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We study the problem of a single Dirac fermion in a quantizing orbitalmagnetic field, when the chemical potential is at the Dirac point. This can berealized on the surface of a topological insulator, such as Bi2Se3, tuned toneutrality. We study the effect of both long range Coulomb interactions(strength alpha=e^2/(epsilon hbar v_F).) and local repulsion U which capturethe effect of electron correlations. Interactions resolve the degeneracy offree fermions in the zeroth Landau level at half filling, but in a mannerdifferent from that in graphene. For weak interactions, U=0 and alpha<<1, acomposite Fermi liquid is expected. However, in the limit of strong localcorrelations (large U but alpha<<1), a charge density wave phase is predicted,which we term "axion stripe". While reminiscent of quantum Hall stripe phases,its wavelength is parametrically larger than the magnetic length, and theinduced fermion mass term (axion) also oscillates with the charge density. Thisphase is destroyed by sufficiently strong Zeeman coupling. A phase diagram isconstructed and consequences for experiments are discussed.

Composite Fermions and Quantum Hall Stripes on the Topological Insulator Surface