Surface Andreev bound states of superfluid 3He and Majorana fermions

Transport of bound quasiparticle states in a two-dimensional boundary superfluid

The B phase of superfluid 3He can be cooled into the pure superfluid regime, where the thermal quasiparticle density is negligible. The bulk superfluid is surrounded by a quantum well at the boundaries of the container, confining a sea of quasiparticles with energies below that of those in the bulk. We can create a non-equilibrium distribution of these states within the quantum well and observe the dynamics of their motion indirectly. Here we show that the induced quasiparticle currents flow diffusively in the two-dimensional system. Combining this with a direct measurement of energy conservation, we conclude that the bulk superfluid 3He is effectively surrounded by an independent two-dimensional superfluid, which is isolated from the bulk superfluid but which readily interacts with mechanical probes. Our work shows that this two-dimensional quantum condensate and the dynamics of the surface bound states are experimentally accessible, opening the possibility of engineering two-dimensional quantum condensates of arbitrary topology.

Nonlinear two-level dynamics of quantum time crystals

A time crystal is a macroscopic quantum system in periodic motion in its ground state. In our experiments, two coupled time crystals consisting of spin-wave quasiparticles (magnons) form a macroscopic two-level system. The two levels evolve in time as determined intrinsically by a nonlinear feedback, allowing us to construct spontaneous two-level dynamics. In the course of a level crossing, magnons move from the ground level to the excited level driven by the Landau-Zener effect, combined with Rabi population oscillations. We demonstrate that magnon time crystals allow access to every aspect and detail of quantum-coherent interactions in a single run of the experiment. Our work opens an outlook for the detection of surface-bound Majorana fermions in the underlying superfluid system, and invites technological exploitation of coherent magnon phenomena – potentially even at room temperature.

Recent work has reported a realization of a time crystal in the form of the Bose-Einstein condensate of magnons in superfluid ³He. Here, the authors study the dynamics of a pair of such quantum time crystals and show that it closely resembles the evolution of a two-level system, modified by nonlinear feedback.

Fragility of surface states in topological superfluid 3He

Superfluid ³He, with unconventional spin-triplet p-wave pairing, provides a model system for topological superconductors, which have attracted significant interest through potential applications in topologically protected quantum computing. In topological insulators and quantum Hall systems, the surface/edge states, arising from bulk-surface correspondence and the momentum space topology of the band structure, are robust. Here we demonstrate that in topological superfluids and superconductors the surface Andreev bound states, which depend on the momentum space topology of the emergent order parameter, are fragile with respect to the details of surface scattering. We confine superfluid ³He within a cavity of height D comparable to the Cooper pair diameter ξ₀. We precisely determine the superfluid transition temperature T_c and the suppression of the superfluid energy gap, for different scattering conditions tuned in situ, and compare to the predictions of quasiclassical theory. We discover that surface magnetic scattering leads to unexpectedly large suppression of T_c, corresponding to an increased density of low energy bound states.

Surface states in topological quantum matter are protected by their band structure. Here, on confined superfluid ³He as a model for topological superconductors, the authors report experimental evidence on the fragility of surface Andreev bound states with respect to the details of surface scattering.

Fundamental dissipation due to bound fermions in the zero-temperature limit

The ground state of a fermionic condensate is well protected against perturbations in the presence of an isotropic gap. Regions of gap suppression, surfaces and vortex cores which host Andreev-bound states, seemingly lift that strict protection. Here we show that in superfluid 3He the role of bound states is more subtle: when a macroscopic object moves in the superfluid at velocities exceeding the Landau critical velocity, little to no bulk pair breaking takes place, while the damping observed originates from the bound states covering the moving object. We identify two separate timescales that govern the bound state dynamics, one of them much longer than theoretically anticipated, and show that the bound states do not interact with bulk excitations.

Andreev bound states in superconducting films and confined superfluid 3He

This paper reviews confinement-driven phase transitions in superconductors and Bardeen-Cooper-Schrieffer superfluids, and the appearance in thin films of new phases that break the time-reversal or translational symmetry. The origins of the new phases are closely tied to the Andreev scattering processes involving particle-hole conversions that create surface quasiparticle states with energies inside the superconducting gap. Restructuring of the low-energy spectrum in the surface region of several coherence lengths ξ₀ results in large spatial variations of the superconducting order parameter. In confined geometry, such as slabs, films, pores or nano-dots, with one or more physical dimensions D∼10ξ₀, the Andreev bound states can dominate properties of a superconductor, leading to modified experimental signatures. They can significantly change the energy landscape, and drive transitions into new superconducting phases. The new phases are expected in a variety of materials, from singlet d-wave superconductors to multi-component triplet superfluid ³He, but properties of the new phases will depend on the symmetry of the parent state. I will highlight the connection between the Andreev surface states and confinement-stabilized phases with additional broken symmetries, describe recent progress and open questions in the theoretical and experimental investigation of superfluids in confined geometry.This article is part of the theme issue 'Andreev bound states'.

Multifaceted properties of Andreev bound states: interplay of symmetry and topology

Andreev bound states (ABSs) ubiquitously emerge as a consequence of non-trivial topological structures of the order parameter of superfluids and superconductors and significantly contribute to thermodynamics and low-energy quantum transport phenomena. We here share the current status of our knowledge on their multifaceted properties such as Majorana fermions and odd-frequency pairing. A unified concept behind ABSs originates from a soliton state in the one-dimensional Dirac equation with mass domain wall and interplay of ABSs with symmetry and topology enrich their physical characteristics. We make an overview of ABSs with a special focus on superfluid 3He. The quantum liquid confined to restricted geometries serves as a rich repository of noteworthy quantum phenomena, such as the mass acquisition of Majorana fermions driven by spontaneous symmetry breaking, topological quantum criticality, Weyl superfluidity and the anomalous magnetic response. The marriage of the superfluid 3He and nano-fabrication techniques will take one to a new horizon of topological quantum phenomena associated with ABSs.This article is part of the theme issue 'Andreev bound states'.

Scattering Theory on Surface Majorana Fermions by an Impurity in ^{3}He-B

We have formulated the scattering theory on Majorana fermions emerging in the surface bound state of the superfluid ^{3}He B phase (^{3}He-B) by an impurity. By applying the theory to the electron bubble, which is regarded as the impurity, trapped below a free surface of ^{3}He-B, the observed mobility of the electron bubble [J. Phys. Soc. Jpn. 82, 124607 (2013)JUPSAU0031-901510.7566/JPSJ.82.124607] is quantitatively reproduced. The mobility is suppressed in low temperatures from the expected value in the bulk ^{3}He-B by the contribution from the surface Majorana fermions. By contrast, the mobility does not depend on the trapped depth of the electron bubble in spite of the spatial variation of the wave function of the surface Majorana fermions. Our formulated theory demonstrates the depth-independent mobility by considering intermediate states in the scattering process. Therefore, we conclude that the experiment has succeeded in observing Majorana fermions in the surface bound state.

Spin-dependent acoustic response in the nonunitary A1 and A2 phases of superfluid 3He under high magnetic fields

The transverse acoustic impedance of superfluid ^{3}He was measured in the A1 and A2 phases up to 13 T to investigate the surface states in nonunitary superfluids. The temperature dependence of the impedance was much larger in the A1 phase than in the A2 phase. This nonsymmetric behavior indicates that momentum exchange with walls for spin-down surface states is quite different from that for spin-up surface states. The spin-dependent response might be a reflection of an essential feature of the nonunitary states where gap amplitudes depend on spin states. Weak-coupling theories ignore any spin-dependent processes and do not account for the nonsymmetric behavior.