findings

• The superconducting transition temperature (Tc) is estimated at 166 K for H3S and 76 K for H3P, despite H3P having a higher electron-phonon coupling strength (λ = 1.66 vs. 1.38).
• The effective phonon frequency ωln is 1580 K for H3S and only 610 K for H3P, indicating a significant reduction in the average phonon energy driving superconductivity.
• Low-frequency bond-bending modes (below 50 meV) in H3P show enhanced coupling to electrons near the Fermi surface, contributing to the increased λ, but their low energy limits Tc enhancement.
• The Eliashberg spectral function α²F(ω) in H3S is dominated by high-frequency H–S stretching modes at the Γ-point, while in H3P, contributions are spread across multiple modes along the Γ–H–N directions.
• The discrepancy between higher λ and lower Tc in H3P is attributed to the shift in dominant phonon mode energy from high (150–200 meV) to low (≤50 meV) frequencies, reducing the effective coupling energy.
• The results are consistent with experimental observations of Tc ≈ 200 K in H3S and Tc ≈ 100 K in H3P, suggesting that phonon softening in H3P may be overestimated in the calculation due to ignored unstable modes.