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

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.

arXiv comment5 pages, 3 figures

References in corpus (24)

• Topological insulators and superconductors
• Classification of topological insulators and superconductors in three spatial dimensions
• Periodic table for topological insulators and superconductors
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Topological Superconductivity and Superfluidity
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Topology of Andreev Bound States with Flat Dispersion
• Edge modes, edge currents, and gauge invariance in $p_x+i{p}_y$ superfluids and superconductors
• Topological odd-parity superconductors
• Detecting the Majorana fermion surface state of ${}^3$He-B through spin relaxation
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Thermodynamic properties of thin films of superfluid 3He-A
• Fermion zero modes at the boundary of superfluid 3He-B
• Topological invariant for superfluid 3He-B and quantum phase transitions
• Strong Anisotropy in Spin Suceptibility of Superfluid 3He-B Film Caused by Surface Bound States
• Surface Majorana Cone of the Superfluid ${}^3$He B Phase
• Topological superfluid 3He-B in magnetic field and Ising variable
• Majorana surface states of superfluid 3He A- and B-phases in a slab
• Quantum impurity spin in Majorana edge fermions
• Superfluid 3He in a restricted geometry with a perpendicular magnetic field
• Majorana edge modes of superfluid 3He A-phase in a slab
• Majorana states and longitudinal NMR absorption in ${}^3$He-B film

Cited by in corpus (69)

• Topological superconductors: a review
• Topology of crystalline insulators and superconductors
• Majorana Fermions and Topology in Superconductors
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topology of nonsymmorphic crystalline insulators and superconductors
• Symmetry-Protected Majorana Fermions in Topological Crystalline Superconductors: Theory and Application to Sr2RuO4
• Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Topological Phase Transition without Gap Closing
• Interplay of topological phases in magnetic adatom-chains on top of a Rashba superconducting surface
• UPt${}_3$ as a Topological Crystalline Superconductor
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology
• Topological Properties of Time Reversal Symmetric Kitaev Chain and Applications to Organic Superconductors
• Classification of engineered topological superconductors
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Majorana Excitations, Spin- and Mass Currents on the Surface of Topological Superfluid ${}^3$He-B
• Möbius topological superconductivity in UPt${}_3$
• Topological phases of quasi-one-dimensional fermionic atoms with a synthetic gauge field
• Superconducting doped topological materials
• Paramagnetically induced gapful topological superconductors
• Andreev-Majorana bound states in superfluids
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Anisotropic magnetic responses of topological crystalline superconductors
• Majorana multipole response of topological superconductors
• Chiral Ising Gross-Neveu criticality of a single Dirac cone: A quantum Monte Carlo study
• ${}^3{P}_2$ Superfluids Are Topological
• Topology and symmetry of surface Majorana arcs in cyclic superconductors
• Mirror Majorana zero modes in spinful superconductors/superfluids -Non-Abelian braiding of integer quantum vortices-
• Magnetically robust topological edge states and flat bands
• Multifaceted properties of Andreev bound states: Interplay of symmetry and topology
• Magnetoelectrically-Tunable Andreev-Bound-State Spectra and Spin Polarization in P-Wave Josephson Junctions
• Symmetry protected vortex bound state in superfluid ${}^3$He B-phase
• New types of topological superconductors under local magnetic symmetries
• Odd-frequency pairing and Ising spin susceptibility in time-reversal invariant superfluids and superconductors
• Surface Majorana fermions and bulk collective modes in superfluid 3He-B
• Majorana vortex-bound states in three-dimensional nodal noncentrosymmetric superconductors
• Manipulation of Majorana Kramers Qubit and its Tolerance in Time-Reversal-Invariant Topological Superconductor
• Study of superfluid ${}^3$He under nanoscale confinement. A new approach to the investigation of superfluid ${}^3$He films
• Majorana multipole response: General theory and application to wallpaper groups
• Magnetic Response of Majorana Kramers Pairs Protected by Z2 Invariants
• Topological flat bands in optical checkerboard-like lattices
• Magnetic response of Majorana Kramers pairs with an order-two symmetry
• Review: Observation of Majorana Bound States at a Free Surface of ${}^3$He-B
• Symmetry conditions of a nodal superconductor for generating robust flat-band Andreev bound states at its dirty surface
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Appearance of flat surface bands in three-dimensional topological insulators in a ferromagnetic exchange field
• Spin-orbital polarization of Majorana edge states in oxides nanowires
• A-B transition in superfluid ${}^3$He and cosmological phase transitions
• Robustness of Gapless Interface State in a Junction of Two Topological Insulators
• Weyl Fermions and Broken Symmetry Phases of Laterally Confined ${}^3$He Films
• Topological matter: graphene and superfluid 3He
• Electric Multipoles of Double Majorana Kramers Pairs
• Anisotropic paramagnetic response of topological Majorana surface states in the superconductor ${\text{UTe}}_2$
• Continuous phase transitions between fractional quantum Hall states and symmetry-protected topological states
• On the Excitations of a Balian-Werthamer Superconductor
• Magnetic Susceptibility of Andreev Bound States in Superfluid ${}^3$He-B
• Three-dimensional symmetry breaking topological matters
• Locally gauge-invariant spin response of ${}^3$He-$B$ films with Majorana surface states
• Bosonic Surface States and Acoustic Spectroscopy of Confined Superfluid ${}^3$He-B
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Majorana multipole response with magnetic point group symmetry
• Nanofluidic platform for studying the first-order phase transitions in superfluid helium-3
• NMR-like effect on Anisotropic Magnetic Moment of Surface Bound States in Topological Superfluid ${}^3$He-B
• Majorana edge states and topological properties in 1D/2D Rashba semiconductor proximity coupled to iron-based superconductor
• Dimensional crossover of superfluid ${}^3$He in a magnetic field
• Euler band topology in superfluids and superconductors
• Influence of Magnetic Field on Surface Andreev Bound States in Superfluid ${}^3$He-B Studied by Mobility of Electron Bubble