  The recently synthesized hydrogen boride monolayer in the Cmmm phase is a
promising super-conductor due to its similarity to MgB2 and the large hydrogen
content in its structure. Making use of first-principles calculations based on
density functional theory, we study its electronic, vibrational,and
superconducting properties and conclude that, despite the expectations,
hydrogen boride does not have a sizable superconducting critical temperature.
The presence of hydrogen in the system alters the boron-boron bonding,
weakening the electron-phonon interaction. We have studied the effect of
enhancing the critical temperature by doping the system, but the inclusion of
electrons or holes reveals ineffective. We attribute the small critical
temperature of this system to the vanishing hydrogen character of the states at
the Fermi level, which are dominated by boron p states. Our results determine
that a large proportion of hydrogen-like states are needed at the Fermi level
to attain a large superconducting critical temperature in hydrogenated
monolayers.
