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

Nagato, Yasushi; Higashitani, Seiji; Nagai, Katsuhiko

doi:10.1143/jpsj.80.113706

Cited by 20 publications

(27 citation statements)

References 28 publications

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“…Á B . Recently, Nagato et al 306) elucidated the physical origin of the subgap Á Ã which is a consequence of the level repulsion between the bound states and scattering states. The two different energy scales, Á Ã and Á B , were observed as a kink and peak in the complex impedance ZðTÞ.…”

Section: Observations Of Surface Bound States In 3 He-bmentioning

confidence: 99%

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

et al. 2016

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In this article, we give a comprehensive review of recent progress in research on symmetry-protected topological superfluids and topological crystalline superconductors, and their physical consequences such as helical and chiral Majorana fermions. We start this review article with the minimal model that captures the essence of such topological materials. The central part of this article is devoted to the superfluid 3 He, which serves as a rich repository of novel topological quantum phenomena originating from the intertwining of symmetries and topologies. In particular, it is emphasized that the quantum fluid confined to nanofabricated geometries possesses multiple superfluid phases composed of the symmetry-protected topological superfluid B-phase, the A-phase as a Weyl superfluid, the nodal planar and polar phases, and the crystalline ordered stripe phase. All these phases generate noteworthy topological phenomena, including topological phase transitions concomitant with spontaneous symmetry breaking, Majorana fermions, Weyl superfluidity, emergent supersymmetry, spontaneous edge mass and spin currents, topological Fermi arcs, and exotic quasiparticles bound to topological defects. In relation to the mass current carried by gapless edge states, we also briefly review a longstanding issue on the intrinsic angular momentum paradox in 3 He-A. Moreover, we share the current status of our knowledge on the topological aspects of unconventional superconductors, such as the heavy-fermion superconductor UPt 3 and superconducting doped topological insulators, in connection with the superfluid 3 He.In Sect. 3, we will share the topological aspect of a spinpolarized chiral p-wave superconducting state as a specific model having nontrivial w 2d ¼ Ch 1 . Topology subject to discrete symmetriesNaively, any one-dimensional closed loop S 1 cannot cover the target space S 2 . Thus, a generic 2 Â 2 Hamiltonian in one dimension cannot provide a stable topological structure. However, discrete symmetries of H in Eq. (3) impose strong constraints on the spinorm, and thus nontrivial topological numbers can be introduced even in one dimension, as illustrated below.Particle-hole symmetry C 2 ¼ þ1 (class D)-Let us first suppose that the minimal Hamiltonian (13) holds the PHS C ¼ x K (C 2 ¼ þ1). The operation of PHS changes the spinor mðkÞ to ½Àm x ðÀkÞ; Àm y ðÀkÞ;m z ðÀkÞ. For the momentum space characterized by S 2 , there are two particle-hole invariant momenta, k ¼ 0 and jkj ¼ 1, where the infinite points are identical to a single point. At the particle-hole invariant momenta, the spinorm must point to the north or south pole on S 2 . Therefore, we have two different situations: One is that the spinorsm at k ¼ 0 and jkj ¼ 1 point in the same direction,m z ð0Þ ¼m z ð1Þ; ð26Þ Fig. 3. (Color online) Target spaces M subject to discrete symmetries T and C. Possible trajectories ofm on M with C 2 ¼ þ1 are also depicted.Fig. 24. (Color online) Low-lying quasiparticle spectra for the axisymmetric w-vortex (a) and v-vortex (b) with k z ¼ 0 and ...

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Section: Observations Of Surface Bound States In 3 He-bmentioning

confidence: 99%

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

et al. 2016

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“…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%

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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“…Despite the fact that previous studies revealed important aspects of these phenomena [84][85][86], there is still a need for systematic study and quantitative predictions. The purpose of this study is to evaluate the influence of the degree of diffusive electron scattering at interfaces in p-wave superconductors on the DoS.…”

Section: Introductionmentioning

confidence: 99%

Anomalous surface states at interfaces inp-wave superconductors

et al. 2014

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We present the results of theoretical study of surface state properties in a two-dimensional model for triplet p-wave superconductors. We derive boundary conditions for Eilenberger equations at rough interfaces and develop the approach for self-consistent solution for the spatial dependence of px and px + i py -wave pair potentials. In the px case we demonstrate the robustness of the zero-energy peak in the density of states (DoS) with respect to surface roughness, in contrast to the suppression of such a peak in the case of dxy symmetry. This effect is due to stability of oddfrequency pairing state at the surface with respect to disorder. In the case of the chiral px + i py state we demonstrate the appearance of a complex multi-peak subgap structure in the spectrum with increasing surface roughness.

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

Cited by 20 publications

References 28 publications

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

Symmetry protected topological superfluid³He-B

Anomalous surface states at interfaces inp-wave superconductors

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

Cited by 20 publications

References 28 publications

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to3He—

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to3He—

Symmetry protected topological superfluid3He-B

Anomalous surface states at interfaces inp-wave superconductors

Contact Info

Product

Resources

About

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

Symmetry protected topological superfluid³He-B