Abstract
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.
Highlights
In recent few years, there has been a surge of interest in the study of the topological phases of free fermions.[1,2,3] In these phases, the system is fully gapped in bulk and has a unique ground state on a compact spatial manifold M without boundary
We investigate two dimensional(2D) chiral dx2−y2 ± idx y 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
The chiral edge modes or gapless surface states of our 2D or 3D models are studied in details
Summary
There has been a surge of interest in the study of the topological phases of free fermions.[1,2,3] In these phases, the system is fully gapped in bulk and has a unique ground state on a compact spatial manifold M without boundary. One of the purposes of the present paper is to investigate the 2D chiral topological superconductors with dx2−y2 ± idx y (d + id) pairing symmetry through concrete Hamiltonian models. We demonstrate that this kinds of topological superconductors are the simplest examples of the more general 2D class C topological superconductors. T′ ≫ t, the quartic term is just a small perturbation This perturbation can mathematically guarantee the existence of the topologically nontrivial phase with c1 = 2, as one will see in our explicitly calculation to the Chern number c1.
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