# Multiple superionic states in helium–water compounds

## Abstract

Superionic states are phases of matter that can simultaneously exhibit some of the properties of a liquid and of a solid. For example, in superionic ice, hydrogen atoms can move freely while oxygen atoms are fixed in their sublattice. ‘Superionicity’ has attracted much attention in both fundamental science and applications. Helium is the most inert element in nature and it is generally considered to be unreactive. Here, we use ab initio calculations to show that He and H2O can form stable compounds within a large pressure range that can exist even close to ambient pressure. Surprisingly, we find that they can form two previously unknown types of superionic state under high pressure and high temperature. In the first of these phases, the helium atoms exhibit liquid behaviour within a fixed ice-lattice framework. In the second phase, both helium and hydrogen atoms move in a liquid-like fashion within a fixed oxygen sublattice. As the He–O interaction is weaker than the H–O interaction, the helium atoms in these superionic states have larger diffusion coefficients and lower ‘melting’ temperatures than those of hydrogen, although helium is heavier than hydrogen. The insertion of helium atoms substantially decreases the pressure at which superionic states may be formed, compared to those in pure ice.

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## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

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## Acknowledgements

J.S. gratefully acknowledges financial support from the MOST of China (grant nos. 2016YFA0300404 and 2015CB921202), the National Natural Science Foundation of China (grant nos. 11574133 and 11834006), the NSF of Jiangsu Province (grant no. BK20150012), the Science Challenge Project (no. TZ2016001), and the Fundamental Research Funds for the Central Universities and Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the 2nd phase) under grant no. U1501501. C.J.P. and R.J.N. acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the UK under grants [EP/G007489/2] (C.J.P.) and [EP/P034616/1] (R.J.N.). C.J.P. also acknowledges financial support from the EPSRC and the Royal Society through a Royal Society Wolfson Research Merit award. The calculations were carried out using supercomputers at the High Performance Computing Center of Collaborative Innovation Center of Advanced Microstructures, the high-performance supercomputing centre of Nanjing University, ‘Tianhe-2’ at NSCC-Guangzhou and the CSD3 Peta4 CPU/KNL machine at the University of Cambridge.

## Author information

J.S. conceived the project. J.S. and H.-T.W. led the project. C.L., H.G., Y.W. and C.J.P. performed the calculations. C.L., H.G., C.J.P. and J.S. analysed the data. C.L., J.S., R.J.N., H.-T.W. and D.X. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Correspondence to Jian Sun or Hui-Tian Wang.

## Ethics declarations

### Competing interests

C.J.P. is an author of the CASTEP code, and receives royalty payments from its commercial sales by Dassault Systèmes.

Peer review information: Nature Physics thanks Marius Millot and Ronald Redmer for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–8 and Tables 1–3.

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