Spin-polarized edge modes and snake states in HgTe/CdTe quantum wells under an antisymmetric magnetic field

We demonstrate the effect of an antisymmetric magnetic field on the edge states in inverted HgTe quantum wells using the Landauer-Buttiker formula coupled with the Green's function technique. At any width of the zero-field region, gapless edge modes appear inside the bulk band gap. By calculating the wave function distribution, we find that (i) for Fermi energies inside the bulk gap, the edge states propagate helically along the sample boundaries as a quantum spin-Hall insulator; and (ii) for Fermi energies outside the bulk gap, a pair of states propagate along the boundaries, while the other pair of "snake states" appear and counterpropagate along the central zero-field region. We show numerically that the edge modes in the latter case are robust against the short-range Anderson disorder.