A Polar State in a Slab as a Soluble Model of p-Wave Fermi Superfluid in Finite Geometry

Hara, Junichiro; Nagai, Katsuhiko

doi:10.1143/ptp.76.1237

Cited by 144 publications

(40 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[162][163][164]167,171) Studies on the confinement effect and phase diagram were followed by numerous works based on the quasiclassical theory. 47,48,73,74,80,158,293,295,296) These works underline the role of the surface Andreev bound states in thermodynamics. Boundary conditions that describe quasiparticle scattering from an atomically rough surface were developed in several ways.…”

Section: He In a Slab Geometry: Overviewmentioning

confidence: 93%

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

et al. 2016

View full text Add to dashboard Cite

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 ...

show abstract

Section: He In a Slab Geometry: Overviewmentioning

confidence: 93%

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

et al. 2016

View full text Add to dashboard Cite

show abstract

“…The current density is negative for 8 < x/ξ 0 , is positive for 6 < x/ξ 0 < 8, and is negative again for 0 < x/ξ 0 < 6. Figure 7(b) shows that the spatial dependence of the current components j 23 , j 43 , and j 34 are responsible for such a complicated current profile. We note that j 21 and j 32 (not shown) have almost the same profile as j 34 .…”

Section: Disk With a Specular Surfacementioning

confidence: 99%

Spontaneous edge current in a small chiral superconductor with a rough surface

Suzuki

Asano

2016

Phys. Rev. B

View full text Add to dashboard Cite

We study theoretically the spontaneous edge current in a small chiral superconductor with surface roughness. We obtained self-consistent solutions of the pair potential and the vector potential by solving the quasiclassical Eilenberger equation and the Maxwell equation simultaneously. We then employed them to calculate numerically the spatial distribution of the chiral edge current in a small superconductor. The characteristic behavior of the spontaneous edge current depends strongly on the symmetries of the order parameters such as chiral p-, chiral d-, and chiral f -wave pairing. The edge current is robust under the surface roughness in the chiral p-and chiral d-wave superconductors. In the chiral d-wave case, the surface roughness tends to flip the direction of the chiral current. On the other hand, the edge current in a chiral f -wave superconductor is fragile when there is surface roughness. We also discuss the temperature dependence of a spontaneous magnetization, which is a measurable value in standard experiments.

show abstract

“…(3) satisfy s + s − = −1 for all the propagating channels. Therefore, such an unconventional superconductor hosts dispersionless ZESs at its clean surface [21][22][23][24][25]. The effects of the flat ZESs on the conductance depend on the parity of the pair potential.…”

Section: Conductance Minimummentioning

confidence: 99%

“…(9). It is well known that the self-consistently calculated pair potential is suppressed near the interface as (x) = tanh(x/ξ 0 ) [22,[40][41][42] in p x -, d xy , and f cases, where ξ 0 = v F /π is the coherence length in a superconductor. We have numerically confirmed that the conductance under such suppressed pair potential shows the same limiting behaviors as those in Fig.…”

Section: Atiyah-singer Indexmentioning

confidence: 99%

Quantization of conductance minimum and index theorem

et al. 2016

View full text Add to dashboard Cite

We discuss the minimum value of the zero-bias differential conductance G min in a junction consisting of a normal metal and a nodal superconductor preserving time-reversal symmetry. Using the quasiclassical Green function method, we show that G min is quantized at (4e 2 /h)N ZES in the limit of strong impurity scatterings in the normal metal at the zero temperature. The integer N ZES represents the number of perfect transmission channels through the junction. An analysis of the chiral symmetry of the Hamiltonian indicates that N ZES corresponds to the Atiyah-Singer index in mathematics.

show abstract

A Polar State in a Slab as a Soluble Model of p-Wave Fermi Superfluid in Finite Geometry

Cited by 144 publications

References 1 publication

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

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

Spontaneous edge current in a small chiral superconductor with a rough surface

Quantization of conductance minimum and index theorem

Contact Info

Product

Resources

About

A Polar State in a Slab as a Soluble Model of p-Wave Fermi Superfluid in Finite Geometry

Cited by 144 publications

References 1 publication

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

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

Spontaneous edge current in a small chiral superconductor with a rough surface

Quantization of conductance minimum and index theorem

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—