Morita, Kohmoto, and Maki Reply:

Morita, Yoshifumi; Kohmoto, Mahito; Maki, Kazumi

doi:10.1103/physrevlett.79.4514

Cited by 32 publications

(56 citation statements)

References 6 publications

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“…While the analysis in the quantum limit k F ξ ≈ 1 brings us the understanding of physics at extremely low temperatures, where the quantum effects becomes important, [17][18][19][20] the quasiclassical condition k F ξ ≫ 1 is satisfied in Sr 2 RuO 4 with a ξ 0 (the coherence length at low temperature) ≈ 660Å. 21) In this paper, we will study the structure of chiral p-wave vortices by adopting a more appropriate framework; the quasiclassical theory of superconductivity.…”

Section: )mentioning

confidence: 99%

Kramer–Pesch Effect in Chiral p-Wave Superconductors

Kato

Hayashi

2001

J. Phys. Soc. Jpn.

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The pair-potential and current density around a single vortex of the two-dimensional chiral p-wave superconductor with d = z (px ± ipy) are determined self-consistently within the quasiclassical theory of superconductivity. Shrinking of the vortex core at low temperatures are considered numerically and analytically. Temperature-dependences of the spatial variation of pair-potential and circular current around the core and density of states at zero energy are the same as those in the isotropic s-wave case. When the senses of vorticity and chirality are opposite, however, we find two novel results; 1) the scattering rate due to non-magnetic impurities is considerably suppressed, compared to that in the s-wave vortex. From this observation, we expect that the chiral p-wave superconductors provide the best chance to observe the shrinking of the vortex ("Kramer-Pesch effect") experimentally.2) The pair-potential of chiral p-wave superconductors inside vortex core recovers a combined time-reversal-Gauge symmetry, although this symmetry is broken in the region far from the vortex core. This local recovery of symmetry leads to the suppression of the impurity effect inside vortex core.KEYWORDS: Superconductivity, vortex, quasiclassical theory, Kramer-Pesch effect, chiral superconductors §1. IntroductionThe superconducting state in Sr 2 RuO 4 1) is expected to be unconventional; a Knight shift measurement in planar magnetic field suggests odd-parity pairing with d vector perpendicular to the RuO 2 plane.2) Muon spin relaxation experiment suggests spontaneous magnetization;3) this means that time-reversal symmetry is broken spontaneously in the superconducting state. The simplest pairing symmetry which is consistent with the above two experimental results and the tetragonal crystal symmetry is given by the odd-parity pairing with d =ẑ (p x ± ip y ).4) This is commonly called the "chiral p-wave superconducting state" because the Cooper pair has a definite angular momentum L z = ±1 in the internal motion. A singly quantized vortex is, on the other hand, a configuration of the pair-potential where the center-of-mass motion of Cooper pair has an angular momentum. The interplay between vorticity and chirality would bring about intriguing phenomena in vortex physics of Sr 2 RuO 4 . Indeed, several authors 5-8) have argued that the impurity effects in vortex core of chiral p-wave superconductor is considerably suppressed, compared to that in s-wave vortex core. The fact that the superclean regime is realized within the core of chiral pwave vortex has several implications. First, the flux flow conductivity is expected to be enhanced at low temperatures in the chiral p-wave vortex states.8) Second, a large Hall effect is also expected. Third, the shrinkage of vortex cores at low temperatures, which is referred to as "the Kramer-Pesch (KP) effect", 9) is free from the * E-mail: yusuke@phys.c.u-tokyo.ac.jp * * E-mail: hayashi@mp.okayama-u.ac.jp smearing due to impurities. The vortex shrinking effect in chiral p-wave superconductors i...

