This talk is about a series of supersymmetric lattice models called the Mk models. The focus will be on the M2 model on a one-dimensional lattice. In this model a maximum of two neighbouring sites can be  occupied by spinless fermions.  At the critical point the Mk model corresponds to the k-th N=2 superconformal minimal model. By introducing boundary defects on the lattice, all fields in the CFT can be identified. The Mk models can be tuned off-criticality by a staggering perturbation. For the right values of the staggering parameters the Mk models are integrable. We find that the M2 model perturbed by an integrable staggering corresponds to the supersymmetric sine-Gordon model at the point where there is an additional N=2 supersymmetry. In a limit of `extreme staggering'. We are able to compare the kinks in between the M2 model ground states to the solitons of the supersymmetric sine-Gordon model.