Translation invariant topological superconductors on lattice

Abstract

In this paper we introduce four Z_2 topological indices zeta_k=0,1 at k=(0,0), (0,pi), (pi, 0), (pi, pi) characterizing 16 universal classes of 2D superconducting states that have translation symmetry but may break any other symmetries. The 16 classes of superconducting states are distinguished by their even/odd numbers of fermions on even-by-even, even-by-odd, odd-by-even, and odd-by-odd lattices. As a result, the 16 classes topological superconducting states exist even for interacting systems. For non-interacting systems, we find that zeta_k is the number of electrons on k=(0,0), (0,pi), (pi, 0), or (pi,pi) orbitals (mod 2) in the ground state. For 3D superconducting states with only translation symmetry, there are 256 different types of topological superconductors.

4 pages, RevTeX4

References in corpus (4)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• The effects of interactions on the topological classification of free fermion systems

Cited by in corpus (6)

• An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators
• Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models
• Theory of weak symmetry breaking of translations in ${\mathbb{Z}}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice ${\mathbb{Z}}_2$ charge-flux attachment
• Berry Phases of Vison Transport in ${\mathbb{Z}}_2$ Topologically Ordered States from Exact Fermion-Flux Lattice Dualities
• Majorana Edge States for Z2 Topological Orders of the Wen-plaquette Model and the Toric-code Model
• Anyon polarons as a window into competing phases of the Kitaev honeycomb model under a Zeeman field