Hydrogen in metals has attracted much attention for a long time from both basic scientific and technological points of view. Its electronic state has been investigated in terms of a proton embedded in the electron gas mostly by the local spin density approximation (LSDA) to the density functional theory (DFT). At high electronic densities, it is well described by a bare proton H⁺ screened by metallic electrons (charge resonance), while at low densities two electrons are localized at the proton site to form a closed-shell negative ion H^– protected from surrounding metallic electrons by the Pauli exclusion principle. However, no details are known about the transition from H⁺ to H^– in the intermediate-density region.
In my talk, by accurately determining the ground-state electron density n(r) by diffusion Monte Carlo (DMC) simulations with the total electron number N up to 170 combined with LSDA up to N→∞, I will give a complete picture of the transition, in particular, a sharp transition from H⁺ screening charge resonance with a short screening length to Kondo-like spin-singlet resonance with a very long screening length. The emergence of the Kondo singlet state is confirmed by the presence of an anomalous (oscillation-period shortened) Friedel oscillation characteristic to the Kondo singlet state with quantitatively determining its Kondo temperature T_K, which is well beyond 1,000K for the electronic density parameter r_s in the region of 3-8.
This study not only reveals interesting competition between charge and spin resonances, enriching the century-old paradigm of metallic screening to a point charge, but also discovers a long-sought novel high-T_K system. Note that according to heavy-fermion physics, superconductivity occurs in a Kondo lattice near quantum critical point at a temperature as high as 0.1T_K. Thus, if a macroscopic number of protons are embedded into a metal (like in the metal hydrides) and those hydrogens are so synthesized as to be arranged in the form of a periodic Kondo lattice with the host metal in this intermediate-density region, we may expect the occurrence of superconductivity at T_c near 0.1T_K (which is of the order of the room temperature) at the ambient pressure, contrary to the case of solid hydrogen or sulfur hydrides under very high pressures in which r_s is about 1.4.

Reference: YT, R. Maezono, and K. Yoshizawa, arXiv1507.06432.