Thermodynamically Stable Hydride Superconductors

• Thermodynamically stable hydride superconductors are hydrogen-rich metallic compounds that remain energetically favored at high pressures by balancing enthalpic and entropic contributions with robust electron–phonon interactions.
• Advanced computational methods and high-pressure experimental techniques, such as convex-hull analyses and diamond anvil cells, validate their stability and superconducting properties based on precise phase diagrams.
• These materials offer promising pathways for achieving elevated Tc values—often exceeding 200 K—by leveraging structured frameworks like clathrate and perovskite motifs for enhanced electronic states.

Thermodynamically stable hydride superconductors are hydrogen-rich metallic compounds that remain energetically favored against decomposition within a specified thermodynamic ensemble, typically at high or ultrahigh pressures. These phases combine quantum mechanical lattice stability, favorable enthalpic and entropic contributions, and robust electron–phonon coupling to support superconductivity—often with critical temperatures (Tc) reaching or exceeding 200 K at elevated pressures. The interplay between crystal chemistry, electron–phonon coupling, and entropic stabilization mechanisms determines the formation, persistence, and superconducting properties of hydride superconductors. This article reviews the structural, thermodynamic, and electronic principles underlying their stability and superconductivity, and examines the computational and experimental strategies for their identification and validation.

1. Thermodynamic Stability Criteria in Hydride Superconductors

Hydride superconductors are considered thermodynamically stable when, under the relevant thermodynamic conditions (pressure P, temperature T, and composition), their Gibbs free energy G is lower than any combination of decomposition products, e.g., metal hydrides of lower hydrogen content or molecular hydrogen. The quantitative stability condition can be formulated as

$$\Delta G = G_\text{hydride} - \sum_j \nu_j G_j < 0,$$

where $G_\text{hydride}$ is the Gibbs energy of the (superconducting) hydride phase, $G_j$ are those of potential decomposition products, and $\nu_j$ are stoichiometric coefficients.

This stability is pressure dependent. For example, Fm-3m–LaH₁₀ becomes thermodynamically favored over LaH₃ + H₂ above about 150 GPa, with $\Delta G<0$ at these conditions, as confirmed by quantum chemistry calculations and long-term synthetic/structural characterization (Minkov et al., 3 Jul 2025). Similarly, in CaH₆ (Im-3m, cI14), stability is achieved above 150 GPa via electron transfer from Ca to hydrogen cages, reinforced by lattice vibrations and associated zero-point energy (Wang et al., 2012).

Advanced phase diagrams, convex-hull constructions, and enthalpy/entropy calculations (including zero-point and configurational entropy) are now systematically applied to screen for hydrides that are both dynamically and thermodynamically stable across multi-GPa pressure fields (Shipley et al., 2021, Lumley et al., 2014).

2. Energetic and Entropic Contributions to Phase Stability

A rigorous description of hydride phase stability—especially under high P–T synthesis conditions—requires a complete accounting of the origin of $\Delta G$:

$$\Delta G = (\Delta H_\text{latent} + \Delta H_\text{sensible}) - T(\Delta S_\text{vibrational} + \Delta S_\text{configurational}),$$

where $\Delta H_\text{latent}$ is the temperature-independent bond formation enthalpy, $\Delta H_\text{sensible}$ is the thermal (phonon) enthalpy, and $\Delta S_\text{vibrational}$ and $\Delta S_\text{configurational}$ denote the vibrational- and disorder-driven entropic contributions, respectively (Lumley et al., 2014).

• Sensible enthalpy is obtained from the lattice heat capacity, often via integration over the phonon density of states using quasi-harmonic or anharmonic corrections.
• Configurational entropy ($S_c=k_B\ln\Omega$) accounts for the microstates associated with hydrogen atom disorder on (often multiply degenerate) interstitial sites, impacting formation at high temperature or low H content.
• Vibrational entropy is derived from the full phonon spectrum, and typically opposes ordering—a significant driver limiting hydride precipitation at elevated T.

For instance, in Mg₂IrH₅, finite-temperature configurational entropy from hydrogen site disorder stabilizes the ordered phase at low and moderate pressures, making it more favorable than the fully hydrogenated Mg₂IrH₆ predicted in earlier calculations (Hansen et al., 13 Jun 2024). In zirconium hydrides, only local, not global, H accumulation drives precipitation out of solid solution below certain thresholds, due to the competition between enthalpic and entropic contributions (Lumley et al., 2014).

