Abstract
The monopole harmonic superconductor (SC), proposed in doped Weyl semimetals as a pairing between the Fermi surfaces enclosing the Weyl points, is rather unusual, as it features the monopole charge inherited from the parent metallic phase. However, this state can compete with more conventional spherical harmonic pairings, such as an $s$-wave. We here demonstrate, within the framework of the weak coupling mean-field BCS theory, that the monopole and a conventional spherical harmonic SC quite generically coexist, while the repulsion can take place when the absolute value of the monopole charge matches the angular momentum quantum number of the spherical harmonic. As we show, this feature is a direct consequence of the topological nature of the monopole SC, and we dub it \emph{topological repulsion}. We illustrate the above principle with the example of the conventional $s-$ and $(p_x\pm ip_y)-$wave pairings competing with the monopole SC $Y_{-1,1,0}(\theta,\phi)$, which coexist in a finite region of the parameter space, and repel, respectively. Furthermore, the s-wave pairing is more stable both when the chemical potentials at the nodes are unequal, and in the presence of point-like charged impurities. Since the phase transition is discontinuous, close to the phase boundary, we predict that the Majorana surface modes at the interfaces between domains featuring the monopole and the trivial phases, such as an $s-$wave, will be the experimental signature of the monopole SC.
Highlights
Topological semimetals feature the nodal points in the Brillouin zone where the conduction and valence bands touch, yielding a rather rich landscape of emergent lowenergy quasiparticles [1,2,3,4,5,6]
The exotic electronic properties in Weyl semimetals (WSMs), such as Fermi arc surface states and anomalous magnetotransport, arise from the two topological nodal points in the Brillouin zone featuring pseudorelativistic Weyl fermions [7,8,9,10,11], which were experimentally observed in mostly binary compounds, such as TaAs and NbP [12,13,14,15]
Even in this fine-tuned situation, when fluctuation effects are accounted for, we expect that the phases repel each other due to their incompatible topological structures: while the monopole SC features a double vortex coming from individual Fermi surfaces FS±, the p-wave harmonic picks up a vortex-antivortex pair at each of them
Summary
Topological semimetals feature the nodal points in the Brillouin zone where the conduction and valence bands touch, yielding a rather rich landscape of emergent lowenergy quasiparticles [1,2,3,4,5,6]. The exotic electronic properties in Weyl semimetals (WSMs), such as Fermi arc surface states and anomalous magnetotransport, arise from the two topological nodal points in the Brillouin zone featuring pseudorelativistic Weyl fermions [7,8,9,10,11], which were experimentally observed in mostly binary compounds, such as TaAs and NbP [12,13,14,15]. Q with 0 being the order parameter This is possibly the simplest pairing between the Fermi surfaces FS± enclosing the two nodal points at ζ K0 and involves the two Weyl quasiparticles with momenta K0 + q and −K0 − q, where ±q lives on the sphere S± obtained after shifting FS± by ∓K0 toward the origin.
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