Helical conducting edge states in narrow-gap semiconductors without band inversion

Band inversion accompanied by the emergence of gapless and helical edge states at the boundary is a hallmark of 2D topological insulators. However, a recent experiment reports the existence of edge states before band inversion in InAs/GaSb quantum wells [F. Nichele et al., New J. Phys. 18, 083005 (2016)]. The underlying physics remains an open problem. Here we provide a possible solution by showing that helical edge states emerge before band inversion as long as the bulk gap falls below a positive threshold determined by the particle-hole asymmetry and interband coupling. In the presence of quantum confinement or local electrostatic potential near the boundary, these edge states may enter the gap of bulk states and be detected as edge conductance in transport measurements. Our work reveals the possible existence of the helical conducting edge states in a large class of narrow-gap semiconductors.