3. Structural Motifs and Electronic Properties

Many thermodynamically stable hydride superconductors feature sodalite-like clathrate, perovskite, or fluorite-related host frameworks, wherein a metallic or semi-metallic hydrogen sublattice is spatially “precompressed” by metal/ionic cages. For example:

• Sodalite-like clathrates: CaH₆ adopts a body-centered cubic Im-3m structure consisting of interconnected H₄ square units forming cages around Ca atoms (Wang et al., 2012). The electron transfer from Ca to the hydrogen network creates building blocks key to 3D stability.
• Perovskite hydrides: Compounds such as KGaH₃, CsInH₃, and AXH₃ (A = alkali metal, X = group IIIA/IVA) stabilize a cubic Pm-3m lattice with alkali metals conferring charge and structural stability, while the X–H framework produces high-frequency phonons and strong electron–phonon coupling (Du et al., 4 Jul 2024).
• Double perovskite or fluorite derivatives: At ambient pressure, the highest-Tc hydrides that are thermodynamically stable fall into vacancy-ordered double perovskite or fluorite families, with maximal Tc ~17 K (Sanna et al., 27 Aug 2025).
• Clathrate-type ternaries: Li₂NaH₁₇ (type-II clathrate, Fd-3m) and LiNa₃H₂₃ (type-I clathrate, Pm-3n) host hydrogen networks formed by large polyhedral cages (28-vertex or 24-/20-vertex, respectively), which facilitate high hydrogen DOS near the Fermi level and robust Fermi surface nesting (An et al., 2023).

A characteristic feature is a high density of hydrogen-derived electronic states at the Fermi level (N(E_F)), and frequent proximity to van Hove singularities that enhance electron–phonon interaction strength, particularly in clathrate or densely packed frameworks (Fan et al., 1 Aug 2024).

4. Superconducting Mechanisms and Electron–Phonon Coupling

Superconductivity in these systems is predominantly mediated by conventional phonon-induced pairing, with critical temperatures determined by the spectrum and strength of the electron–phonon interaction. The Eliashberg spectral function α²F(ω) and total electron–phonon coupling constant λ are computed via integration over density functional perturbation theory (DFPT) and closely related methods:

$$\lambda = 2 \int_0^{\omega_\text{max}} \frac{\alpha^2F(\omega)}{\omega} d\omega$$

The superconducting Tc can be estimated with semi-empirical modifications of McMillan’s formula, e.g.,

$$T_c = \frac{\omega_{\log}}{1.2} \exp\left(-\frac{1.04(1+\lambda)}{\lambda - \mu^*(1+0.62\lambda)}\right)$$

where ω_log is the logarithmic average phonon frequency, and μ* is the Coulomb pseudopotential (usually ~0.1).

In hydride superconductors, λ values of 2–3 are typical at optimal pressures, with 80–85% of the coupling arising from high-frequency hydrogen vibrational modes (Pickett, 25 Aug 2025). This is exemplified in CaH₆ (λ ≈ 2.69 at 150 GPa, Tc ≈ 220–235 K), where strong EPC is further boosted by dynamic Jahn–Teller instabilities—i.e., fluctuating symmetry-breaking lattice distortions that lift orbital degeneracies and enhance electron–phonon matrix elements (Wang et al., 2012).

Enhanced electron–phonon coupling is also observed in ternary clathrates such as CaLuH₁₂ (λ up to 5.18 at 120 GPa, Tc ≈ 294 K at 180 GPa), where hydrogenic cage phonons dominate the Eliashberg function and the band structure features multiple van Hove singularities (Fan et al., 1 Aug 2024). In perovskite hydrides, the X−H cubic framework provides the high-energy modes essential for elevated Tc (Du et al., 4 Jul 2024).

5. Synthesis Routes, Phase Persistence, and Experimental Validation

Synthesis of thermodynamically stable hydride superconductors primarily exploits high-pressure techniques such as laser heating in diamond anvil cells (DACs) with hydrogen-rich precursors (e.g., LaH₃ + NH₃BH₃ for LaH₁₀) (Minkov et al., 3 Jul 2025). Subsequent X-ray diffraction, Raman/FTIR vibrational spectroscopy, and four-probe resistance methods provide long-term structural and superconducting stability benchmarks. For Fm-3m–LaH₁₀, such measurements unambiguously show stability of both the superhydride and its high-Tc superconductivity over >5 years at formation pressure (Minkov et al., 3 Jul 2025).

Synthesis at moderate pressure is a major goal. Several recent studies identify ternary or double perovskite hydrides as stable below 10–50 GPa (e.g., KGaH₃, CsInH₃), supporting high-Tc with enhanced experimental feasibility (Du et al., 4 Jul 2024, Cataldo et al., 2021). Even at ambient pressure, candidates such as Mg₂XH₆ (X = Rh, Ir, Pd, Pt) have been predicted to be thermodynamically stable, with Tc between 45–100 K, enabled by meticulous high-throughput ML-accelerated screening (Sanna et al., 2023). Experimental realization at such low pressures would mark a paradigmatic shift for practical application.

Kinetic limitations and metastability are also relevant. For instance, Mg₂IrH₆ is predicted to be superconducting (Tc ~65–170 K) but is metastable at ambient pressure. However, bulk Mg₂IrH₅—an insulating, nearly isostructural vacancy phase—is robustly synthesized by conventional or high-pressure routes, and hydrogenation to Mg₂IrH₆ is feasible due to a low energetic barrier, opening a practical path to stabilization via non-equilibrium processing (Hansen et al., 13 Jun 2024).

