Massive Relativistic Spin-3/2 Rarita-Schwinger Quasiparticle in Condensed Matter Systems

We study the possibility to realize the massive relativistic spin-3/2 Rarita-Schwinger (RS) quasiparticles in condensed matter systems (CMS). The main obstacle to be jumped is the nontrivial constraints that eliminate the redundant degrees of freedom in the representation of the Poincar'e group. We propose a generic method to construct a Hamiltonian which automatically contains the RS constraints, and prove that the RS modes always exist and can be separated from the other non-RS ones. Focusing on the two dimensions (2D), we find a novel property for this RS quasiparticle: Due to the nontrivial constraints, although the intrinsic orbital magnetic moment of an energy band is formally like its Berry curvature under symmetry operations, the former is exactly zero-valued in this case despite the latter is finite. Through symmetry considerations, we show that the 2D massive RS quasiparticle can emerge in several trigonal and hexagonal lattices. Based on ab initio calculations, we predict that the thin film of CaLiX (X=Ge and Si) are the candidates.