Metallic : A Superconductor? Craig M. Tenney, Zachary F. Croft, and Jeffrey M. McMahon∗ Department of Physics and Astronomy, Washington State University

Introduction Liquid Structure

Background In an ordinary liquid, atoms do not show any form of long-range order. The prior features result in high- superconductivity:

1 380 In 1935, Wigner and Huntington predicted that high would 500 K Qualitatively, this is seen in liquid metallic hydrogen: 370 1000 K dissociate molecular hydrogen into an atomic, metallic . 360

350 (K)

2 c 340 Theoretical arguments suggest that () metallic hydrogen should T be a high-temperature superconductor: 330 320

310 • The ions in the system are protons; their small mass should 300 400 500 600 700 800 900 (GPa) cause the vibrational energy scale of the to be high. Figure: Superconducting critical Tc. • The electron–ion interaction is due to the bare Coulomb at- Figure: Snapshots from dynamical simulations, at 550 GPa and 500 K. traction; the electron– coupling should thus be strong. 5 Quantitative measures, however, show anomalous local structure: Note: These temperatures are above those calculated for melting. • The electronic density of states at the Fermi surface should be 1.75 2.5

300 K 300 K large; and the Coulomb repulsion between electrons low. 500 K 500 K 700 K 700 K 1.40 900 K 2.0 900 K

3 1.05 1.5 ) ) r q ( Such arguments further suggest that metallic hydrogen may be super- ( g S conducting even in the liquid phase: 0.70 1.0 Concluding Remarks • The superconducting critical temperature (in the solid) is ex- 0.35 0.5 0.00 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 2 4 6 8 10 12 -1 pected to be greater than the melting temperature. r (Å) q (Å ) Summary • The phonon spectrum should be similar in both the solid and Figure: Structural measures, at 500 GPa. • Liquid metallic hydrogen is a high-temperature superconductor liquid phases. • ... (above the melting temperature5). • Disorder doesn’t inhibit superconductivity. Phonons Future work 4,5 Recent calculations support these arguments. • Determine and analyze the uncertainties in the calculations. Phonon spectra calculated from dynamical simulations are similar to Motivation those from (static) snapshots:

0.04

Determining whether liquid metallic hydrogen is a high-temperature dynamic 1 2 superconductor is important for several reasons: 0.03 3 Acknowledgments • 0.02 Fundamental physics: There is no known liquid supercon- / proton ω) F( ductor. Such would constitute a new . 0.01 • Planetary physics: Gas giants () are comprised pri- Startup support: 0 0 1000 2000 3000 4000 marily of liquid metallic hydrogen. ω (cm-1) • Applications: High- and room-temperature superconductors Figure: Phonon density of states F(ω). would have significant applications in energy, electronics, etc. Department of Physics and Astronomy Electron–Phonon Coupling

The bare Coulomb attraction results in large electron–phonon cou- Methods pling: 1.2 1 1.0 2 3 References General approach 0.8

ω) 0.6 F( 2 α 1. E. Wigner and H. B. Huntington, J. Chem. Phys. 3, 764 (1935) 1. Simulate liquid metallic hydrogen. 0.4 2. N. W. Ashcroft, Phys. Rev. Lett. 21, 1748 (1968) 2. Calculate phonons (spectrum). 0.2 0 3. J. E. Jaffe and N. W. Ashcroft, Phys. Rev. B 23, 6176 (1981) 0 1000 2000 3000 4000 3. Calculate electron–phonon coupling. ω (cm-1) 4. J. M. McMahon and D. M. Ceperley, Phys. Rev. B 84, 144515 (2011) 4. Calculate superconducting critical temperature. Figure: Electron–phonon spectral function α2F(ω). 5. J. M. McMahon et al., Submitted (2017)

https://labs.wsu.edu/mcmahon/ ∗[email protected]