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A superconductor to superfluid phase transition in liquid metallic hydrogen


Although hydrogen is the simplest of atoms, it does not form the simplest of solids or liquids. Quantum effects in these phases are considerable (a consequence of the light proton mass) and they have a demonstrable and often puzzling influence on many physical properties1, including spatial order. To date, the structure of dense hydrogen remains experimentally elusive2. Recent studies of the melting curve of hydrogen3,4 indicate that at high (but experimentally accessible) pressures, compressed hydrogen will adopt a liquid state, even at low temperatures. In reaching this phase, hydrogen is also projected to pass through an insulator-to-metal transition. This raises the possibility of new state of matter: a near ground-state liquid metal, and its ordered states in the quantum domain. Ordered quantum fluids are traditionally categorized as superconductors or superfluids; these respective systems feature dissipationless electrical currents or mass flow. Here we report a topological analysis of the projected phase of liquid metallic hydrogen, finding that it may represent a new type of ordered quantum fluid. Specifically, we show that liquid metallic hydrogen cannot be categorized exclusively as a superconductor or superfluid. We predict that, in the presence of a magnetic field, liquid metallic hydrogen will exhibit several phase transitions to ordered states, ranging from superconductors to superfluids.

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Figure 1: Local splitting of a composite vortex line in liquid metallic hydrogen, LMH.
Figure 2: A schematic phase diagram of LMH as a function of applied magnetic field B and temperature T.

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  1. Hemley, R. J. & Mao, H.-K. Dense molecular hydrogen; order, disorder and localization. J. Non.-Cryst. Solids 205, 282–289 (1996)

    Article  ADS  Google Scholar 

  2. Ashcroft, N. W. The hydrogen liquids. J. Phys. A 12, A129–A137 (2000)

    CAS  Google Scholar 

  3. Datchi, F., Loubeyre, P. & LeToullec, R. Extended and accurate determination of the melting curves of argon, helium, ice (H2O), and hydrogen (H2). Phys. Rev. B 61, 6535–6546 (2000)

    Article  ADS  CAS  Google Scholar 

  4. Bonev, S. A., Schwegler, E., Ogitsu, T. & Galli, G. A quantum fluid of metallic hydrogen. Nature (submitted)

  5. Guillot, T. Probing the giant planets. Phys. Today 57, 63–69 (2004)

    Article  CAS  Google Scholar 

  6. Stevenson, D. J., Ashcroft, N. W. Phys. Rev. A 9, 782–789 (1974)

    Article  ADS  CAS  Google Scholar 

  7. Ashcroft, N. W. Hydrogen dominant metallic alloys: High temperature superconductors? Phys. Rev. Lett. 92, 187002 (2004)

    Article  ADS  CAS  Google Scholar 

  8. Moulopolos, K. & Ashcroft, N. W. Generalized Coulomb pairing in condensed state. Phys. Rev. Lett. 66, 2915–2918 (1991)

    Article  ADS  Google Scholar 

  9. Babaev, E., Faddeev, L. D. & Niemi, A. J. Hidden symmetry and duality in a charged two-condensate Bose system. Phys. Rev. B 65, 100512 (2002)

    Article  ADS  Google Scholar 

  10. Babaev, E. Vortices with fractional flux in two-gap superconductors and in extended Faddeev model. Phys. Rev. Lett. 89, 067001 (2002)

    Article  ADS  Google Scholar 

  11. Jaffe, J. & Ashcroft, N. W. Superconductivity in liquid metallic hydrogen. Phys. Rev. B 23, 6176–6179 (1981)

    Article  ADS  CAS  Google Scholar 

  12. Jaffe, J. & Ashcroft, N. W. Critical fields of liquid superconducting metallic hydrogen. Phys. Rev. B 27, 5852–5855 (1983)

    Article  ADS  CAS  Google Scholar 

  13. Fossheim, K. & Sudbø, A. Superconductivity: Physics and Applications Ch. 8 (Wiley & Sons, New York, 2004)

    Book  Google Scholar 

  14. Smiseth, J., Smørgrav, E. & Sudbø, A. Critical properties of the N-color London model. Phys. Rev. Lett. 93, 077002 (2004)

    Article  ADS  CAS  Google Scholar 

  15. Penrose, O. & Onsager, L. Bose-Einstein condensation and liquid helium. Phys. Rev. 104, 576–584 (1956)

    Article  ADS  CAS  Google Scholar 

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This work was supported by the National Science Foundation, the Research Council of Norway, NANOMAT and by STINT and the Swedish Research Council.

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Correspondence to Egor Babaev.

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Babaev, E., Sudbø, A. & Ashcroft, N. A superconductor to superfluid phase transition in liquid metallic hydrogen. Nature 431, 666–668 (2004).

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