Anomalous Weyl superfluid in three-dimensional ultracold fermionic gases

• Weyl superfluid with anomalous Fermi arc surface state is introduced.
• Conditions realizing anomalous Weyl superfluid from layer construction are pointed out.
• An experimentally feasible model realizing anomalous Weyl superfluid is suggested.

In this paper we use layer construction method to construct an experimentally feasible model to realize one type of anomalous Weyl superfluids (WS) in the context of cold fermionic gases. This exotic phase still characterizes the Weyl points in the bulk but completely different Majorana Fermi arc surface state (MFASS) on the boundaries. In contrast to conventional WS, where MFASS only connects the projection of Weyl points, new MFASS continuously stretches to the border of surface Brillouin zone. We self-consistently determine the phase diagram of model at the mean-field level to claim the achievement of anomalous WS. In addition, inversion symmetry and band inversion in this model are analyzed in detail to provide unique feature of identifying anomalous WS experimentally by momentum-resolved radio-frequency spectroscopy.