Superfluid 3He in a restricted geometry with a perpendicular magnetic field

Abstract

We theoretically investigate the role of surface Andreev bound states (SABSs) on the phase diagram and spin susceptibilities of superfluid 3He confined to a restricted geometry. We first explicitly derive the dispersion of the SABS in 3He-B in the presence of a magnetic field, where the Majorana Ising spin and the spin susceptibility contributed from the SABS are associated with the SO(3) order parameter manifold. Subsequently, based on the quasiclassical Eilenberger theory with Fermi liquid corrections, we discuss the nonlinear effect of a magnetic field on the SABS, where the magnetic field is perpendicular to the specular surface. It is directly demonstrated that a gapped SABS strongly enhances the magnetization density and spin susceptibility at the surface, compared with that in the normal 3He. To capture the characteristics of the SABS, we show the field- and temperature-dependences of the spatially averaged susceptibility which is detectable through NMR experiments. It turns out that the contribution of the SABS leads to nonmonotonic temperature-dependence of the spin susceptibility. Furthermore, we present the superfluid phase diagram, where the B-phase undergoes a first-order (second-order) phase transition to A-phase or planar phase at low (high) temperatures.

18 pages, 12 figures

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• Superfluid phases of ${}^3$He in nano-scale channels
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• Ultra-Low Dissipation Superfluid Micromechanical Resonator
• Topology and symmetry of surface Majorana arcs in cyclic superconductors
• ${}^3{P}_2$ Superfluids Are Topological
• Multifaceted properties of Andreev bound states: Interplay of symmetry and topology
• Symmetry protected vortex bound state in superfluid ${}^3$He B-phase
• Odd-frequency pairing and Ising spin susceptibility in time-reversal invariant superfluids and superconductors
• Hard domain walls in superfluid 3He-B
• Critical endpoint and universality class of neutron ${}^3{P}_2$ superfluids in neutron stars
• Review: Observation of Majorana Bound States at a Free Surface of ${}^3$He-B
• New Phases of Superfluid ${}^3$He Confined in Aerogels
• Weyl Fermions and Broken Symmetry Phases of Laterally Confined ${}^3$He Films
• Anisotropic paramagnetic response of topological Majorana surface states in the superconductor ${\text{UTe}}_2$
• Surface scattering effect and the stripe order in films of the superfluid ${}^3$He B phase
• Magnetic Susceptibility of Andreev Bound States in Superfluid ${}^3$He-B
• Planar and Nematic Aerogels: DLCA and Superfluid 3He
• Anomalous Thermal Hall Effect in Chiral Phases of ${}^3$He-Aerogel
• Dimensional crossover of superfluid ${}^3$He in a magnetic field
• Quasiclassical theory of spin dynamics in superfluid ${}^3$He: kinetic equations in the bulk and spin response of surface Majorana states
• Influence of Magnetic Field on Surface Andreev Bound States in Superfluid ${}^3$He-B Studied by Mobility of Electron Bubble