Broadening of the surface Andreev bound states band of superfluid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mtext>H</mml:mtext><mml:mprescripts /><mml:none /><mml:mn>3</mml:mn></mml:mmultiscripts><mml:mtext>e-</mml:mtext><mml:mi>B</mml:mi></mml:mrow></mml:math>on a partially specular wall

Wada, Yuji; Murakawa, Satoshi; Tamura, Yasutaka; Saitoh, Masafumi; Aoki, Yuki; Nomura, R.; Okuda, Y.

doi:10.1103/physrevb.78.214516

Cited by 34 publications

(44 citation statements)

References 31 publications

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“…If one temporary neglects the Zeeman fields H, our system is invariant under the mirror reflection with respect to the zx-plane, as well as the time-reversal, as shown in Eq. (164). Once the Zeeman fields are applied, the mirror symmetry is lost, but a combination of the mirror reflection and the time-reversal is still preserved if H y = 0.…”

Section: Promising Examples Of Topological Crystalline Superconductorsmentioning

confidence: 99%

“…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%

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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: Promising Examples Of Topological Crystalline Superconductorsmentioning

confidence: 99%

Section: Thermodynamics In the Absence Of Dipole-dipole Interactionmentioning

confidence: 99%

Section: 3mentioning

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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“…The surface roughness can be controlled experimentally by coating the surface with 4 He atoms [30]. The angular momenta L MJ and L cont can be suppressed by the different rates as a function of the surface roughness.…”

mentioning

confidence: 99%

Edge mass current and the role of Majorana fermions inA-phase superfluid3He

Machida

2012

Phys. Rev. B

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The total angular momentum associated with the edge mass current flowing at the boundary in the superfluid 3 He A-phase confined in a disk is proved to be L = N /2, consisting of L MJ = N from the Majorana quasi-particles (QPs) and L cont = −N /2 from the continuum state. We show it based on an analytic solution of the chiral order parameter for quasi-classical Eilenberger equation. Important analytic expressions are obtained for mass current, angular momentum, and density of states (DOS). Notably the DOS of the Majorana QPs is exactly N0/2 (N0: normal state DOS) responsible for the factor 2 difference between L MJ and L cont . The current decreases as E −3 against the energy E, and L(T ) ∝ −T 2 . This analytic solution is fully backed up by numerically solving the Eilenberger equation. We touch on the so-called intrinsic angular momentum problem. The superfluid is a paradigmatic and fertile testing ground to investigate the central questions concerning the origin of anisotropic superfluidity since the p-wave pairing symmetry for the 3 He A-phase and B-phase is firmly established [1]. Recently the topological aspect of the 3 He A-and B-phases has become a focus because there has been no other concrete topological superfluids or superconductors established so far. The topological superfluid defined by a topological number [2]. At an edge of the superfluid 3 He faced to a topologically trivial vacuum, a superfluid gap is closed by a topological phase transition at the interface. The surface Andreev bound state of Majorana Fermions must appear [3]. The topological features are quite different in the 3 He A-and B-phases. The 3 He A-phase is a chiral superfluid with the spontaneous edge mass current while B-phase is a helical superfluid with the edge spin current [4]. The Majorana nature for the A-and B-phases is also distinctive; Majorana Fermions have the surface Andreev bound state with linear dispersion relation centered at the zero energy forming a "Majorana valley" in the A-phase [4,5] and a "Majorana cone" in the B-phase [6][7][8]. This Majorana cone is emerging by recent experiments [9,10]. However, there has been no firm evidence for detecting the Majorana zero mode. We are still in the process to better characterize this elusive quasi-particle.The edge mass current spontaneously generated at the boundary in the superfluid 3 He A-phase is carried both by the Majorana quasi-particles (QPs) within the energy gap and by QPs in the continuum state outside the gap. Those two kinds of QPs play a different role for the edge mass current and associated total angular momentum L of the whole system, such as a disk. Stone and Roy [11] proved that in the A-phase the magnitude of the total angular momentum by the edge mass current is N /2 at the zero temperature (N is the total number of 3 He atoms in disk geometry).Here we pose problems on what amount of this mass current or the angular momentum L carried by the Majorana QPs and the remaining continuum state. It will turn out that exactly L MJ = N for Majorana QPs and L...

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