Topological nodal Cooper pairing in doped Weyl metals

TL;DR

This paper explores how topological properties of Fermi surfaces in doped Weyl metals influence Cooper pairing, leading to topologically protected nodal structures and novel pairing symmetries related to monopole charges.

Contribution

It introduces a topological framework for understanding Cooper pairing in Weyl metals, revealing monopole structures in pairing Berry phases and their impact on gap functions.

Findings

Pairing gap functions exhibit topologically protected nodal vortices.

Lowest pairing channel has angular momentum j=|q_p| with holomorphic gap functions.

Nodal structures behave as Weyl-Majorana points in the Bogoliubov-de Gennes Hamiltonian.

Abstract

We generalize the concept of Berry connection of the single-electron band structure to the two-particle Cooper pair states between two Fermi surfaces with opposite Chern numbers. Because of underlying Fermi surface topology, the pairing Berry phase acquires non-trivial monopole structure. Consequently, pairing gap functions have the topologically-protected nodal structure as vortices in the momentum space with the total vorticity solely determined by the monopole charge $q_p$. The pairing nodes behave as the Weyl-Majorana points of the Bogoliubov-de Gennes pairing Hamiltonian. Their relation with the connection patterns of the surface modes from the Weyl band structure and the Majorana surface modes inside the pairing gap is also discussed. Under the approximation of spherical Fermi surfaces, the pairing symmetry are represented by monopole harmonic functions. The lowest possible pairing channel carries angular momentum number $j=|q_p|$, and the corresponding gap functions are holomorphic or anti-holomorphic functions on Fermi surfaces.