Symmetry Protected Topological Order and Spin Susceptibility in Superfluid 3He-B

TL;DR

This paper demonstrates that superfluid 3He-B maintains a topological phase protected by symmetry under a magnetic field, with gapless surface Majorana fermions and observable spin susceptibility changes during a quantum phase transition.

Contribution

It reveals the existence of a symmetry protected topological order in superfluid 3He-B under magnetic fields and characterizes the associated quantum phase transition and surface spin behavior.

Findings

Surface Majorana fermions remain gapless due to symmetry protection.

Quantum phase transition involves spontaneous symmetry breaking.

Surface spin susceptibilities exhibit anisotropic criticality detectable by NMR.

Abstract

We here demonstrate that the superfluid 3He-B under a magnetic field in a particular direction stays topological due to a discrete symmetry, that is, in a symmetry protected topological order. Due to the symmetry protected topological order, helical surface Majorana fermions in the B phase remain gapless and their Ising spin character persists. We unveil that the competition between the Zeeman magnetic field and dipole interaction involves anomalous quantum phase transition where topological phase transition takes place together with spontaneous breaking of symmetry. Based on the quasiclassical theory, we illustrate that the phase transition is accompanied by anisotropic quantum criticality of spin susceptibilities on the surface, which is detectable in NMR experiments.