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

The spin-3/2 elementary particle, known as Rarita-Schwinger (RS) fermion, is described by a vector-spinor field ψ_μα, whose number of components is larger than its independent degrees of freedom (DOF). Thus the RS equations contain nontrivial constraints to eliminate the redundant DOF. Consequently the standard procedure adopted in realizing relativistic spin-1/2 quasi-particle is not capable of creating the RS fermion in condensed matter systems. In this work, we propose a generic method to construct a Hamiltonian which implicitly contains the RS constraints, thus includes the eigenstates and energy dispersions being exactly the same as those of RS equations. By implementing our 16X16 or 6X6 Hamiltonian, one can realize the 3 dimensional or 2 dimensional (2D) massive RS quasiparticles, respectively. In the non-relativistic limit, the 2D 6X6 Hamiltonian can be reduced to two 3X3 Hamiltonians which describe the positive and negative energy parts respectively. Due to the nontrivial constraints, this simplified 2D massive RS quasiparticle has an exotic property: it has vanishing orbital magnetic moment while its orbital magnetization is finite. Finally, we discuss the material realization of RS quasiparticle. Our study provides an opportunity to realize higher spin elementary fermions with constraints in condensed matter systems.