  We study the properties of interacting line defects in the four-dimensional
Chern Simons (CS) gauge theory with invariance given by the $SL\left(
m|n\right) $ super-group family. From this theory, we derive the oscillator
realisation of the Lax operator for superspin chains with $SL(m|n)$ symmetry.
To this end, we investigate the holomorphic property of the bosonic Lax
operator $\mathcal{L}$ and build a differential equation $%
\mathfrak{D}\mathcal{L}=0$ solved by the Costello-Gaioto-Yagi realisation of
$\mathcal{L}$ in the framework of\ the CS theory. We generalize this
construction to the case of gauge super-groups, and develop a Dynkin
super-diagram algorithm to\ deal with the decomposition of the Lie
superalgebras. We obtain the generalisation of the Lax operator describing the
interaction between the electric Wilson super-lines and the magnetic 't Hooft
super-defects. This coupling is given in terms of a mixture of bosonic and
fermionic oscillator degrees of freedom in the phase space of magnetically
charged 't Hooft super-lines. The purely fermionic realisation of the superspin
chain Lax operator is also investigated and it is found to coincide exactly
with the $\mathbb{Z}_{2}$- gradation of Lie superalgebras.\ \newline Keywords:
4D Chern-Simons theory, Super-gauge symmetry, Lie superalgebras and Dynkin
super-diagrams, Superspin chains and integrability, Super- Lax operator.
