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 density approximation (LDA) to the density functional theory. At high electronic densities, it is well described by a bare proton ${\mathrm{H}}^{+}$ 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 ${\mathrm{H}}^{-}$ protected from surrounding metallic electrons by the Pauli exclusion principle. However, no details are known about the transition from ${\mathrm{H}}^{+}$ to ${\mathrm{H}}^{-}$ in the intermediate-density region. Here, by accurately determining the ground-state electron distribution $n\left(\mathit{r}\right)$ by the use of LDA and diffusion Monte Carlo simulations with the total electron number up to 170, we obtain a complete picture of the transition, in particular, a sharp transition from short-range ${\mathrm{H}}^{+}$ screening charge resonance to long-range Kondo-type spin-singlet resonance, the emergence of which is confirmed by the presence of an anomalous Friedel oscillation characteristic to the Kondo singlet state with the Kondo temperature $T_{\mathrm{K}}$ well beyond 1000 K. 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 $\text{high-}{T}_{\mathrm{K}}$ system long sought in relation to the development of exotic superconductivity in the quantum critical regime.

• Received 31 October 2014
• Revised 9 July 2015

DOI:https://doi.org/10.1103/PhysRevB.92.155140