From orthosymplectic structure to super topological matter

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