Chiral edge mode for single-cone Dirac fermions

We study the appearance of a chiral edge mode on the two-dimensional (2D) surface of a 3D topological insulator (TI). The edge mode appears along the 1D boundary with a magnetic insulator (MI), dependent on the angle $\theta$ which the magnetization $M$ makes with the normal to surface and on the chemical potential mismatch $\delta\mu$ across the TI--MI interface (assuming $1>\delta\mu/M\equiv\sin\phi)$. The propagation along the interface is chiral, with velocity $v\cos(\theta-\phi)$ smaller than the Dirac fermion velocity $v$. In momentum space the edge mode is an arc state, extending over the finite momentum interval that connects the Dirac point of the gapless Dirac fermions with the magnetic band gap. An electric field parallel to the boundary pumps charge between TI and MI via this arc state.