  We have studied the topological properties of free standing Sn doped cadmium
chalcogenide (CdSnX, X = S, Se and Te) nanoribbons of varying widths and three
types of edges viz., distorted armchair, normal armchair and normal zigzag
edges. The unsatisfied bonds of X and Sn atoms at the edges cause non-zero
values of the magnetic moment. This introduces an exchange field leading to
inverted band structure. The electronic band structures of distorted armchair
edge nanoribbons also exhibit different types of spin splitting property for
different X atoms due to the different local orbital angular momentum at
specific X atomic site with the inclusion of spin orbit coupling (SOC). The gap
opening at the band crossings near the Fermi level after inclusion of SOC are
mainly due to SOC of Sn atom and are responsible for the electron and hole
pockets making the system topologically exotic. All the distorted edge
nanoribbons show metallic behaviour with non-zero magnetic moments. Amongst CdX
(X = S, Se and Te) nanoribbons, systems containing S atoms exhibit Weyl-like
semi-metallic behavior and not much change with width, that of Se atoms exhibit
Zeeman-type spin splitting and significant change with varying width, whereas
systems containing Te atoms show signature of Rashba spin splitting along with
Zeeman-type spin splitting and moderate change with varying width. The armchair
edge nanoribbons show wide gap semiconducting behaviour. Zeeman-type spin
splitting is seen in the valence band region for systems containing S atoms and
Rashba spin splitting is visible in the conduction band region for systems
containing Se and Te atoms. For zigzag edge nanoribbons, no such signature of
spin splitting is observed although all the nanoribbons acquire very high
magnetic moments.
