Theory of Nuclear Spin Relaxation in Superconductors

Hebel, L. C.

doi:10.1103/physrev.116.79

Cited by 114 publications

(60 citation statements)

References 5 publications

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“…Because of the inevitable damping effect of quasiparticles in real materials, here, N s (E) and M s (E) are averaged over an energy broadening function, assuming a rectangle shape with a width 2δ and a height 1/2δ. 9 In Fig. 3, it is observed that a theoretical curve based on an isotropic s-wave model is actually in good agreement with the experiment using 2∆(0)/k B T c = 4.4 and δ/∆ = 0.25, as shown by the solid curve.…”

supporting

confidence: 67%

Conventional s-Wave Superconductivity in Noncentrosymmetric Ir₂Ga₉: ⁷¹Ga-NQR Evidence

et al. 2009

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Superconductivity without spatial inversion symmetry has begun to attract much attention since the discovery of the superconductor CePt 3 Si.1 It is presumed that the absence of spatial inversion symmetry causes an admixture between even and odd parities of superconducting pairing due to antisymmetric spin-orbit coupling (ASOC).2 However, there has been no clear evidence of the admixture thus far, and hence the spatial noncentrosymmetric effect on superconductivity remains experimentally controversial. Recently, ASOC has also been discussed in transition-metal superconductors. In this system, we can consider ASOC without strongly correlated electron systems, which would be appropriate for tracing the effect of ASOC. Interestingly, in Li 2 Pt 3 B, it was reported that unconventional superconductivity with a line node and a spin-triplet pairing state emerge, which are ascribed to ASOC.3, 4 These reports suggest that ASOC can induce a novel superconducting state even though there is no strong electron correlation.The intermetallic binary Ir 2 Ga 9 does not possess spatial inversion symmetry and becomes superconducting below T c = 2.2 K.5, 6 Specific heat and resistivity measurements showed that the compound is a weak-coupling BCS superconductor with an isotropic gap, and located near the boundary between type-I and type-II superconductivities with an upper critical field H c2 ∼ 150 Oe. 5, 6In this letter, we report on the characteristics of superconductivity in noncentrosymmetric Ir 2 Ga 9 probed by 71 Ga-nuclear-quadrupole-resonance (NQR) measurement at a zero field (H = 0). The spatial noncentrosymmetric effect on the superconducting state is discussed.A single crystal of Ir 2 Ga 9 was grown by the Ga flux method.6 Powder X-ray diffraction indicated that the compound forms in the primitive monoclinic Rh 2 Ga 9 type structure.6, 7 The sample of Ir 2 Ga 9 was crushed into coarse powder for NQR measurement to allow the penetration of the rf field. The NQR measurement was performed by the conventional spin-echo method in the temperature (T ) range of 1-280 K. T 1 was measured at f ∼ 26.45 MHz, which was the 1ν Q (±1/2 ↔ ±3/2) transition of 71 Ga (I = 3/2), as shown in Fig. 1. The NQR

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confidence: 67%

Conventional s-Wave Superconductivity in Noncentrosymmetric Ir₂Ga₉: ⁷¹Ga-NQR Evidence

et al. 2009

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“…13 We use δ/∆(0) = 0.3 in the calculation. A theoretical curve based on the multigap model is actually in good agreement with the experiment using β = 0.75 and 2∆ β /k B T c = 5 for the main band, and α = 0.25 and 2∆ α /k B T c = 2 for other bands as shown by the solid curve in Fig.…”

Section: Abstract: Lanthanoid Carbide Metal Superconductivity Multmentioning

confidence: 99%

“…We report on the superconducting (SC) properties of Y2C3 with a relatively high transition temperature Tc = 15.7 K investigated by 13 C nuclear-magnetic-resonance (NMR) measurements under a magnetic field. The 13 C Knight shift has revealed a significant decrease below Tc, suggesting a spin-singlet superconductivity.…”

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Multigap Superconductivity in Y₂C₃: A ¹³C-NMR Study

