Rotation symmetry-protected topological phases of fermions

We study classification of interacting fermionic symmetry-protected topological (SPT) phases with both rotation symmetry and Abelian internal symmetries in one, two, three dimensions. By working out this classification, on the one hand, we demonstrate recently proposed correspondence principle between crystalline those through explicit block-state constructions. find that for precise to hold it is necessary change central extension structure group by $\mathbb{Z}_2$ fermion parity. On other uncover new classes intrinsically SPT are only enabled interactions, 2D 3D four-fold rotation. Moreover, several instances Lieb-Schultz-Mattis-type theorems Majorana-type SPTs obtained discuss their interpretations from perspective bulk-boundary correspondence.