d + id and d wave topological superconductors and new mechanisms for bulk boundary correspondence

We investigate two dimensional(2D) chiral dx2−y2 ± idxy topological superconductors and three dimensional(3D) d wave topological superconductors, through concrete models. We demonstrate that these two kinds of topological superconductors are the simplest cases of more general 2D class C topological superconductors and 3D class CI topological superconductors, respectively. We then give general methods to systematically build models for all 2D class C and 3D class CI topological superconductors. Our theoretical constructions may be a critical step to experimentally realize these exotic topologically superconducting phases. The chiral edge modes or gapless surface states of our 2D or 3D models are studied in details. In all the situations, we find novel mechanisms for bulk boundary correspondence