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Section: )mentioning

confidence: 99%

Kramer–Pesch Effect in Chiral p-Wave Superconductors

Kato

Hayashi

2001

J. Phys. Soc. Jpn.

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“…E so ∼10 3 K in these systems. Recently in [19], we have proposed that the triplet superconductors in non-centrosymmetric crystals should be like the one in 3 He-A 1 , in contrast to the previous proposals. The superconductivity occupies the Fermi surface associated with one spin component (say, up-spin) while the other Fermi surface remains in the normal state.…”

Section: Introductionmentioning

confidence: 76%

Triplet Superconductivity in a Nutshell

Maki

Morita

2008

J Supercond Nov Magn

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The triplet superconductors have been around us since 1980, when Jerome et al. discovered the Bechgaard salts (TMTSF) 2 PF 6 and (TMTSF) 2 ClO 4 . Now there are more than 20 or so triplet superconductors discovered. Recently we found that most of them with the known gap symmetries can be mapped to the superfluid phase of 3 He-A and 3 He-A 1 . Further, in most of them,l (the chiral vector, i.e. the quantization axis of the pair angular momentum) is fixed parallel to one of the crystal axes and all the topological defects are considered in terms ofd-textures, wherê d is the spin vector. Then Sr 2 RuO 4 , UPt 3 , PrOs 4 Sb 12 and (TMTSF) 2 ClO 4 belong to type-A, which is an analog of superfluid 3 He-A. In these superconductors, a vortex splits into a pair of half quantum vortices (HQVs) at low temperatures. On the other hand, CePt 3 Si, CeIrSi 3 , CeRhSi 3 , UIr and Li 2 Pt 3 B (those in non-centrosymmetric crystals) belong to type-A 1 , which is an analog of superfluid 3 He-A 1 . In all of these triplet superconductors, vortices harbor the zero mode or the Majorana fermions, the implications of which deserves further exploration.

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“…3. For PrOs 4 Sb 12 , the stability region of HQV (inside the line without circles) is shown [24], which is close to the phase (whose boundary is given by black circles) determined by Izawa et al [31]. T c /5) which can be accessible by STM, micromagnetometry and SANS.…”

Section: Discussionmentioning

confidence: 99%

“…Instead we consider that thê d-soliton or thed-domain wall is most readily created. As a consequence, half quantum vortices (HQV) are generated in type-A triplet superconductors [22][23][24]. Sincê l-vector is fixed parallel to the crystalineĉ-axis, we limit ourselves to the texture free energy associated with thê d-vector.…”

Section: Stability Region Of Half Quantum Vorticesmentioning

confidence: 99%

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New Paradigm of Triplet Superconductivity

Morita

Maki

2009

Acta Phys. Pol. A

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Since 1980, more than 10 or so triplet superconductors have been discovered. Now we can put them into two separate classes. Type A consists of e.g. (TMTSF) 2 PF 6 , (TMTSF) 2 ClO 4 , UPt 3 , Sr 2 RuO 4 , PrOs 4 Sb 12 . These triplet superconductors are characterized with the extreme smallness of the spin-orbit coupling energy E so ( ∆, where ∆ is the superconducting gap). Also like superfluid 3 He-A, the order parameter of these superconductors are characterized byl (the chiral vector) andd (the spin vector). In these superconductors, an Abrikosov vortex splits into a pair of half quantum vortices at low temperatures. Type A1 comprises most of non-centrosymmetric triplet superconductors discovered recently, e.g. CePt3Si, CeIrSi3, CeRhSi3, and Li2Pt3B. They are characterized byl andd1 + id2 like superfluid 3 He-A1. The spin-orbit coupling energy Eso is extremely large Eso ≈ 10 3 K. Therefore, as noted by Frigeri et al., the Fermi surface splits for the up-spin one and the down-spin one. However, contrary to Frigeri et al., the superconductivity should occupy only the larger Fermi surface (say for spin-up). The other Fermi surface remains in the normal state. Also in type A1 superconductors, an Abrikosov vortex does not split into a pair of half quantum vortices. Further all thase triplet superconductors (both type A and type A1) harbor the zero mode or the Majorana fermion attached to each vortex, of which implication should be further explored.

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Morita, Kohmoto, and Maki Reply:

Cited by 32 publications

References 6 publications

Kramer–Pesch Effect in Chiral p-Wave Superconductors

Kramer–Pesch Effect in Chiral p-Wave Superconductors

Triplet Superconductivity in a Nutshell

New Paradigm of Triplet Superconductivity

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