Topological surface states in dense solid hydrogen
  It has recently been established that two-dimensional massless graphene-like systems and three-dimensional line-node topological semimetals comprise a special class of centrosymmetric materials where edge/surface states of topological nature inevitably appear in some k-regions. We show that the phases of solid hydrogen produced at megabar pressures can be line-node topological semimetals. In such phases, the material exhibits topological surface states and therefore can be a poor bulk metal but good surface conductor. The results may help to explain discrepant high-pressure experimental data reported for dense hydrogen as well as provide predictions for future measurements, including possible surface superconductivity in hydrogen. Related topological behavior may be expected in high-pressure phases formed in other elements including simple metals. 
Ivan I. Naumov and Russell J. Hemley
cond-mat.mtrl-sci