  The Anderson and midgap models are often used in the study of semiconductor
heterojunctions, but for van der Waals (vdW) vertical heterostructures they
have shown only very limited success. Using the group-IV monochalcogenide
vertical heterostructures as a prototypical system, we propose a linear
response model and compare the effectiveness of these models in predicting
density functional theory (DFT) band alignments, band types and bandgaps. We
show that the DFT band alignment is best predicted by the linear response
model, which falls in between the Anderson and midgap models. Our proposed
model can be characterized by an interface dipole
$\alpha\times(E_{m2}-E_{m1})$, where the linear response coefficient $\alpha$ =
0 and 1 corresponds to the Anderson and midgap model respectively, and $E_{m}$
is the midgap energy of the monolayer, which can be viewed as an effective
electronegativity. For group-IV monochalcogenides, we show that $\alpha$ = 0.34
best captures the DFT band alignment of the vdW heterostructure, and we discuss
the viability of the linear response model considering other effects such as
strains and band hybridization, and conclude with an application of the model
to predict experimental band alignments.
