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Relativistic massless Weyl and Dirac fermions have isotropic and lineardispersion relations to maintain Poincar\'{e} symmetry, which is the most basicsymmetry in high-energy physics. The situation in condensed matter physics isless constrained; only certain subgroups of Poincar\'{e} symmetry -- the 230space groups that exist in 3D lattices -- need be respected. Then, the freefermionic excitations that have no high energy analogues could exist in solidstate systems. Here, We discovered a type of nonlinear Dirac fermion withouthigh-energy analogue in SrAgBi and named it type-IV Dirac fermion. The type-IVDirac fermion has a nonlinear dispersion relationship and is similar to thetype-II Dirac fermion, which has electron pocket and hole pocket. The effectivemodel for the type-IV Dirac fermion is also found. It is worth pointing outthat there is a type-II Dirac fermion near this new Dirac fermion. So we usedtwo models to describe the coexistence of these two Dirac fermions. Topologicalsurface states of these two Dirac points are also calculated. We envision thatour findings will stimulate researchers to study novel physics of type-IV Diracfermions, as well as the interplay of type-II and type-IV Dirac fermions.

Coexistence of Type-II and Type-IV Dirac Fermions in SrAgBi