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We report on numerical study of the Dirac fermions in partially filled N=3Landau level (LL) in graphene. At half-filling, the equal-time density-densitycorrelation function displays sharp peaks at nonzero wavevectors $\pm {\bfq^{*}}$. Finite-size scaling shows that the peak value grows with electronnumber and diverges in the thermodynamic limit, which suggests an instabilitytoward a charge density wave. A symmetry broken stripe phase is formed at largesystem size limit, which is robust against purturbation from disorderscattering. Such a quantum phase is experimentally observable through transportmeasurements. Associated with the special wavefunctions of the Dirac LL, bothstripe and bubble phases become possible candidates for the ground state of theDirac fermions in graphene with lower filling factors in the N=3 LL.

Broken-Symmetry States of Dirac Fermions in Graphene with A Partially Filled High Landau Level