Fig. 1. (a) Crystal structure of Im-3m H₃S.⁴⁴ (b) Band structure of Im-3m H₃S.⁶⁴ (c) Main pocket of the Fermi surface of H₃S.⁶⁴ (d) Phonon dispersion curves and Eliashberg spectral function.⁴⁴ (e) and (f) Integrated XRD patterns obtained by subtraction of the background for sulfur hydride and sulfur deuteride, respectively.⁶⁶ (g) Pressure dependence of T_C of sulfur hydride (black points) and sulfur deuteride (red points).⁶⁶ (h) DOS and λ vs substitution concentration.⁶⁷ (i) Linear relationship between λ and DOS.⁶⁷ (j) T_C of H₃S_0.925P_0.075 (red solid line) and H₃S_0.9P_0.1 (black dashed line) vs pressure.⁶⁷ (k) DOS of H₃S at 220 GPa (black), H₃S_0.960C_0.040 at 220 GPa (solid red), and H₃S_0.960C_0.040 at 240 GPa (dashed red), with their Fermi energies set to be zero.⁴³ (l) T_C (shaded) vs pressure at x = 0.040.⁴³ (m) Temperature-dependent electrical resistance of the C–S–H system at high pressure.²² (a) and (d) Reprinted with permission from Duan et al., Sci. Rep. 4, 6968 (2014). Copyright 2014 Nature Publishing Group. (b) and (c) Reprinted with permission from Bernstein et al., Phys. Rev. B 91, 060511 (2015). Copyright 2015 American Physical Society. (e)–(g) Reprinted with permission from Einaga et al., Nat. Phys. 12, 835 (2016). Copyright 2016 Nature Publishing Group. (h)–(j) Reprinted with permission from Ge et al., Phys. Rev. B 93, 224513 (2016). Copyright 2016 American Physical Society. (k) and (l) Reprinted with permission from Ge et al., Mater. Today Phys. 15, 100330 (2020). Copyright 2020 Elsevier. (m) Reprinted with permission from Snider et al., Nature 586, 373 (2020). Copyright 2020 Nature Publishing Group.

Fig. 2. (a) Structure of LaH₁₀.⁶⁵ (b) Total charge density ρ_tot of LaH₁₀.⁶⁵ (c) Partial DOS of LaH₁₀.⁶⁵ (d) Band structure of LaH₁₀.⁶⁵ (e) Observed superconductivity in LaH₁₀.⁴⁷ (f) Summary of experimental and theoretical T_C values in LaH₁₀.⁶² (g) Structure of YH₉.⁵⁰ (h) Phonon spectra and Eliashberg spectral function for YH₉.⁴⁶ (i) Temperature-dependent electrical resistance of yttrium superhydride at high pressures.⁵⁰ (a)–(d) Reprinted with permission from Liu et al., Phys. Rev. B 99, 140501 (2019). Copyright 2019 American Physical Society. (e) Reprinted with permission from Drozdov et al., Nature 569, 528 (2019). Copyright 2019 Nature Publishing Group. (f) Reprinted with permission from Errea et al., Nature 578, 66 (2020). Copyright 2020 Nature Publishing Group. (g) and (i) Reprinted with permission from Snider et al., Phys. Rev. Lett. 126, 117003 (2021). Copyright 2021 American Physical Society. (h) Reprinted with permission from Peng et al., Phys. Rev. Lett. 119, 107001 (2017). Copyright 2017 American Physical Society.

Fig. 3. (a) Structure of CaH₆.⁷⁵ (b) Phonon dispersion relation and Eliashberg spectral function.⁷⁵ (c) Synchrotron XRD pattern of superconducting calcium hydrides.⁷⁴ (d) Superconducting measurements in the calcium hydride CaH_x.⁷⁴ (e) XRD patterns and Le Bail refinements of Im-3m YH₆ and I4/mmm YH4.⁹¹ (f) Temperature dependence of electrical resistance in YH₆ and YD₆.⁹¹ (g) Structure of Li₂MgH₁₆.²¹ (h) Phonon dispersion relations, projected phonon densities of states (PHDOS), and Eliashberg spectral function.²¹ (i) Structure of AcH₁₀.⁹⁴ (j) Structure of AcH₁₆.⁹⁴ (k) T_C(P) functions.⁹⁴ (a) and (b) Reprinted with permission from Wang et al., Proc. Natl. Acad. Sci. U. S. A. 109, 6463 (2012). Copyright 2012 Proceedings of the National Academy of Sciences of the United States of America. (c) and (d) Reprinted with permission from Ma et al., arXiv:2103.16282v2 (2021). (e) and (f) Reprinted with permission from Troyan et al., Adv. Mater. 33, 2006832 (2021). Copyright (2021) Wiley-VCH. (g) and (h) Reprinted with permission from Sun et al., Phys. Rev. Lett. 123, 097001 (2019). Copyright (2019) American Physical Society. (i)–(k) Reprinted with permission from Semenok et al., J. Phys. Chem. Lett. 9, 1920 (2018). Copyright (2018) American Chemical Society.

Fig. 4. (a) Cmca structure of molecular hydrogen at 300 GPa.⁹⁵ (b) Structure of SrH₁₀.⁹⁵ (c) δT_C/δα²F(ω) (red solid curve) and α²F(ω) (green dashed curve) as functions of frequency ω for SrH₁₀ at 300 GPa.⁹⁵ (d) Structure of HfH₁₀ and electron localization function on the (001) plane.⁹⁶ (e) Projected electronic DOS of HfH₁₀ and ZrH₁₀ and total electronic DOS of H₃S, LaH₁₀, HfH₁₀, and ZrH₁₀.⁹⁶ (f) Superconducting parameters for YH₁₀, LaH₁₀, HfH₁₀, and ZrH₁₀.⁹⁶ (a)–(c) Reprinted with permission from Tanaka et al., Phys. Rev. B 96, 100502 (2017). Copyright 2017 American Physical Society. (d)–(f) Reprinted with permission from Xie et al., Phys. Rev. Lett. 125, 217001 (2020). Copyright (2020) American Physical Society.