Context and results Through first-principles calculations, we comprehensively elucidate the non-monotonic variation of the superconducting transition temperature (Tc) of phosphorus (P) over 0–400 GPa. By comparing structural distortions, elastic modulus softening, and the evolution of electronic density of states across pressure phases, alongside electron–phonon coupling analysis, we ascertain that <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="894_2025_6496_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="77" /> </InlineMediaObject> <EquationSource Format="TEX">$P6/mmm$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>P</mi> <mn>6</mn> <mo stretchy="false">/</mo> <mi>m</mi> <mi>m</mi> <mi>m</mi> </mrow> </math></EquationSource> </InlineEquation> at 80 GPa, a layer phase transition triggers low-frequency phonon softening and resonance with the p-orbital van Hove singularity, culminating in a Tc of 18.3 K. With increasing pressure, systematic hardening of the phonon spectrum reduces the electron–phonon coupling constant (λ). Consequently, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="894_2025_6496_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">$I\overline{4 }3d$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>I</mi> <mover> <mn>4</mn> <mo>¯</mo> </mover> <mn>3</mn> <mi>d</mi> </mrow> </math></EquationSource> </InlineEquation> at 400 GPa, Tc sharply decreases to 3.5 K. The Tc fluctuation primarily stems from the interplay between λ and TDOS near the Fermi level. This discovery offers new opportunities for exploring high-pressure superconductor characteristics and enhances understanding of electronic structure-lattice dynamics interplay under extreme conditions. Computational methods Electronic properties were computed using density functional theory (DFT) in CASTEP; the exchange–correlation interaction is described using the PBE functional within the generalized gradient approximation (GGA). Electron–phonon coupling and superconducting properties were calculated using QUANTUM ESPRESSO with optimized norm-conserving Vanderbilt pseudopotentials (ONCVPSP).

Non-monotonic evolution of superconductivity in phosphorus under high pressure: a first-principles study

期刊论文
发表日期：

2025年9月13日

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Lan-Xi Luo,
Wen-Guang Li,
Zheng-Tang Liu,
Juan Ren

摘要

Context and results

Through first-principles calculations, we comprehensively elucidate the non-monotonic variation of the superconducting transition temperature (T_c) of phosphorus (P) over 0–400 GPa. By comparing structural distortions, elastic modulus softening, and the evolution of electronic density of states across pressure phases, alongside electron–phonon coupling analysis, we ascertain that $P6/mmm$ $P 6 / m m m$ at 80 GPa, a layer phase transition triggers low-frequency phonon softening and resonance with the p-orbital van Hove singularity, culminating in a T_c of 18.3 K. With increasing pressure, systematic hardening of the phonon spectrum reduces the electron–phonon coupling constant (λ). Consequently, $I\overline{4 }3d$ $I \bar{4} 3 d$ at 400 GPa, T_c sharply decreases to 3.5 K. The T_c fluctuation primarily stems from the interplay between λ and TDOS near the Fermi level. This discovery offers new opportunities for exploring high-pressure superconductor characteristics and enhances understanding of electronic structure-lattice dynamics interplay under extreme conditions.

Computational methods

Electronic properties were computed using density functional theory (DFT) in CASTEP; the exchange–correlation interaction is described using the PBE functional within the generalized gradient approximation (GGA). Electron–phonon coupling and superconducting properties were calculated using QUANTUM ESPRESSO with optimized norm-conserving Vanderbilt pseudopotentials (ONCVPSP).