et al. 2007

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We report on the superconducting (SC) properties of Y2C3 with a relatively high transition temperature Tc = 15.7 K investigated by 13 C nuclear-magnetic-resonance (NMR) measurements under a magnetic field. The 13 C Knight shift has revealed a significant decrease below Tc, suggesting a spin-singlet superconductivity. From an analysis of the temperature dependence of the nuclear spin-lattice relaxation rate 1/T1 in the SC state, Y2C3 is demonstrated to be a multigap superconductor that exhibits a large gap 2∆/kBTc = 5 at the main band and a small gap 2∆/kBTc = 2 at other bands. These results have revealed that Y2C3 is a unique multigap s-wave superconductor similar to MgB2.KEYWORDS: lanthanoid carbide, metal, superconductivity, multigap, NMR, Y2C3The discovery of superconductivity in MgB 2 , which exhibits a high superconducting (SC) transition temperature T c ∼ 40 K, has attracted much interest.1 Motivated by this discovery, intensive effort is devoted to the search for a new high-T c material in a similar system that contains light elements B and C. Meanwhile, Amano et al. reported that Y 2 C 3 prepared under high pressure (∼ 5 GPa) is a superconductor with a relatively high T c ∼ 18 K, 2 although the superconductivity in this compound was already reported to emerge at T c ∼ 6−11 K.3 As for SC characteristics, the specific heat measurements on the newly synthesized high-purity samples of Y 2 C 3 have revealed that a gap size of the respective samples with T c = 11.6, 13.6, and 15.2 K increases as 2∆/k B T c =3.6, 4.1, and 4.4.4 This result raises a question why T c and 2∆/k B T c vary significantly depending on sintering conditions. Further systematic experiments are required to gain deep insight into the SC characteristics of this compound.Y 2 C 3 crystallizes in the cubic Pu 2 C 3 -type structure (space group I43d) without an inversion center, consisting of the dimers of carbon atoms. The SC properties of the sample previously reported by Amano et al. did not exhibit a single SC transition as seen in the inset of Fig. 1(a), pointing to a contamination of extrinsic multiple phases.2 Recently, Akutagawa et al. have succeeded in preparing a single phase of Y 2 C 3 , which enables us to extract intrinsic electronic and SC properties in Y 2 C 3 . From the specific-heat measurements of this sample, the Sommerfeld coefficient γ ∼ 6.3 mJ/mol·K 2 and Debye temperature θ D ∼ 530 K were estimated for the sample with T c = 15.2 K.4 This result suggests that its high Debye temperature makes T c relatively high despite its small Sommerfeld coefficient. As in MgB 2 , the lightelement constituent like boron and carbon plays a vital role in enhancing T c in general. In the SC state, the temperature (T ) dependence of the specific heat exhibits an exponential decrease with 2∆/k B T c = 4.4 upon cooling well below T c , suggesting a strong-coupling isotropic su- * E-mail address: aharada@nmr.mp.es.osaka-u.ac.jp perconductivity. From an other context, it is noteworthy that a novel SC nature for CePt 3 Si and Li 2 Pt 3 B without ...

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“…In the full-gap case, we averaged N i S ðEÞ at approximately E $ Á i ðTÞ with the width 2 i [< Á i ðTÞ] in order to reduce the size of the coherence peak. 27,28) Here, Á i ðTÞ is the SC gap; for simplicity, the (; ') dependence is given by Á i ðT; ; 'Þ ¼ Á i ðTÞ cos for the nodal gap and by Á i ðT; ; 'Þ ¼ Á i ðTÞ for the full gap. A concrete function for the average N i S ðEÞ is described in ref.…”

mentioning

confidence: 99%

“…A concrete function for the average N i S ðEÞ is described in ref. 27. This procedure corresponds to the anisotropy of the SC gaps or finite lifetime of Cooper pairs arising from pair breaking.…”

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confidence: 99%

Possible Multiple Gap Superconductivity with Line Nodes in Heavily Hole-Doped Superconductor KFe₂As₂ Studied by ⁷⁵As Nuclear Quadrupole Resonance and Specific Heat

et al. 2009

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We report the 75 As nuclear quadrupole resonance (NQR) and specific heat measurements of the heavily hole-doped superconductor KFe 2 As 2 (superconducting transition temperature T c ' 3:5 K). The spin-lattice relaxation rate 1=T 1 in the superconducting state exhibits a gradual temperature dependence with no coherence peak below T c . The quasiparticle specific heat C QP =T shows a small jump, which is about 30% of the electronic specific heat coefficient just below T c . The C QP =T suggests the existence of low-energy quasiparticle excitation at the lowest measurement temperature T ¼ 0:4 K ' T c =10. The T dependences of 1=T 1 and C QP =T can be explained by a multiple nodal superconducting gap scenario rather than by a multiple fully gapped s AE -wave scenario determined using simple gap analysis.

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Theory of Nuclear Spin Relaxation in Superconductors

Cited by 114 publications

References 5 publications

Conventional s-Wave Superconductivity in Noncentrosymmetric Ir₂Ga₉: ⁷¹Ga-NQR Evidence

Conventional s-Wave Superconductivity in Noncentrosymmetric Ir₂Ga₉: ⁷¹Ga-NQR Evidence

Multigap Superconductivity in Y₂C₃: A ¹³C-NMR Study

Possible Multiple Gap Superconductivity with Line Nodes in Heavily Hole-Doped Superconductor KFe₂As₂ Studied by ⁷⁵As Nuclear Quadrupole Resonance and Specific Heat

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Theory of Nuclear Spin Relaxation in Superconductors

Cited by 114 publications

References 5 publications

Conventional s-Wave Superconductivity in Noncentrosymmetric Ir2Ga9: 71Ga-NQR Evidence

Conventional s-Wave Superconductivity in Noncentrosymmetric Ir2Ga9: 71Ga-NQR Evidence

Multigap Superconductivity in Y2C3: A 13C-NMR Study

Possible Multiple Gap Superconductivity with Line Nodes in Heavily Hole-Doped Superconductor KFe2As2 Studied by 75As Nuclear Quadrupole Resonance and Specific Heat

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Conventional s-Wave Superconductivity in Noncentrosymmetric Ir₂Ga₉: ⁷¹Ga-NQR Evidence

Conventional s-Wave Superconductivity in Noncentrosymmetric Ir₂Ga₉: ⁷¹Ga-NQR Evidence

Multigap Superconductivity in Y₂C₃: A ¹³C-NMR Study

Possible Multiple Gap Superconductivity with Line Nodes in Heavily Hole-Doped Superconductor KFe₂As₂ Studied by ⁷⁵As Nuclear Quadrupole Resonance and Specific Heat