Symmetry protected topological superfluid³He-B

Abstract

Abstract.Owing to the richness of symmetry and well-established knowledge on the bulk superfluidity, the superfluid 3 He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of 3 He in a multifaceted manner, including symmetry consideration, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the 3 He-B confined in a slab geometry. The 3 He-B under a magnetic field is separated to two different sub-phases: The symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered off by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnetic dipole interaction of 3 He nucleus. It is also demonstrated that odd-frequency evenparity Cooper pair amplitudes are emergent in low-lying quasiparticles. The key ingredients, symmetry protected Majorana fermions and odd-frequency pairing, bring an important consequence that the coupling of the surface states to an applied field is prohibited by the hidden discrete symmetry, while the topological phase transition with the spontaneous symmetry breaking is accompanied by anomalous enhancement and anisotropic quantum criticality of surface spin susceptibility. We also illustrate common topological features between topological crystalline superconductors and symmetry protected topological superfluids, taking UPt 3 and Rashba superconductors as examples.

Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials

“…In particular, there are now intensive efforts on classifying and studying TCI phases protected by various crystal symmetries (102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116), as well as superconducting analogs of TCIs (117,118,119,120). The role of crystal symmetry in protecting topological nodal semimetals has also been studied (121,122,123,124,125).…”

Measurements of the anisotropic mass of magnons confined in a harmonic trap in superfluid 3He-B

“…He-B is the topological superfluid with gapless Majorana fermions on the boundary (see recent review [1]). Optical magnons in a magneto-textural trap proved to be a useful and convenient experimental tool for studying various properties of superfluid 3 He-B.…”

P23superfluids are topological

“…Nontrivial topology embedded in bulk brings about topological quantization in transport and anomalous electromagnetic responses [1,2]. The topological viewpoint has also shed light on a new facet of unconventional superconductors/superfluids [3][4][5][6][7][8][9][10]. The key ingredient is Majorana fermions, which behave as non-abelian anyons [11,12] and possess Ising spins [13][14][15][16].…”