Quasi-two-dimensional Dirac fermions and quantum magnetoresistance in LaAgBi$_2$

We report quasi-two-dimensional Dirac fermions and quantum magnetoresistance in LaAgBi$_2$. The band structure shows several narrow bands with nearly linear energy dispersion and Dirac-cone-like points at the Fermi level. The quantum oscillation experiments revealed one quasi-two-dimensional Fermi pocket and another complex pocket with small cyclotron resonant mass. The in-plane transverse magnetoresistance exhibits a crossover at a critical field $B^*$ from semiclassical weak-field $B^2$ dependence to the high-field unsaturated linear magnetoresistance which is attributed to the quantum limit of the Dirac fermions. Our results suggest the existence of quasi 2D Dirac fermions in rare-earth based layered compounds with two-dimensional double-sized Bi square nets, similar to (Ca,Sr)MnBi$_{2}$, irrespective of magnetic order.