  The magnetically-induced valley-spin filtering in transition metal
dichalcogenide monolayers ($MX_{2}$, where $M$=Mo, W and $X$=S, Se, Te)
promises new paradigm in information processing. However, the detailed
understanding of this effect is still limited, regarding its underlying
transport processes. Herein, it is suggested that the filtering mechanism can
be greately elucidated by the concept of metal-induced gap states (MIGS),
appearing in the electrode-terminated $MX_{2}$ materials {\it i.e.} the
referential filter setup. In particular, the gap states are predicted here to
mediate valley- and spin-resolved charge transport near the ideal
electrode/$MX_{2}$ interface, and therefore to initiate filtering. It is also
argued that the role of MIGS increases when the channel length is diminished,
as they begin to govern the overall valley-spin transport in the tunneling
regime. In what follows, the presented study yields fundamental scaling trends
for the valley-spin selectivity with respect to the intrinsic physics of the
filter materials. As a result, it facilitates insight into the analyzed effects
and provide design guidelines toward efficient valley-spin filter devices, that
base on the discussed materials or other hexagonal monolayers with a broken
inversion symmetry.
