Klein tunneling of helical edge states in narrow strips of a two-dimensional topological insulator

The quantum transmission of helical edge states across a square potential barrier is numerically investigated in narrow channels of a two-dimensional topological insulator. Although the transmission probability in general decreases when a potential offset is introduced in the middle of the channels, the transmission remains almost perfect regardless of the amplitude and length of the potential offset when the hybridization energy gap is closed by tuning the off-diagonal spin-orbit terms in the effective four-band Hamiltonian. The approximate absence of scattering resembling the Klein tunneling, where the transmission is unimpeded as an electron propagates relativistically as a hole in the barrier without decay, improves further when an interference condition is satisfied within the barrier. The dependence of the residual reflection on the Fermi level reveals anomalous characteristics in the Klein tunneling regime.