  We study superconductivity in a Weyl semimetal with a tilted dispersion
around two Weyl points of opposite chirality. In the absence of any tilt, the
state with zero momentum pairing between two Fermi sheets enclosing each Weyl
point has four point nodes in the superconducting gap function. Moreover, the
surface of the superconductor hosts Fermi arc states and Majorana flat bands.
We show that a quantum phase transition occurs at a critical value of the tilt,
at which two gap nodes disappear by merging at the center of the first
Brillouin zone, or by escaping at its edges, depending on the direction of the
tilt. The region in the momentum space that the Majorana flat band occupies is
found to increase as the tilt parameter is made larger. Additionally, the
superconducting critical temperature and electronic specific heat can be
enhanced in the vicinity of the quantum phase transition due to the singularity
in the electronic density of states.
