Winding numbers of nodal points in Fe-based superconductors

TL;DR

This paper studies the topological properties of nodal points in Fe-based superconductors, showing how they move, merge, and annihilate during Lifshitz transitions, with implications for their topological invariants.

Contribution

It provides a topological analysis of nodal point dynamics in Fe-based superconductors, highlighting the conservation of winding numbers during Lifshitz transitions.

Findings

Nodal points can be moved by external parameters.

Nodal points merge and annihilate via Lifshitz transition.

Merging nodal points have opposite winding numbers.

Abstract

We analyze the nodal points in multi-orbital Fe-based superconductors from a topological perspective. We consider the $s^{+-}$ gap structure with accidental nodes, and the $d$-wave gap with nodes along the symmetry directions. In both cases, the nodal points can be moved by varying an external parameter, e.g., a degree of inter-pocket pairing. Eventually, the nodes merge and annihilate via a Lifshitz-type transition. We discuss the Lifshitz transition in Fe-based superconductors from a topological point of view. We show, both analytically and numerically, that the merging nodal points have winding numbers of opposite sign. This is consistent with the general reasoning that the total winding number is a conserved quantity in the Lifshitz transition.