6. Theoretical Approaches and Future Directions

Systematic computational workflows integrating crystal structure prediction (e.g., USPEX, AIRSS), convex hull construction, DFPT, and advanced ML (e.g., graph neural networks such as ALIGNN) now underpin most searches for thermodynamically stable hydride superconductors (Shipley et al., 2021, Wines et al., 2023, Sanna et al., 27 Aug 2025). Large databases (e.g., GNoME) and high-throughput screening accelerate the identification of stable phases, with subsequent first-principles calculations (Allen–Dynes/McMillan formula, Eliashberg theory) yielding detailed predictions of superconducting properties (Sanna et al., 27 Aug 2025).

A limit in ambient-pressure hydride superconductivity is that robust thermodynamic stability at zero pressure typically excludes phases with high Tc. Only double perovskite and fluorite-like hydrides with Tc ≲ 17 K have been found in a recent comprehensive search (Sanna et al., 27 Aug 2025), whereas the highest-Tc predicted at ambient pressure (e.g., Mg₂IrH₆, up to 160 K)—even though kinetically accessible—is only marginally metastable (Dolui et al., 2023, Hansen et al., 13 Jun 2024).

Current theoretical efforts are seeking more efficient and physically transparent computational strategies. The application of enatom formalism to decompose atomic displacement perturbations and the use of symmetry constraints can both accelerate the calculation of electron–phonon kernels and deepen understanding of the origins of high-Tc in hydrides, particularly clarifying the dominance of hydrogen vibrational contributions (Pickett, 25 Aug 2025). Human-guided intuition combined with vast chemical exploration is expected to refocus the search for materials combining genuine thermodynamic stability with higher critical temperatures, especially at low or ambient pressures (Pickett, 25 Aug 2025).

7. Summary Table: Selected Thermodynamically Stable Hydride Superconductors

Compound	Tc (K)	Pressure Range (GPa)	Structural Motif
Fm-3m–LaH₁₀	250	>150	Clathrate/sodalite
Im-3m–CaH₆	220–235	>150	Sodalite-like clathrate
Fm-3m–CeH₁₀	115	95	Cubic clathrate
LaMg₃H₂₈ (P6/mmm)	164	200	Ternary, high-coordination
LaBH₈	126	50	Sodalite-like
KGaH₃ (Pm-3m)	146	10	Perovskite hydride
CaLuH₁₂ (Pm-3m)	294	180	Sodalite-like clathrate
Li₂NaH₁₇ (Fd-3m)	340	300	Type-II clathrate
LiNa₃H₂₃ (Pm-3n)	310	350	Type-I clathrate
Mg₂IrH₆ †	65–170	0	Anti-perovskite (metastable)
LiZrH₆Ru	17	0	Double perovskite

†Mg₂IrH₆ is experimentally accessible via hydrogen insertion into the stable Mg₂IrH₅ lattice (Hansen et al., 13 Jun 2024), though it remains technically metastable at ambient pressure (Dolui et al., 2023).

• (Wang et al., 2012) Superconductive "sodalite"-like clathrate calcium hydride at high pressures
• (Lumley et al., 2014) The thermodynamics of hydride precipitation: the importance of entropy, enthalpy and disorder
• (Chen et al., 2021) High-Temperature Superconductivity in Cerium Superhydrides
• (Shipley et al., 2021) High-throughput discovery of high-temperature conventional superconductors
• (Cataldo et al., 2021) LaBH$_{8}$: the first high-T$_{c}$ low-pressure superhydride
• (An et al., 2023) Thermodynamically stable room-temperature superconductors in Li-Na hydrides under high pressures
• (Shutov et al., 2023) Ternary superconducting hydrides in the La-Mg-H system
• (Sanna et al., 2023) Prediction of Ambient Pressure Conventional Superconductivity above 80K in Thermodynamically Stable Hydride Compounds
• (Dolui et al., 2023) Feasible route to high-temperature ambient-pressure hydride superconductivity
• (Hansen et al., 13 Jun 2024) Synthesis of Mg$_2$IrH$_5$: A potential pathway to high-$T_c$ hydride superconductivity at ambient pressure
• (Du et al., 4 Jul 2024) High-temperature Superconductivity in Perovskite Hydride below 10 GPa
• (Fan et al., 1 Aug 2024) Superconductive Sodalite-like Clathrate Hydrides MXH$_{12}$ with Critical Temperatures of near 300 K under Pressures
• (Minkov et al., 3 Jul 2025) Long-Term Stability of Superconducting Metal Superhydrides
• (Pickett, 25 Aug 2025) Why Compressed Metal Hydrides are Near-room-temperature Superconductors
• (Sanna et al., 27 Aug 2025) Search for thermodynamically stable ambient-pressure superconducting hydrides in GNoME database