Erratum: High-temperature superconductivity in atomic metallic hydrogen [Phys. Rev. B 84 , 144515 (2011)]

Abstract

PACS number(s): 74.20.Pq, 74.10.+v, 74.62.Fj, 74.20.Fg, 99.10.Cd In Ref. 1, herein referred to as I, labels designating the crystal structures under consideration were omitted from some figures, which could be a source of confusion. Moreover, superconducting parameters necessary to estimate critical tem-peratures, T c , were calculated using the nonweighted phonon density of states, F (ω), rather than the proper normalized weighting function of the Eliashberg theory, 2 g(ω). In this Erratum, we first review the theoretical background for calculating the parameters needed to estimate T c , in particular their evaluation using g(ω). We then present and discuss results analogous to Figs. 4, 5, and 13 of I with revised calculations and including crystal-structure labels. Finally, we provide a brief summary of the differences between calculations. In order to evaluate the McMillan formula 2,3 or the Allen-Dynes equation 4 to estimate T c , Eqs. (2) and (3) of I, respectively, we must determine λ, ω, ¯ ω 2 , ω ln , and μ * ; these correspond to the attractive electron-phonon-induced interaction, the first and square root of the second moments of g(ω), the logarithmic average phonon frequency [i.e., ln(ω ln) = =ln ω], and the renormalized Coulomb repulsion, respectively. As in I, below we take the approximate, yet reasonable, 5 value of 0.089 for μ * . Further, λ is a direct measure of the strength of the electron-phonon spectral function α 2 F (ω), which is readily calculable via ab initio calculations, 6 λ = 2 ∞ 0 dω α 2 F (ω) /ω. (1) ω, ¯ ω 2 , and ω ln can also be calculated directly from α 2 F (ω), ω = ∞ 0 dω g(ω) ω, (2) ¯ ω 2 = ∞ 0 dω g(ω) ω 2 1/2 , (3) ω ln = exp ∞ 0 dω g(ω) ln (ω) , (4) where g(ω) = 2 λω α 2 F (ω) . (5) The difference between Eqs. (2)–(4) and those presented and used in I is via the use of g(ω) in place of F (ω), which results in weighted averages. λ, ω, and ω ln calculated using Eqs. (1), (2), and (4), as well the corresponding estimates of T c calculated using Eqs. (2) and (3) of I, are presented and discussed below. λ. The use of g(ω) in Eqs. (2)–(4) does not affect the calculation of λ. Nonetheless, in Fig. 1, we show again λ values for both the I 4 1 /amd and R-3m structures 7 considered in I, but we now include crystal-structure labels. Note that values for R-3m are not shown between ∼1 and 2 TPa (as in I), because of complications in applying Eqs. (2)–(4) in the presence of (unphysical) imaginary phonon frequencies (see below). ω and ω ln . Temperature prefactors ω/k B and ω ln /k B , where k B is Boltzmann's constant, calculated using Eqs. (2)– (4), including crystal-structure labels, are shown in Fig. 2.