Quantum structural fluxion in superconducting lanthanum polyhydride

Abstract

The discovery of 250-kelvin superconducting lanthanum polyhydride under high pressure marked a significant advance toward the realization of a room-temperature superconductor. X-ray diffraction (XRD) studies reveal a nonstoichiometric LaH_9.6 or LaH_10±δ polyhydride responsible for the superconductivity, which in the literature is commonly treated as LaH₁₀ without accounting for stoichiometric defects. Here, we discover significant nuclear quantum effects (NQE) in this polyhydride, and demonstrate that a minor amount of stoichiometric defects will cause quantum proton diffusion in the otherwise rigid lanthanum lattice in the ground state. The diffusion coefficient reaches ~10^-7 cm²/s in LaH_9.63 at 150 gigapascals and 240 kelvin, approaching the upper bound value of interstitial hydrides at comparable temperatures. A puzzling phenomenon observed in previous experiments, the positive pressure dependence of the superconducting critical temperature T_c below 150 gigapascals, is explained by a modulation of the electronic structure due to a premature distortion of the hydrogen lattice in this quantum fluxional structure upon decompression, and resulting changes of the electron-phonon coupling. This finding suggests the coexistence of the quantum proton fluxion and hydrogen-induced superconductivity in this lanthanum polyhydride, and leads to an understanding of the structural nature and superconductivity of nonstoichiomectric hydrogen-rich materials.

Fig. 1. Vacancy formation enthalpy and pressure-volume relation.

a The formation enthalpy (H_f) of a single vacancy in fcc-LaH₁₀ at two inequivalent lattice sites in the clathrate hydrogen framework, V_T and V_C, and their configurational average calculated at different pressures using 2 × 2 × 2 extension of conventional unit cell of fcc-LaH₁₀. The locations of V_T and V_C are illustrated in a conventional unit cell of the fcc-LaH₁₀ structure by red and black balls, respectively. b The experimental pressure-volume relations of fcc-LaH_9.6 and fcc-LaD₁₀ measured by Drozdov et al. compared to the theoretical values of fcc-LaH₁₀, fcc-LaH₉ and fcc-LaD₁₀ derived from quantum simulations at constant pressure and temperature of 300 K. The volumes selected for subsequent quantum simulation (V_CMD) for fcc-LaH_9.63 are thereby linked to the ‘quantum’ pressure. Formula unit is abbreviated as f.u.

Fig. 2. Structural fluxion in LaH_9.63 at 150 GPa.

a The proton MSD derived from centroid trajectories of the CMD simulations and those of MD simulations. b The [100] view of the quantum nuclear density distribution at 60 K extracted from a CMD simulation, with full consideration of the 16 beads. Neighboring protons are illustrated in different colors. c the [100] view of the classical nuclear density distribution in 16 MD simulation runs of 4 ps distinguished by various proton colors. The 16 runs were initialized from different centroid configurations of the 4-picosecond CMD trajectory with a sampling interval of 0.25 ps.

Fig. 3. Pressure effects on the diffusivity and structural distortions.

a The proton diffusion coefficient D derived from the MSD in CMD simulations (run1) of 4 ps, and from the average MSD of four MD simulations of 24 ps. The D in three additional CMD simulations of 4 ps at 150 GPa are also shown. These are two simulations at 120 K and 60 K, and a simulation using higher total-energy convergence criteria (run2). The MSD in the CMD simulations is derived from the centroid trajectories. The measured D in Cu₂H and FeH, and calculated D in phase IV hydrogen are shown for comparison. b The configurational distance ξ (with error bar indicating the standard deviation) of QFS from the crystal lattices of static fcc and C2m phases, and a triclinic P1 structure for H and La substructure. The P1 structure is built by scaling the lattice parameter a of a QFS sampled from the CMD simulation of LaH_9.63 at 176 GPa.

Fig. 4. Pressure effects on electronic properties and superconductivity.

a The pressure trend of the averaged electronic density of states at the Fermi level $N\left({ϵ}_F\right)$ in quantum fluxional LaH_9.63 (with distributions and standard deviation of statics shown in Supplementary Fig. 5), and the pressure trend of $N\left({ϵ}_F\right)$ in static P1-LaH_9.63, fcc-LaH₁₀, and C2/m-LaH₁₀. The $N\left({ϵ}_F\right)$ of LaH_9.63 in fcc and C2/m phase estimated using the rigid-band approximation are also shown for comparison. b The pressure trend of T_c in quantum fluxional LaH_9.63 calculated based on various Gaussian smearings (σ) of the phonon spectrum $F\left(\omega \right)$, together with the values measured for LaH_9.6 by Drozdov et al. and those derived from AD, Migdal–Eliashberg equations (ME), and superconducting DFT (SCDFT) for fcc-LaH₁₀ by Errea et al.. Fitted lines are shown to guide the sight.