Rotational Symmetry and A Light Mode in Two-Dimensional Staggered Fermions

To obtain a light mode in two-dimensional staggered fermions, we introduce four new local operators keeping the rotational invariance for a staggered Dirac operator. To split masses of tastes, three cases are considered. The mass matrix and the propagator for free theories are analyzed. We find that one of three cases is a good candidate for taking a single mode by the mass splitting. In the case, it is possible that a heavy mode obtains infinite mass on even sites or odd sites.