Hydrogen-Induced High-Temperature Superconductivity in Two-Dimensional Materials: The Example of Hydrogenated Monolayer ${\mathrm{MgB}}_2$

Hydrogen-based compounds under ultrahigh pressure, such as the polyhydrides ${\mathrm{H}}_3\mathrm{S}$ and ${\mathrm{LaH}}_{10}$, superconduct through the conventional electron-phonon coupling mechanism to attain the record critical temperatures known to date. Here we exploit the intrinsic advantages of hydrogen to strongly enhance phonon-mediated superconductivity in a completely different system, namely, a two-dimensional material with hydrogen adatoms. We find that van Hove singularities in the electronic structure, originating from atomiclike hydrogen states, lead to a strong increase of the electronic density of states at the Fermi level, and thus of the electron-phonon coupling. Additionally, the emergence of high-frequency hydrogen-related phonon modes in this system boosts the electron-phonon coupling further. As a concrete example, we demonstrate the effect of hydrogen adatoms on the superconducting properties of monolayer ${\mathrm{MgB}}_2$, by solving the fully anisotropic Eliashberg equations, in conjunction with a first-principles description of the electronic and vibrational states, and their coupling. 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.

Figure 1

Structural and electronic properties of H-$\mathrm{Mg}{\mathrm{B}}_2$. (a) Top view of the crystal structure. (b) The electronic band structure and density of states (DOS). The $\sigma$ and $\pi$-$\mathrm{H}s$ bands crossing $E_F$ are also indicated. (c) The norm of the wave function of the $\pi$-$\mathrm{H}s$ state at $E_F$ obtained along the path $\mathrm{\Gamma }\text{−}K$.

Figure 2

Phonons and electron-phonon interaction in H-${\mathrm{MgB}}_2$. (a) Phonon band structure (where both the colors and the dot sizes indicate the strength of the $e\text{−}\mathrm{ph}$ coupling $\lambda$), phonon density of states (PHDOS, including the atom-resolved contributions), and isotropic Eliashberg function ${\alpha }^{2}F$ (plus the $e\text{−}\mathrm{ph}$ coupling constant $\lambda$). (b) Phonon modes with the strongest $e\text{−}\mathrm{ph}$ coupling, labeled as indicated in (a).

Figure 3

Superconducting properties of H-${\mathrm{MgB}}_2$, calculated with fully anisotropic Eliashberg theory. (a) The superconducting gap spectrum on the Fermi surface, calculated at 1 K, and the corresponding distribution $\rho (\mathrm{\Delta })$ with the color code. (b) The evolution of $\rho (\mathrm{\Delta })$ with temperature, yielding $T_c=67\mathrm{K}$.

Figure 4

Superconducting properties of H-${\mathrm{MgB}}_2$ under the influence of strain. (a) Isotropic Eliashberg function ${\alpha }^{2}F$ and electron-phonon coupling constant $\lambda$ for applied 5% tensile strain. The data for the nonstrained case are shown by the gray shadow for comparison. (b) The superconducting gap spectrum on the Fermi surface, from fully anisotropic calculations for applied 5% tensile strain, and the corresponding color-coded $\rho (\mathrm{\Delta })$. (c) The evolution of $\rho (\mathrm{\Delta })$ with temperature for 5% tensile strain, yielding $T_c=103\mathrm{K}$. The inset shows $T_c$ as a function of strain.