Revisiting YH$_9$ Superconductivity and Predicting High-T$_c$ in GdYH$_5$

TL;DR

This work revisits high-pressure superconductivity in hydrides by applying the parameter-free lowest-order constrained variational (LOCV) method to YH$_9$ and by predicting high-$T_c$ behavior in GdYH$_5$. Thermodynamic and magnetic properties are computed from a cluster expansion of the fluid-electron system, treating valence electrons as a conducting fluid in an ionic lattice and solving a spin-dependent two-body Euler–Lagrange problem, with magnetic response derived from the free energy. The results reproduce the experimental $T_c$ vs pressure for YH$_9$ and predict a superconducting transition at $T_c\approx223.2\ \mathrm{K}$ for GdYH$_5$ at $P_c\approx157.8\ \mathrm{GPa}$, including Meissner behavior, large gap ratios ($\alpha\approx6.27$ and $7.06$), and high upper critical fields. The study demonstrates LOCV as an efficient framework for predicting stable, high-$T_c$ hydride phases and provides a guided route for discovering near-room-temperature superconductors under practical pressures.

Abstract

The discovery of superconductivity in $\mathrm{YH_{9}}$ with a critical temperature of approximately $T_c\sim 243 \ K$ has opened a new window toward room temperature superconductivity. In this work, we employ the lowest order constrained variational method to investigate the thermodynamic and magnetic properties of the $\mathrm{YH_{9}}$ structure, obtaining results in good agreement with experimental data. % Based on the robustness of the LOCV approach for describing high-$T_c$ superconductors, we further extend our analysis to the gadolinium-yttrium-hydrogen system across various stoichiometries. The key finding of this study is the prediction of a superconducting phase transition at $T_c = 223.2~\mathrm{K}$ for $\mathrm{GdYH_{5}}$ under a critical pressure of approximately $157~\mathrm{GPa}$. This compound crystallizes in a tetragonal structure with space group $P4/mmm$. Moreover, the calculated gap ratio confirms that $\mathrm{GdYH_{5}}$ is a type-II superconductor with a critical current density suitable for potential industrial applications.

Figures (8)

• Figure 1: Dependence of the free energy per electron on the volume per particle for $\mathrm{YH}_{9}$ (left) $\mathrm{GdYH}_{5}$ (right). Points A correspond to the normal electronic state, while points B indicate a superconducting state for the fluid electrons. Points B represent a more stable state, as they correspond to a lower free energy.
• Figure 2: The magnetic susceptibility of the fluid electrons in $\mathrm{YH}_{9}$ near the phase transition is shown. It is small and positive above $T_c$, indicating a paramagnetic response. For $T \lesssim T_c$, the correlation length diverges due to the second-order phase transition, causing $\chi$ to rapidly decrease to approximately $-1$, which indicates the appearance of the Meissner effect.
• Figure 3: $T_c$ as a function of pressure for superconductivity in $P6_{3}/mmc$$\mathrm{YH}_{9}$. The labels $\mathrm{S}$ and $\mathrm{D}$ represent “sample” and “decreasing pressure,” respectively. Experimental data are taken from Ref. A11; further details about the samples are provided therein.
• Figure 4: Crystal structure of tetragonal $\mathrm{GdYH_{5}}$ with space group $P4/mmm$. Blue, orange, and white spheres represent Gd, Y, and H atoms, respectively. Atomic sizes are adjusted for clarity, and the distances between molecular units are increased to provide a clearer perspective.
• Figure 5: Phase diagram of $\mathrm{GdYH_{5}}$ illustrating the perfect diamagnetic (Meissner) state below $H_{c_1}=2.26~\mathrm{T}$, the mixed (vortex) state between $H_{c_1}$ and $H_{c_2}=113.34~\mathrm{T}$, and the paramagnetic phase above $H_{c_2}$. The magnetic field is applied along the Y direction.