Superconductivity in Type-II Weyl Metals

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.