Coupled Wire Models of Interacting Dirac Nodal Superconductors

TL;DR

This paper introduces a coupled wire model for topological nodal superconductors with Dirac points, demonstrating symmetry-preserving interactions that induce a gapped, topologically ordered phase with fractionalization.

Contribution

It presents an exactly solvable coupled wire construction for Dirac nodal superconductors, revealing new gapping interactions and topological orders, including a trivial $E_8$ phase for 16 Dirac fermions.

Findings

Exact many-body interactions can gap Dirac nodes while preserving symmetries.

Gapped phases exhibit fractionalization and non-trivial topological order.

Special case with 16 Dirac fermions leads to a trivial $E_8$ topological order.

Abstract

Topological nodal superconductors possess gapless low energy excitations that are characterized by point or line nodal Fermi surfaces. In this work, using a coupled wire construction, we study topological nodal superconductors that have protected Dirac nodal points. In this construction, the low-energy electronic degrees of freedom are confined in a three dimensional array of wires, which emerge as pairing vortices of a microscopic superconducting system. The vortex array harbors an antiferromagnetic time-reversal and a mirror glide symmetry that protect the massless Dirac fermion in the single-body non-interacting limit. Within this model, we demonstrate exact-solvable many-body interactions that preserve the underlying symmetries and introduce a finite excitation energy gap. These gapping interactions support fractionalization and generically lead to non-trivial topological order. We also construct a special case of $N=16$ Dirac fermions where corresponding the gapping interaction leads to a trivial $E_8$ topological order that is closely related to the cancellation of the large gravitational anomaly.