Complex sentence: Materials with zincblende strucuture are non-centrosymmetric (i.e. lack of inversion symmetry), this bulk inversion asymmetry (BIA) forces the perturbative Hamiltonian to be composed of only odd powers of the linear momentum.
Split into simpler sentences: Materials with zincblende strucuture are non-centrosymmetric (i.e., they lack inversion symmetry). This bulk inversion asymmetry (BIA) forces the perturbative Hamiltonian to contain only odd powers of the linear momentum.