Hydrogen-based compounds under ultra-high pressure, such as the polyhydrides H3S and LaH10, superconduct through the conventional electron-phonon coupling mechanism to attain the record critical temperatures known to date. We demonstrate here that the intrinsic advantages of hydrogen for phonon-mediated superconductivity can be exploited in a completely different system, namely two-dimensional (2D) materials. We find that hydrogen adatoms can strongly enhance superconductivity in 2D materials due to flatband states originating from atomic-like hydrogen orbitals, with a resulting high density of states, and due to the emergence of high-frequency hydrogen-related phonon modes that boost the electron-phonon coupling. As a concrete example, we investigate the effect of hydrogen adatoms on the superconducting properties of monolayer MgB2, by solving the fully anisotropic Eliashberg equations, in conjunction with a first-principles description of the electronic and vibrational states, and the coupling between them. We show that hydrogenation leads to a high critical temperature of 67 K, which can be boosted to over 100 K by biaxial tensile strain.In seminal work of 1968 Ashcroft showed that dense metallic hydrogen, if ever produced, could be a hightemperature superconductor [1]. The main reason would be its very high Debye temperature, as a result of its minimal mass, enabling very strong phonon-mediated superconducting pairing according to the Bardeen-Cooper-Schrieffer (BCS) theory.Subsequent detailed firstprinciples studies yielded critical temperature (T c ) values up to 242 K, along with descriptions of the multiband nature of superconductivity [2], and the role of phonon anharmonicities [3]. However, as creating metallic hydrogen requires immense pressures of ∼400 GPa [4, 5], a confirmation of high-T c superconductivity in pure hydrogen systems is still pending [6].Instead, in search of hydrogen-induced hightemperature superconductivity, most researchers have turned to polyhydrides, compounds with a large hydrogen content, but also containing at least one other chemical element. The latter enables stabilizing the structure under lower applied pressure compared to metallic hydrogen itself. Notably, the chalcogen hydrides display experimentally proven high-T c superconductivity, e.g., T c = 203 K in H 3 S, supplemented by comparable theoretical predictions for H-Te compounds [7]. The record T c 's among all currently known superconductors are held by the rare-earth hydrides, notably LaH 10 , with T c of 250 − 260 K [8,9], and there is also a theoretical prediction of an even higher T c = 303 K in YH 10 [10].In this work we demonstrate a different approach to establish high-T c superconductivity based on hydrogen, namely by adding hydrogen adatoms to two-dimensional (2D) superconductors [11][12][13], exploiting the changes in the electronic and vibrational properties that hydrogen induces. Such 2D superconductivity has been realized in recent years in very diverse ultrathin materials, ranging from atomically-thin ele...

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Among the large variety of two-dimensional (2D) materials discovered to date, elemental monolayers that host superconductivity are very rare. Using ab initio calculations we show that recently synthesized gallium monolayers, coined gallenene, are intrinsically superconducting through electron-phonon coupling. We reveal that Ga-100 gallenene, a planar monolayer isostructural with graphene, is the structurally simplest 2D superconductor to date, furthermore hosting topological edge states due to its honeycomb structure. Our anisotropic Eliashberg calculations show distinctly three-gap superconductivity in Ga-100, in contrast to the alternative buckled Ga-010 gallenene which presents a single anisotropic superconducting gap. Strikingly, the critical temperature (Tc) of gallenene is in the range of 7 − 10 K, exceeding the Tc of bulk gallium from which it is exfoliated. Finally we explore chemical functionalization of gallenene with hydrogen, and report induced multigap superconductivity with an enhanced Tc in the resulting gallenane compound.

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