On the Excitations of a Balian-Werthamer Superconductor

TL;DR

This paper reviews the excitation spectra and phenomenology of the Balian-Werthamer superconductor, highlighting its topological properties, collective modes, and experimental signatures relevant for superfluid $^3$He-B and potential electronic analogs.

Contribution

It provides a comprehensive reflection on the excitation spectra and topological features of the Balian-Werthamer state, connecting superfluid $^3$He-B to electronic superconductors.

Findings

Identification of collective modes via NMR, acoustic, and microwave spectroscopies

Topological nature leads to gapless Majorana modes at boundaries

Signatures of BW state in acoustic and electromagnetic responses

Abstract

My contribution to this collection of articles in honor of David Lee and John Reppy on their 90th birthdays is a reflection on the remarkable phenomenology of the excitation spectra of superfluid $^3$He, in particular the B-phase which was identified by NMR and acoustic spectroscopy as Balian-Werthamer state shown in 1963 to be the ground state of a spin-triplet, p-wave superconductor within weak-coupling BCS theory. The superfluid phases of $^3$He provide paradigms for electronic superconductors with broken space-time symmetries and non-trivial ground-state topology. Indeed broken spin- and orbital rotation symmetries lead to a rich spectrum of collective modes of the order parameter that can be detected using NMR, acoustic and microwave spectroscopies. The topology of the BW state implies its low-temperature, low-energy transport properties are dominated by gapless Majorana modes confined on boundaries or interfaces. Given the central role the BW state played I discuss the acoustic and electromagnetic signatures of the BW state, the latter being relevant if an electronic analog of superfluid $^3$He-B is realized.