  Topological supermatter is given by ordinary topological matter constrained
by supersymmetry or graded supergroups such as OSP(2N|2N). Using results on
super oscillators and lattice QFT$_{d}$, we construct a super tight binding
model on hypercubic super lattice with supercharge $
\boldsymbol{Q}=\sum_{\mathbf{k}}\hat{F}_{\mathbf{k}}.\boldsymbol{q}_{\mathbf{k}}.\hat{B}_{\mathbf{k}}$.
We first show that the algebraic triplet $(\Omega ,G,J)$ of super oscillators
can be derived from the $OSp(2N|2N)$ supergroup containing the symplectic
$Sp(2N)$ and the orthogonal $SO(2N)$ as even subgroups. Then, we apply the
obtained result on super oscillating matter to super bands and investigate its
topological obstructions protected by TPC symmetries. We also give a
classification of the Bose/Fermi coupling matrix $\boldsymbol{q}_{\mathbf{k}}$
in terms of subgroups of $OSp(2N|2N)$\ and show that there are $2P_{N}$
(partition of $N$) classes $\boldsymbol{q}_{\mathbf{k}}$ given by unitary
subgroups of $U\left( 2\right) \times U\left( N\right) $. Other features are
also given.
