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We study the semiclassical ground states of the Dirac equation with critical nonlinearity: -ihα · δw + aβw + V (x)w = W(x)(g(|w|) + |w|)w for x ε ℝ3. The Dirac operator is unbounded from below and above so the associate energy functional is strongly indefinite. We develop an argument to establish the existence of least energy solutions for h small. We also describe the concentration phenomena of the solutions as h → 0. © 2012 Society for Industrial and Applied Mathematics.

Existence and Concentration of Semiclassical Solutions for Dirac Equations with Critical Nonlinearities