  In this paper, we are concerned with local minimizers of an interaction
energy governed by repulsive-attractive potentials of power-law type in one
dimension. We prove that sum of two Dirac masses is the unique local minimizer
under the $\lambda-$Wasserstein metric topology with $1\le \lambda<\infty$,
provided masses and distance of Dirac deltas are equally half and one,
respectively. In addition, in case of $\infty$-Wasserstein metric, we
characterize stability of steady-state solutions depending on powers of
interaction potentials.
