Superconductivity in multi-Weyl semimetals: Conditions for the coexistence of topological and conventional phases

TL;DR

The paper investigates superconductivity in multi-Weyl semimetals with Weyl nodes of chirality $|\nu|\ge 1$, showing that intra-nodal pairing is described by monopole harmonics while inter-nodal pairing follows conventional spherical harmonics. Using a Bogoliubov–de Gennes framework, it derives coupled gap equations for intra- and inter-nodal pairings, identifies a topological repulsion that can suppress coexistence in certain angular configurations, and computes the critical temperatures and temperature-dependent gaps. It also demonstrates that the specific heat exhibits two distinct jumps corresponding to the monopole and conventional transitions, with the slopes depending on $\nu$, offering a concrete experimental probe of the chirality. The results generalize previous simple-Weyl findings to multi-Weyl systems and highlight thermodynamic signatures as a route to characterize topological pairing in these materials.

Abstract

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 $|ν| \ge 1$ leads to an effective description of the intra-nodal pairings in terms of monopole harmonics, in contrast to inter-nodal 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 $ν$ in the material.

Figures (5)

• Figure 1: Phase diagram in the coupling space for s-wave vs monopole, for chiralities $\nu=1,2,3$ and $c=0.1, 1, 10$ to illustrate the behavior when $c\rightarrow 0$, intermediate $c$ and $c\rightarrow \infty$, respectively. Blue line is Eq. \ref{['Diagrama: curva s wave > monopolo']} and red line is Eq. \ref{['Diagrama: curva monopolo > s wave']}, respectively.
• Figure 2: Phase diagram in the coupling space for $\boldsymbol{p_{z}}$-wave vs monopole, for chiralities $\nu=1,2,3$ and $c=0.1, 1, 7$ to illustrate the behavior when $c\rightarrow 0$, intermediate $c$ and $c\rightarrow \infty$, respectively. Blue line is Eq. \ref{['Diagrama: curva p wave > monopolo']} and red line is Eq. \ref{['Diagrama: curva monopolo > p wave']}, respectively.
• Figure 3: Pairings $\Delta_{0}$ (s-wave in the intra-nodal channel) and $\Delta_{1}$ (monopole in the inter-nodal channel), both in units of $10^{-3}\hbar\omega_D$, as function of $T$ (in units of $10^{-3}\hbar\omega_D/k_B$) near the critical temperatures.
• Figure 4: Pairings $\Delta_{0}$ ($p_{z}$-wave in the intra-nodal channel) and $\Delta_{1}$ (monopole in the inter-nodal channel), both in units of $10^{-3}\hbar\omega_D$
• Figure 5: Total specific heaet $C_{v} = C_{v}^{\text{norm}} + C_{v}^{SC}$ (in units of $k_B\omega_{D}/\left[v_{f}\alpha_{\nu}^{2/(\nu-1)}\right]$)