  Iron arsenide superconductors based on the material LaFeAsO1-xFx are
characterized by a two-dimensional Fermi surface (FS) consisting of hole and
electron pockets yielding structural and antiferromagnetic transitions at x =
0. Electron doping by substituting O2- with F- suppresses these transitions and
gives rise to superconductivity with a maximum Tc = 26 K at x = 0.1. However,
the over-doped region cannot be accessed due to the poor solubility of F- above
x = 0.2. Here we overcome this problem by doping LaFeAsO with hydrogen. We
report the phase diagram of LaFeAsO1-xHx (x < 0.53) and, in addition to the
conventional superconducting dome seen in LaFeAsO1-xFx, we find a second dome
in the range 0.21 < x < 0.53, with a maximum Tc of 36 K at x = 0.3. Density
functional theory calculations reveal that the three Fe 3d bands (xy, yz, zx)
become degenerate at x = 0.36, whereas the FS nesting is weakened monotonically
with x. These results imply that the band degeneracy has an important role to
induce high Tc.
