In this work, we explore the possible emergence of superconducting phases in a multi-Weyl semimetal. In particular, we show that the presence of a pair of Weyl nodes with chirality $\left|\nu \right|\ge 1$ leads to an effective description of the intranodal pairings in terms of monopole harmonics, in contrast to internodal pairings that preserve the angular dependence of conventional spherical harmonics. Therefore, we explore the conditions for the competition and/or coexistence between both types of superconducting phases, and we identify the presence of the so-called topological repulsion mechanism, which was previously reported in the context of simple Weyl semimetals. We identified the critical temperatures corresponding to the monopole and conventional superconducting phases, and calculated the specific heat as a function of temperature, thus showing that this thermodynamical parameter may provide an experimental probe to determine the chirality index $\nu$ in the material.

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• Geometric & topological phases
• Phase transitions
• Quantum phase transitions
• Specific heat
• Superconducting phase transition
• Superconductivity
• Topological materials
• Topological phase transition
• Topological phases of matter
• Topological superconductors