Surface Majorana fermions and bulk collective modes in superfluid 3He-B

Abstract

The theoretical study of topological superfluids and superconductors has so far been carried out largely as a translation of the theory of noninteracting topological insulators into the superfluid language, whereby one replaces electrons by Bogoliubov quasiparticles and single-particle band Hamiltonians by Bogoliubov-de Gennes Hamiltonians. Band insulators and superfluids are, however, fundamentally different: while the former exist in the absence of inter-particle interactions, the latter are broken symmetry states that owe their very existence to such interactions. In particular, unlike the static energy gap of a band insulator, the gap in a superfluid is due to a dynamical order parameter that is subject to both thermal and quantum fluctuations. In this work, we explore the consequences of bulk quantum fluctuations of the order parameter in the $B$ phase of superfluid ${}^3$He on the topologically protected Majorana surface states. Neglecting the high-energy amplitude modes, we find that one of the three spin-orbit Goldstone modes in ${}^3$He-$B$ couples to the surface Majorana fermions. This coupling in turn induces an effective short-range two-body interaction between the Majorana fermions, with coupling constant inversely proportional to the strength of the nuclear dipole-dipole interaction in bulk ${}^3$He. A mean-field theory estimate of the value of this coupling suggests that the surface Majorana fermions in ${}^3$He-$B$ are in the vicinity of a quantum phase transition to a gapped time-reversal symmetry breaking phase.

References in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
• Classification of topological insulators and superconductors in three spatial dimensions
• Thermodynamic properties of thin films of superfluid 3He-A
• Symmetry Protected Topological Order and Spin Susceptibility in Superfluid 3He-B
• Surface Majorana Cone of the Superfluid ${}^3$He B Phase
• Majorana surface states of superfluid 3He A- and B-phases in a slab
• Surface Specific Heat of ${}^3$He and Andreev Bound States
• Gauge-field fluctuations in 3D topological Mott insulators
• Anomalous Attenuation of Transverse Sound in 3He
• Phase structure of a three-dimensional Yukawa model
• Effect of thermal fluctuations in topological p-wave superconductors

Cited by in corpus (8)

• Three-Dimensional Majorana Fermions in Chiral Superconductors
• Majorana-Hubbard model on the square lattice
• Chiral Ising Gross-Neveu criticality of a single Dirac cone: A quantum Monte Carlo study
• Triangular pair density wave in confined superfluid ${}^3$He
• Low-temperature environments for quantum computation and quantum simulation
• Surface State Dissipation in Confined 3He-A
• Locally gauge-invariant spin response of ${}^3$He-$B$ films with Majorana surface states
• Interacting Majorana modes at surfaces of noncentrosymmetric superconductors