Surface Bound States in Superfluid <sup>3</sup>He

Nagai, Katsuhiko; Nagato, Yasushi; Yamamoto, Mikio; Higashitani, Seiji

doi:10.1143/jpsj.77.111003

Cited by 56 publications

(115 citation statements)

References 43 publications

(71 reference statements)

Supporting

Mentioning

108

Contrasting

Order By: Relevance

“…[130,131,132,133,134,135,136,137,138,139,140,141,142] with the Ginzburg-Landau theory and Refs. [71,75,76,105,106,107,108,143,144] with the quasiclassical theory. The latter underlines the role of the surface Andreev bound states on thermodynamics.…”

Section: 3mentioning

confidence: 99%

“…There have been numerous works on the effect of surface roughness that causes diffusive scattering of quasiparticles [145,146,147,148,149,150,151,152,153]. 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].…”

Section: 3mentioning

confidence: 99%

See 1 more Smart Citation

Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

View full text Add to dashboard Cite

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.

show abstract

Section: 3mentioning

confidence: 99%

Section: 3mentioning

confidence: 99%

Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

View full text Add to dashboard Cite

show abstract

“…However, Nagato et al 17) found that this sub-gap also occurs when the order parameter is assumed to be spatially constant. Although the existence of the sub-gap played a decisive role in the interpretation of the transverse acoustic impedance of the B phase of superfluid 3 He, [20][21][22][23] the origin of the sub-gap has been a puzzle for a long time.…”

Section: -19)mentioning

confidence: 99%

“…16,17,23) The surface is characterized by an S-matrix for the quasiparticles at the Fermi level in the normal state…”

Section: -19)mentioning

confidence: 99%

See 1 more Smart Citation

Subgap in the Edge States of Two-Dimensional Chiral Superconductor with Rough Surface

2011

Self Cite

View full text Add to dashboard Cite

We discuss the rough surface effects on a two-dimensional chiral kx + iky superconductor. The atomic scale roughness at the surface is considered using the random S matrix model. The roughness effects on the self-consistent order parameter, the surface mass current and the surface density of states are studied using the quasi-classical theory. We find that the surface mass current is suppressed by the surface roughness. The surface density of states shows a quite similar behavior to that of superfluid 3 He B phase. When the surface is specular, the surface Andreev bound states form a band which fills the bulk energy gap ∆ bulk . When the surface becomes diffusive, there occurs a sharp upper edge of the surface bound states band and there opens a sub-gap between the edge and the bulk energy gap. We show that this sub-gap is induced by the repulsion between the surface bound states and the propagating Bogoliubov quasi-particles through the second order process of roughness.KEYWORDS: 2-D Chiral Superconductor, Edge States, Surface Demsity of States, Superfluid 3 He-BThe 2-dimensional chiral k x + ik y state is known as a model system for Sr 2 RuO 4 superconducting state. 1)When there is a surface along the y axis, there occur gapless surface Andreev bound states as in other p-waveand d-wave 4) pairing systems, because the k x component of the order parameter changes its sign under the surface reflection. The surface bound states in chiral system are known to carry spontaneous mass flow along the surface.5, 6) Recently, surface bound states are recognized as edge states which reflect the topological nature of the bulk pairing state. A lot of attention has been paid to the surface Andreev bound states from this aspect. 6-15)In this paper, we consider the effects of atomic scale surface roughness on the chiral k x + ik y state. We use the quasi-classical theory 16,17) developed for the study of pwave Fermi superfluids. We calculate the self-consistent order parameter, the surface mass current and the surface density of states. The surface density of states shows quite a similar behavior to that in the 3-dimensional BW state.17) Existence of the order parameter component parallel to the surface disperses the surface bound state energy. The bound states, therefore, form a band below the bulk energy gap ∆ bulk . When the surface is specular, the band completely fills the bulk energy gap. When the surface becomes diffusive, however, there occurs a sharp upper edge of the band and there opens a sub-gap between the edge and the bulk energy gap. The band edge energy ∆ * increases as the roughness is reduced. Similar sub-gap has been known in the BW state. 17-19)The sub-gap was first reported by Zhang 18) who treated the surface roughness using the thin dirty layer model. He suggested that the sub-gap is due to the suppression of the parallel component of the order parameter by the roughness. However, Nagato et al. 17) found that this sub-gap also occurs when the order parameter is assumed to be spatially constant. Although t...

show abstract

Observation of Majorana Quasiparticles’ Edge States in Superfluid 3He

Bunkov

Gazizulin

2014

Appl Magn Reson

View full text Add to dashboard Cite

We suggest in this article the nuclear magnetic resonance (NMR) method of observation and investigations of Majorana fermions at the edge of Topological Insulator, superfluid 3 He-B. The Majorana fermions form the remarkable quantum state of condensed matter where particle-like and antiparticle (holelike) excitations are indistinguishable. They have been observed recently by deviation of the temperature dependence of the superfluid 3 He-B heat capacity from the well-known exponential law for Bogoliubov quasiparticles at the world limit of ultra-low temperatures. The experimental data are well described by adding the heat capacity of Majorana quasiparticles' edge states with zero energy gap. We report here the results of the similar experiments with extended temperature range down to 125 lK. The possible way to detect these states by means of NMR is also discussed.

show abstract

Surface Bound States in Superfluid ³He

Cited by 56 publications

References 43 publications

Symmetry protected topological superfluid³He-B

Symmetry protected topological superfluid³He-B

Subgap in the Edge States of Two-Dimensional Chiral Superconductor with Rough Surface

Observation of Majorana Quasiparticles’ Edge States in Superfluid 3He

Contact Info

Product

Resources

About

Surface Bound States in Superfluid 3He

Cited by 56 publications

References 43 publications

Symmetry protected topological superfluid3He-B

Symmetry protected topological superfluid3He-B

Subgap in the Edge States of Two-Dimensional Chiral Superconductor with Rough Surface

Observation of Majorana Quasiparticles’ Edge States in Superfluid 3He

Contact Info

Product

Resources

About

Surface Bound States in Superfluid ³He

Symmetry protected topological superfluid³He-B

Symmetry protected topological superfluid³He-B