Cancelation of confinement effect by spin-orbit coupling in narrow strips of two-dimensional topological insulators

The opening of the energy gap at the Dirac point when the helical edge states of two-dimensional topological insulators are hybridized in narrow channels is investigated. While the energy gap widens exponentially as the width is reduced within the block-diagonal effective four-band model, the dependence is no longer monotonic when off-diagonal terms representing spin-orbit coupling are taken into account. The energy gap vanishes periodically as the width is varied with the period being almost inversely proportional to the strength of the spin-orbit coupling. Both the bulk inversion asymmetry and Rashba terms cause the cancellation of the confinement effect. The disappearance of the hybridization takes place when the overlap integral becomes zero in the presence of the spin-orbit coupling due to the oscillatory decay of the transverse wave function.