Phase Diagram of the Topological Superfluid
            <sup>3</sup>
            He Confined in a Nanoscale Slab Geometry

Levitin, L. V.; Bennett, Robert; Casey, A.; Cowan, Brian; Saunders, J.; Drung, D.; Schurig, T.; Parpia, J. M.

doi:10.1126/science.1233621

Cited by 101 publications

(197 citation statements)

References 46 publications

(58 reference statements)

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“…The surface roughness drastically changes the surface structure of order parameters and low-lying surface states in the superfluid 3 He-B [106,108,152,154]. The pair-breaking effect and the enhancement of the surface density of states due to the existence of the surface Andreev bound states have been observed in several experiments [109,110,271,112,113,114,115,116,117,118,155,156,157,158,159]. The contributions of surface Andreev bound states have also been detected through the deviation of the heat capacity from that in the bulk 3 He-B [160] as well as the anomalous attenuation of transverse sound wave [161].…”

Section: 3mentioning

confidence: 89%

“…At the weak coupling limit, the planar is energetically degenerate to the A-phase that is the time-reversal symmetry breaking phase with point nodes, while the strong coupling effect that is the spin-fluctuation feedback effect can stabilize the A-phase relative to the planar phase and the A-B phase boundary becomes the first order transition. The pair breaking effect and the enhancement of the surface density of states due to the surface bound state have been observed by several experiments, by using the NMR techniques [112,113,114,115,116,117,118,155,156,157], the motion of a vibrating wire resonator [158], transverse acoustic impedance [162,163,164,165,166,167,168,169], surface contributions of the heat capacity [160], and anomalous attenuation of transverse sound [161]. Among them, Murakawa et al [165,168] has observed the specularity dependence of the surface density of states by systematically controlling the surface specularity by coating the surface with 4 He layers.…”

Section: Thermodynamics In the Absence Of Dipole-dipole Interactionmentioning

confidence: 99%

“…Among them, Murakawa et al [165,168] has observed the specularity dependence of the surface density of states by systematically controlling the surface specularity by coating the surface with 4 He layers. More recently, the phase diagram was experimentally examined by using the well controlled confinement of nanofluidic samples [117]. Levitin et al [117] confined a sample of the liquid 3 He within a nanofluidic cavity of precisely defined geometry and utilized the SQUID-NMR technique that provides a fingerprint measurement for the order parameter distortion and phase diagram.…”

Section: Thermodynamics In the Absence Of Dipole-dipole Interactionmentioning

confidence: 99%

“…More recently, the phase diagram was experimentally examined by using the well controlled confinement of nanofluidic samples [117]. Levitin et al [117] confined a sample of the liquid 3 He within a nanofluidic cavity of precisely defined geometry and utilized the SQUID-NMR technique that provides a fingerprint measurement for the order parameter distortion and phase diagram. Further details on detecting surface states and their Majorana nature will be discussed in Sec.…”

Section: Thermodynamics In the Absence Of Dipole-dipole Interactionmentioning

confidence: 99%

“…This indicates that the topological phase transition from the time-reversal invariant B-phase to time-reversal breaking Aphase occurs at the critical value of the "thickness" even at zero pressures. Several experiments have observed the confinement-induced A-B phase transition in a slab geometry with a thickness comparable to the superfluid coherence length [109,110,271,112,113,114,115,116,117,118]. We introduce in Sec.…”

mentioning

confidence: 99%

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Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

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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.

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