# Double helix nodal line superconductor

## TL;DR

This paper investigates the conditions under which linked nodal lines, resembling double helix structures, can form in three-dimensional time-reversal invariant superconductors, revealing their topological significance and linking to Chern-Simons theory.

## Contribution

It introduces a model demonstrating linked nodal lines in 3D superconductors, connecting their formation to specific Fermi surface geometries and spin textures, and explores their topological implications.

## Key findings

- Linked nodal lines can form with torus or higher genus Fermi surfaces.
- Spiral spin textures facilitate the emergence of linked nodal lines.
- The linked nodal lines contribute a topological term to the thermal magnetoelectric response.

## Abstract

Time-reversal invariant superconductors in three dimensions may contain nodal lines in the Brillouin zone, which behave exactly as Wilson loops of 3d momentum-space Chern-Simons theory of the Berry connection. Here we study the conditions of realizing linked nodal lines (Wilson loops), which yield a topological contribution to the thermal magnetoelectric coefficient that is given by the Chern-Simons action. We find the essential conditions are the existence of torus or higher genus fermi surfaces and spiral spin textures. We construct such a model with two torus fermi surfaces, where a generic spin-dependent interaction leads to double-helix-like linked nodal lines as the superconductivity is developed.