单极超导体与球谐超导体：拓扑排斥、共存和稳定性
Monopole versus spherical harmonic superconductors: Topological repulsion, coexistence and stability
摘要：
在掺杂的外尔半金属中提出的外尔点费米面之间的配对，是相当不寻常的，因为它具有从母体金属相继承的外尔电荷。然而，这种状态可以与更传统的球谐配对竞争，例如$s$波。在这里，我们证明，在弱耦合平均场BCS理论的框架内，的的π和一个传统的球谐SC相当generally共存，而排斥可以发生时，π电荷的绝对值匹配的角动量量子数的球谐。正如我们所示，这个功能是一个直接的后果的拓扑性质的CNOSC，我们称之为\emph{topological repulsion}。我们用传统的$s-$和$(p_x\pm ip_y)-$波对与PDMATHMSC $Y_{-1,1,0}(θ,ϕ)$竞争的例子来说明上述原理，它们共存于参数空间的有限区域中，并且分别相斥。此外，s波配对是更稳定的节点处的化学势是不相等的，并在点状带电杂质的存在下。由于相变是不连续的，接近相边界，我们预测的Majorana表面模式在具有的微相和平凡的阶段，如$s-$波，域之间的接口，将是实验签名的微相。
英文摘要：
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 $Y_{-1,1,0}(θ,ϕ)$, 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.
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