High-Temperature Superconductivity in Atomic Metallic Hydrogen

📝 Abstract

Superconductivity in the recently proposed ground-state structures of atomic metallic hydrogen is investigated over the pressure range 500 GPa to 3.5 TPa. Near molecular dissociation, the electron–phonon coupling $\lambda$ and renormalized Coulomb repulsion are similar to the molecular phase. A continuous increase in the critical temperature $T_c$ with pressure is therefore expected, to $\jmmapprox 356 $K near 500 GPa. As the atomic phase stabilizes with increasing pressure, $\lambda$ increases, causing $T_c$ to approach $\jmmapprox 481 $K near 700 GPa. At the first atomic–atomic structural phase transformation ( $\jmmapprox 1$ – 1.5 TPa), a discontinuous jump in $\lambda$ occurs, causing a significant increase in $T_c$ of up to 764K.

💡 Analysis

Superconductivity in the recently proposed ground-state structures of atomic metallic hydrogen is investigated over the pressure range 500 GPa to 3.5 TPa. Near molecular dissociation, the electron–phonon coupling $\lambda$ and renormalized Coulomb repulsion are similar to the molecular phase. A continuous increase in the critical temperature $T_c$ with pressure is therefore expected, to $\jmmapprox 356 $K near 500 GPa. As the atomic phase stabilizes with increasing pressure, $\lambda$ increases, causing $T_c$ to approach $\jmmapprox 481 $K near 700 GPa. At the first atomic–atomic structural phase transformation ( $\jmmapprox 1$ – 1.5 TPa), a discontinuous jump in $\lambda$ occurs, causing a significant increase in $T_c$ of up to 764K.

📄 Content

High-Temperature Superconductivity in Atomic Metallic Hydrogen Jeffrey M. McMahon1, ∗and David M. Ceperley1, 2, † 1Department of Physics, University of Illinois at Urbana-Champaign, Illinois 61801, USA 2NCSA, University of Illinois at Urbana-Champaign, Illinois 61801, USA (Dated: October 29, 2018) Abstract Superconductivity in the recently proposed ground-state structures of atomic metallic hydrogen is investigated over the pressure range 500 GPa to 3.5 TPa. Near molecular dissociation, the electron–phonon coupling λ and renormalized Coulomb repulsion are similar to the molecular phase. A continuous increase in the critical temperature Tc with pressure is therefore expected, to ∼356K near 500 GPa. As the atomic phase stabilizes with increasing pressure, λ increases, causing Tc to approach ∼481K near 700 GPa. At the first atomic–atomic structural phase transformation (∼1 – 1.5 TPa), a discontinuous jump in λ occurs, causing a significant increase in Tc of up to 764K. PACS numbers: 74.20.Pq, 74.10.+v, 74.62.Fj, 74.20.Fg 1 arXiv:1106.5526v1 [cond-mat.supr-con] 27 Jun 2011 I. INTRODUCTION At relatively low pressure, hydrogen exists in an insulating molecular phase. In 1935, Wigner and Huntington predicted that sufficient pressure would cause both a molecular-to- atomic transition and metallization1. Recent ab initio calculations support these predictions, and have revealed the precise details associated with both effects. Calculations based on ab initio random structure searching by Pickard and Needs2 as well as McMahon and Ceperley3 suggest that the molecular-to-atomic transition occurs near 500 GPa, the latter study also revealing a profusion of structures that atomic hydrogen adopts; and exact-exchange calcu- lations based on density-functional theory (DFT) by St¨adele and Martin4 suggest a metal- lization pressure of at least 400 GPa. In 1968, Ashcroft predicted an even further transition in high-pressure hydrogen, a metallic-to-superconducting one5. Within the framework of Bardeen–Cooper–Schrieffer (BCS) theory6, three key arguments support this prediction: (i) the ions in the system are single protons, and their small masses cause the vibrational en- ergy scale of the phonons to be remarkably high (e.g., kB⟨ω⟩≈2300K near 500 GPa – see below), as is thus the prefactor in the expression for the critical temperature Tc; (ii) since the electron–ion interaction is due to the bare Coulomb attraction, the electron–phonon coupling should be strong; and (iii) at the high pressures at and above metallization, the electronic density of states N(0) at the Fermi surface should be large and the Coulomb repulsion between electrons should be low, typical features of high-density systems. These arguments will be revisited, and demonstrated to indeed be the case, below. Ever since the prediction of high-Tc superconductivity in hydrogen5, a large number of efforts have focused on determining the precise value(s) of Tc7–22. In the molecular phase, the high-pressure metallic Cmca structure (which transitions to the atomic phase2,3) has recently been studied in-depth20–22, and shown to have a Tc that increases up to 242K near 450 GPa. In the atomic phase, estimations of Tc have varied widely, but in general suggest a large increase with pressure7–19. Early estimates suggested that Tc ≈135 – 170K near 400 GPa (although, it is now believed that this is inside the molecular phase2,3, as discussed above)14; near 480 – 802 GPa, more recent estimations suggest that Tc ≈282 – 291K18; and near 2 TPa, calculations suggest that Tc can reach ∼600 – 631K in the face-centered cubic (fcc) lattice16,17. The latter two studies will be discussed further below. However, previous studies of superconductivity in the atomic phase have simply assumed 2 FIG. 1: (color online). Ground-state structures of atomic metallic hydrogen. (left) Conventional unit-cell of I41/amd at 700 GPa. (right) 2×2×1 supercell of R-3m at 2 TPa. a and c parameters are shown in the figure, as discussed in the text. Fictitious bonds have been drawn for clarity. candidate ground-state structures, in a number of cases the fcc lattice8–10,12,16,17. Recently though, McMahon and Ceperley demonstrated that such structures are incorrect, and pro- vided a comprehensive picture of the (presumably correct) ground-state structures from 500 GPa to 5 TPa3. Molecular hydrogen was shown to dissociate near 500 GPa, consistent with the predictions of Pickard and Needs2. With increasing pressure, atomic hydrogen passes through two ground-state structural phases before transforming to a close-packed lattice, such as fcc or possibly the hexagonal close-packed (hcp) lattice. The first is a body-centered tetragonal structure with space-group I41/amd (Hermann–Mauguin space-group symbol, international notation) with a c/a ratio greater than unity, as shown in Fig. 1. Including es- timates of proton zero-point energies (ZPEs), I41/amd was demonstrated to transform into a layered structure with space-group R

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