Quantum anomalies in superconducting Weyl metals

We theoretically study the quantum anomalies in the superconducting Weyl metals based on the topological field theory. It is demonstrated that the Fermi arc and the surface Andreev bound state, characteristic of the superconducting Weyl metals, are the manifestations of two underlying phenomena, namely, the chiral anomaly and the paritylike anomaly, respectively. The first anomaly is inherited from the Berry curvature around the original Weyl points, while the second is the result of the superconductivity. We show that all the fascinating topological behavior of the superconducting Weyl metals, either the intranode Fulde-Ferrell-Larkin-Ovchinnikov or the internode Bardeen-Cooper-Schrieffer pairing state, can be satisfactorily described and predicted by our topological field theory.

Figure 1

The schematic diagram showing the change of the energy spectrum along $k_z$ of the intranode pairing FFLO SWM phase under the local chiral transformation. (a) For the case chemical potential $\mu \ne 0$. (b) Shows the case $\mu =0$.

Figure 2

The Feynman diagram in the second-order perturbative calculation. The straight lines denote the propagator of the Grassmann field ${\mathrm{\Phi }}_k^{\prime \prime }$ and the dashed lines represent the propagator of the gauge field.

Figure 3

Tight-binding results of the energy spectrum along $k_y$ $\left(k_z=0\right)$. A thin film with 200 layers stacked along the $x$ direction is considered. The parameters chosen are $t=-1,t_z=-2,Q=\pi /4,m=1$, and ${\mathrm{\Delta }}_{+}={\mathrm{\Delta }}_{-}=0.1$. The chemical potential is $\mu =0$ in (a) while $\mu =0.1$ in (b).