[Paper Review] On the high-pressure superconducting phase in platinum hydride

Dominik Szczęśniak, Tomasz P. Zemła|arXiv (Cornell University)|Apr 6, 2015

High-pressure geophysics and materials3 citations

TL;DR

This study investigates the high-pressure superconducting phase in platinum hydride (PtH) using the Eliashberg formalism to analyze thermodynamic properties at 100 GPa. It finds a critical temperature range of $ T_C \in \langle 12.94, 20.01 \rangle $ K for $ \mu^* \in \langle 0.05, 0.15 \rangle $, with thermodynamic ratios exceeding BCS predictions, indicating strong-coupling and retardation effects, supporting the hypothesis that experimental superconductivity in silane may originate from PtH rather than SiH₄.

ABSTRACT

Motivated by the ambiguous experimental data for the superconducting phase in silane (SiH$_{4}$), which may originate from the platinum hydride (PtH), we provide a theoretical study of the superconducting state in the latter alloy. The quantitative estimates of the thermodynamics of PtH at 100 GPa are given for a wide range of the Coulomb pseudopotential values ($μ^{*}$) within the Eliashberg formalism. The obtained critical temperature value ($T_C\in\left<12.94, 20.01 ight>$ for $μ^{*}\in\left<0.05,0.15 ight>$) agrees well with the experimental $T_{C}$ for SiH$_{4}$ which may be ascribed to PtH. Moreover, the calculated characteristic thermodynamic ratios exceed the predictions of the Bardeen-Cooper-Schrieffer theory, implying occurrence of the strong-coupling and retardation effects in PtH. We note that our results can be of high relevance for the future studies on hydrides.

Motivation & Objective

• To resolve ambiguity in experimental superconductivity observed in silane (SiH₄) at high pressure, which may stem from platinum hydride (PtH) contamination.
• To provide a comprehensive theoretical analysis of thermodynamic properties of PtH under high pressure using the Eliashberg formalism.
• To determine whether the experimentally reported high $ T_C $ in SiH₄ is consistent with PtH superconductivity.
• To quantify the role of strong electron-phonon coupling and retardation effects in PtH via thermodynamic ratios.
• To assess the validity of the BCS theory for PtH and evaluate the impact of the Coulomb pseudopotential $ \mu^* $ on superconducting properties.

Proposed method

• The isotropic Eliashberg equations are solved numerically at imaginary Matsubara frequencies and in mixed representation using an iterative method.
• The electron-phonon spectral function $ \alpha^2F(\Omega) $ is adopted from Kim et al. (2011), corresponding to PtH at 100 GPa and hcp structure (space group P6₃).
• Calculations are performed for three values of the Coulomb pseudopotential: $ \mu^* = 0.05, 0.10, 0.15 $, to span the range of physical relevance.
• Thermodynamic ratios such as $ R_H = H_c / (2T_C) $, $ R_C = C_s / C_n $, and $ R_\Delta = 2\Delta(0)/(k_B T_C) $ are computed to assess deviations from BCS theory.
• The order parameter and density of states are analyzed at $ T = 3 $ K to extract the zero-temperature gap $ 2\Delta(0) $.
• The analysis is conducted under conditions matching the Eremets et al. (2008) experiment, specifically at 100 GPa and hcp symmetry.

Experimental results

Research questions

• RQ1 Can the experimentally observed superconductivity in silane (SiH₄) at high pressure be attributed to platinum hydride (PtH) rather than SiH₄ itself?
• RQ2 What is the predicted critical temperature $ T_C $ for PtH at 100 GPa across a range of $ \mu^* $ values?
• RQ3 To what extent do thermodynamic ratios in PtH deviate from BCS theory, indicating strong-coupling and retardation effects?
• RQ4 How does the Coulomb pseudopotential $ \mu^* $ influence the superconducting gap and critical temperature in PtH?
• RQ5 Is the Eliashberg formalism necessary for describing PtH superconductivity, or is BCS theory sufficient?

Key findings

• The critical temperature for PtH at 100 GPa is predicted to be in the range $ T_C \in \langle 12.94, 20.01 \rangle $ K for $ \mu^* \in \langle 0.05, 0.15 \rangle $, with $ T_C \approx 19 $ K at $ \mu^* = 0.10 $, matching experimental observations.
• The zero-temperature energy gap $ 2\Delta(0) $ decreases from 6.87 meV to 4.28 meV as $ \mu^* $ increases from 0.05 to 0.15, indicating stronger pair-breaking effects.
• The thermodynamic ratio $ R_\Delta = 2\Delta(0)/(k_B T_C) $ ranges from 3.98 to 3.84, exceeding the BCS value of 3.53, indicating strong-coupling effects.
• The ratio $ R_H = H_c / (2T_C) \in \langle 0.155, 0.167 \rangle $ and $ R_C = C_s / C_n \in \langle 1.88, 1.82 \rangle $, both exceeding BCS predictions, confirming strong-coupling and retardation effects.
• The observed deviations from BCS theory are consistent across all thermodynamic ratios, indicating that PtH cannot be described by weak-coupling BCS theory.
• The results support the hypothesis that the superconducting phase observed in silane experiments is likely due to PtH formation via hydrogen reaction with platinum, not SiH₄ itself.