Superconductivity in multi-Weyl semimetals: Coexistence and Repulsion between Topological and Conventional phases

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 topological charge |ν| > 1 leads to an effective description of the intra-nodal pairings in terms of monopole (MP) harmonics, in contrast to inter-nodal pairings that preserve the conventional spherical harmonics (SC) angular dependence, in analogy with our previous works[1,2]. 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 that was previously reported in the context of simple Weyl semimetals. We identified the critical temperatures corresponding to the MP and SC phases, and we calculated the specific heat as a function of temperature, thus showing that this thermodynamical parameter may provide an experimental probe to determine the topological charge ν in the material.

References

[1] E. Muñoz, J. Esparza, J. Braun, and R. Soto-Garrido, “Topological versus conventional superconductivity in a Weyl semimetal: A microscopic approach”, Superconductivity 12, 100132 (2024)

[2] E. Muñoz, R. Soto-Garrido, and V. Juricic, “Monopole versus spherical harmonic superconductors: Topological repulsion, coexistence, and stability”, Physical Review B 102, 195121 (2020).