  Kinks, point-like geometrical defects along dislocations, domain walls, and
DNA, are stable and mobile, as solutions of a sine-Gordon wave equation. While
they are widely investigated for crystal deformations and domain wall motions,
electronic properties of individual kinks have received little attention. In
this work, electronically and topologically distinct kinks are discovered along
electronic domain walls in a correlated van der Waals insulator of
1$T$-TaS$_2$. Mobile kinks and antikinks are identified as trapped by pinning
defects and imaged in scanning tunneling microscopy. Their atomic structures
and in-gap electronic states are unveiled, which are mapped approximately into
Su-Schrieffer-Heeger solitons. The twelve-fold degeneracy of the domain walls
in the present system guarantees an extraordinarily large number of distinct
kinks and antikinks to emerge. Such large degeneracy together with the robust
geometrical nature may be useful for handling multilevel information in van der
Waals materials architectures.
