Bogoliubov Fermi surfaces: General theory, magnetic order, and topology

TL;DR

This paper develops a comprehensive theory for Bogoliubov Fermi surfaces in inversion-symmetric, time-reversal-breaking superconductors with internal degrees of freedom, revealing their topological protection, microscopic models, and associated surface states.

Contribution

It introduces a general nonunitary pairing framework with a time-reversal-odd component, demonstrating the topological protection and microscopic realization of Bogoliubov Fermi surfaces.

Findings

Bogoliubov Fermi surfaces are topologically protected by a $Z_2$ invariant.

They are associated with a magnetization of low-energy states.

Surface spectra reveal additional topological indices.

Abstract

We present a comprehensive theory for Bogoliubov Fermi surfaces in inversion-symmetric superconductors which break time-reversal symmetry. A requirement for such a gap structure is that the electrons posses internal degrees of freedom apart from the spin (e.g., orbital or sublattice indices), which permits a nontrivial internal structure of the Cooper pairs. We develop a general theory for such a pairing state, which we show to be nonunitary. A time-reversal-odd component of the nonunitary gap product is found to be essential for the appearance of Bogoliubov Fermi surfaces. These Fermi surfaces are topologically protected by a $\mathbb{Z}_2$ invariant. We examine their appearance in a generic low-energy effective model and then study two specific microscopic models supporting Bogoliubov Fermi surfaces: a cubic material with a $j=3/2$ total-angular-momentum degree of freedom and a hexagonal material with distinct orbital and spin degrees of freedom. The appearance of Bogoliubov Fermi surfaces is accompanied by a magnetization of the low-energy states, which we connect to the time-reversal-odd component of the gap product. We additionally calculate the surface spectra associated with these pairing states and demonstrate that the Bogoliubov Fermi surfaces are characterized by additional topological indices. Finally, we discuss the extension of phenomenological theories of superconductors to include Bogoliubov Fermi surfaces, and identify the time-reversal-odd part of the gap product as a composite order parameter which is intertwined with superconductivity.