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Quadratic band crossing points (QBCPs) and quantum anomalous Hall effect(QAHE) have attracted the attention of both theoretical and experimentalresearchers in recent years. Based on first-principle calculations, we findthat the FeB$_2$ monolayer is a nonmagnetic semimetal with QBCPs at $K$.Through symmetry analysis and $\mathbf{k}\cdot\mathbf{p}$ invariant theory, wefind that the QBCP is not protected by rotation symmetry and consists of twoDirac points with same chirality (Berry phase of $2\pi$). Once introducingCoulomb interactions, we find that there is aspontaneous-time-reversal-breaking instability of the spinful QBCPs, whichgives rise to a $C=2$ QAH insulator with orbital moment ordering.

Unprotected quadratic band crossing points and quantum anomalous Hall effect in FeB2 monolayer