Models for $d$ Wave Topological Superconductors and Quantum Anomalous Hall Effect with Arbitrary Large Chern Numbers

TL;DR

This paper develops theoretical models for 2D and 3D topological superconductors with large Chern numbers, exploring their boundary states and bulk-boundary correspondence.

Contribution

It introduces new models for high Chern number topological superconductors and quantum anomalous Hall effects, expanding understanding of topological phases.

Findings

Models for 2D chiral d-wave superconductors with arbitrary Chern numbers

Models for 3D topological superconductors with arbitrary topological invariants

Verification of bulk-boundary correspondence in these models

Abstract

We construct theoretical models for two dimensional(2d) chiral $d_{x^2-y^2}\pm id_{xy}$ topological superconductors and for three dimensional(3d) $d$ wave topological superconductors. Moreover we build models for any 2d class C and 3d class CI topological superconductors (with any even topological invariants). We also construct concrete models that can realize quantum anomalous Hall effect with arbitrary large Chern numbers. We study the chiral edge modes or gapless surface states of our 2d or 3d models in details. In all the cases, we find novel mechanisms that make the numbers of boundary states always agree with the nontrivial bulk topology, just as required by the bulk boundary correspondence.