Band Bending and Valence Band Quantization at Line Defects in MoS$_2$

The variation of the electronic structure normal to 1D defects in quasi-freestanding MoS$_2$, grown by molecular beam epitaxy, is investigated through high resolution scanning tunneling spectroscopy at $5$K. Strong upwards bending of valence and conduction bands towards the line defects is found for the 4|4E mirror twin boundary and island edges, but not for the 4|4P mirror twin boundary. Quantized energy levels in the valence band are observed wherever upwards band bending takes place. Focusing on the common 4|4E mirror twin boundary, density functional theory calculations give an estimate of its charging, which agrees well with electrostatic modeling. We show that the line charge can also be assessed from the filling of the boundary-localized electronic band, whereby we provide a measurement of the theoretically predicted quantized polarization charge at MoS$_2$ mirror twin boundaries. These calculations elucidate the origin of band bending and charging at these 1D defects in MoS$_2$. The 4|4E mirror twin boundary not only impairs charge transport of electrons and holes due to band bending, but holes are additionally subject to a potential barrier, which is inferred from the independence of the quantized energy landscape on either side of the boundary.