Observation of Surface Andreev Bound States of Superfluid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi>He</mml:mi><mml:mprescripts /><mml:none /><mml:mn>3</mml:mn></mml:mmultiscripts></mml:math>by Transverse Acoustic Impedance Measurements

Aoki, Yuki; Wada, Yuji; Saitoh, Masafumi; Nomura, R.; Okuda, Y.; Nagato, Yasushi; Yamamoto, Mikio; Higashitani, Seiji; Nagai, Katsuhiko

doi:10.1103/physrevlett.95.075301

Cited by 75 publications

(81 citation statements)

References 23 publications

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“…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%

“…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]. The surface acoustic impedance measurement provides another powerful tool to probe the surface structure [162,163,164,165,166,167,168]. The spectrum of the surface bound states and its dependence on surface condition has been investigated by measuring surface acoustic impedance [165,168,169].…”

Section: 3mentioning

confidence: 99%

“…The surface density of states has a very sharp edge at E = ∆ * that is smaller than the bulk energy gap ∆ 0 . The temperature dependence of the complex impedance observed two different energy scales ∆ * and ∆ 0 [162,163,164,165,166,167,168,169] as a kink and peak in Z ′ (T ) and Z ′′ (T ). The remarkable point is that the surface specularity is controllable by coating the wall of the transducer with thin layers of 4 He.…”

Section: Transverse Acousticsmentioning

confidence: 99%

“…Using the AC-cut quartz transducers immersed in liquid 3 He, Aoki et al [162] measured the complex transverse acoustic impedance of the superfluid 3 He-B. The impedance is defined as the ratio of the shear stress Π xz to the wall velocity u x , Z = Z ′ + iZ ′′ ≡ Π xz /u x , where the surface is set to be in the x-y plane.…”

Section: Transverse Acousticsmentioning

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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Section: Thermodynamics In the Absence Of Dipole-dipole Interactionmentioning

confidence: 99%

Section: 3mentioning

confidence: 99%

Section: Transverse Acousticsmentioning

confidence: 99%

Section: Transverse Acousticsmentioning

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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“…21) We have demonstrated in earlier publications that Z is a unique surface probe for SABS in superfluid 3 He and have provided the spectroscopic details of SDOS. 17,[21][22][23] Figure 2 presents the measured ZðT Þ as a function of the normalized energy h " !=ÁðT Þ. ÁðT Þ is the superfluid gap energy at T obtained from the weak-coupling-plus model; 12) thus, a higher (lower) energy corresponds to a higher (lower) temperature. Z 0 is the normal state value of Z just above the transition temperature T c .…”

mentioning

confidence: 99%

Surface Majorana Cone of the Superfluid ³He B Phase

et al. 2011

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The superfluid3 He B phase, one of the oldest unconventional fermionic condensates experimentally realized, is recently predicted to support Majorana fermion surface states. Majorana fermion, which is characterized by the equivalence of particle and antiparticle, has a linear dispersion relation referred to as the Majorana cone. We measured the transverse acoustic impedance Z of the superfluid 3 He B phase changing its boundary condition and found a growth of peak in Z on a higher specularity wall. Our theoretical analysis indicates that the variation of Z is induced by the formation of the cone-like dispersion relation and thus confirms the important feature of the Majorana fermion in the specular limit. KEYWORDS: superfluid3 He, surface Andreev bound states, Majorana fermions, Majorana cone, acoustic impedanceSurface Andreev bound states (SABS) of the superfluid 3 He B phase are receiving renewed attention as ''edge states'' of a three-dimensional (3D) time reversal invariant topological superfluid.1-9) Topological superfluids and superconductors are characterized by a non-trivial topological number in the gapped bulk state and a gapless edge state on their edges or surfaces. SABS of the superfluid 3 He B phase can be regarded as Majorana fermions as they satisfy the Majorana condition, i.e., a particle and its antiparticle are equivalent, because the degrees of freedom of the bound states are halved. When a surface is specular, linear dispersions are predicted for Majorana fermions, 10) which have been recently referred to as a Majorana cone. 4,5) We measured the transverse acoustic impedance Z of the superfluid 3 He B phase changing its boundary condition up to practically specular scattering. The observed variation of Z is well reproduced by theoretical analysis and is shown to be induced by the formation of the cone-like dispersion relation of SABS at higher specularities. This provides an evidence of the existence of the Majorana cone in superfluid 3 He B in the specular limit. Superfluid 3 He is a well established spin-triplet p-wave superfluid where the B phase is the realization of the BalianWerthamer state, which breaks the relative spin-orbit symmetry.11,12) The surface Majorana states of the 3 He B phase should exhibit peculiar features such as a surface spin current and an anisotropic magnetic response.5,7-9) Under the specular scattering boundary condition of the surface, SABS with a finite energy are not degenerate, and have a dispersion relation linear to the momentum, which takes the shape of a 2D cone for massless Dirac fermions. In the spin-triplet p-wave pairing system, the annihilation operator of the negative energy state is equivalent to the creation operator of the positive energy state. Hence, only the positive energy cone, which is called a Majorana cone, is physical.4,5) To date, Majorana surface fermion states have been discussed mostly on smooth surfaces (specular scattering limit). However, intriguing problems are to elucidate how the Majorana cone transforms as the roughness of th...

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