Ultrasonic absorption and thermal conduction in the mixed state of type-II superconductors

Vinen, W. F.; Forgan, E. M.; Gough, C.E.; Hood, M

doi:10.1016/0031-8914(71)90245-x

Cited by 55 publications

(37 citation statements)

References 38 publications

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“…Increasing the field decreases the intervortex spacing d 0 =H p and the states begin to overlap, forming dispersive bands which yield a conductivity that grows exponentially with the ratio of the vortex spacing to the coherence length d= , / H p exp ÿ H c2 =H p , where is a constant. This dependence is observed in simple s-wave superconductors such as Nb [23] for H c1 < H < H c2 =2, and is much different from that in nodal superconductors, where the conductivity is observed to increase as / H=H c2 p [19]. A fit of our data to the simple s-wave form is shown in Fig.…”

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confidence: 60%

Bulk Evidence for Single-Gaps-Wave Superconductivity in the Intercalated Graphite SuperconductorC6Yb

et al. 2007

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We report measurements of the in-plane electrical resistivity and thermal conductivity of the intercalated graphite superconductor C 6 Yb down to temperatures as low as T c =100. When a field is applied along the c axis, the residual electronic linear term 0 =T evolves in an exponential manner for H c1 < H < H c2 =2. This activated behavior is compelling evidence for an s-wave order parameter, and is a strong argument against the possible existence of multigap superconductivity. DOI: 10.1103/PhysRevLett.98.067003 PACS numbers: 74.70.Wz, 74.25.Fy, 74.25.Op Carbon is a remarkably versatile element -in its pure form it may exist as an electronic insulator, semiconductor, or semimetal depending on its bonding arrangement. When dopant atoms are introduced, superconductivity may be added to this list, observed in graphite [1,2], fullerenes [3], and even diamond [4]. Superconductivity in doped carbon was first discovered in the graphite intercalate compounds (GICs), materials composed of sheets of carbon separated by layers of intercalant atoms. The first of these compounds contained alkali atoms, and had modest transition temperatures of 0.13-0.5 K [1]. The recent discovery of T c 's two orders of magnitude higher than this in C 6 Yb [5] and C 6 Ca [5,6] has, however, refocused attention on this intriguing family of compounds.The effects of the intercalant atoms in the GICs are twofold: they dramatically change the electronic properties of the host graphite lattice by both increasing the separation of the carbon sheets, as well as contributing charge carriers. This causes the two-dimensional graphite bands to dip below the Fermi level. The graphite interlayer band, previously unoccupied, also crosses the new Fermi level, contributing three-dimensional, free-electron-like states located between the carbon sheets. This new interlayer band hybridizes strongly with the bands, and its occupation appears to be linked with the occurrence of superconductivity in the GICs [7].There are still several fundamental questions remaining about superconductivity in the GICs, especially in C 6 Yb and C 6 Ca, where little experimental data exist. The pairing mechanism is unresolved, with speculation ranging from a conventional route involving the intercalant phonons [8][9][10] to superconductivity via acoustic plasmons [7].Early theoretical studies motivated by the alkali-metal GICs [11,12] emphasized a two-gap model for the superconducting state, where gaps of different magnitudes exist on different sheets of the Fermi surface. Such a scenario is plausible, as there are notable similarities between the GICs and MgB 2 [7,13], a known multigap superconductor. Indeed, some aspects of graphite intercalate superconductivity can be understood by this two-gap phenomenology; however, there is little direct evidence to support this picture, and recent band structure calculations suggest this scenario is unlikely [14].A necessary starting point is to establish the superconducting order parameter, but in C 6 Yb, this task is complicated as th...

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confidence: 60%

Bulk Evidence for Single-Gaps-Wave Superconductivity in the Intercalated Graphite SuperconductorC6Yb

et al. 2007

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“…As the field is increased and the vortices are brought closer together, tunneling between states on adjacent vortices will cause some delocalization. This conduction is expected to grow exponentially with the ratio of intervortex separation to vortex core size (≃ ξ 0 ), namely as exp(−α H c2 /H), where α is a constant, as is found for Nb at fields below H c2 /3 [19].…”

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confidence: 72%

Highly Anisotropic Gap Function in Borocarbide SuperconductorLuNi2B2C

et al. 2001

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The thermal conductivity of borocarbide superconductor LuNi2B2C was measured down to 70 mK (Tc/200) in a magnetic field perpendicular to the heat current from H = 0 to above Hc2 = 7 T. As soon as vortices enter the sample, the conduction at T → 0 grows rapidly, showing unambiguously that delocalized quasiparticles are present at the lowest energies. The field dependence is very similar to that of UPt3, a heavy-fermion superconductor with a line of nodes in the gap, and very different from the exponential dependence characteristic of s-wave superconductors. This is strong evidence for a highly anisotropic gap function in LuNi2B2C, possibly with nodes.PACS numbers: 74.70. Dd, 74.25.Fy, 74.60.Ec The vast majority of known superconductors are characterized by an order parameter with s-wave symmetry and a gap function which is largely isotropic and without nodes (zeros). Only four families of materials are seriously thought to exhibit a superconducting state with a different symmetry: (1) [4]. A major outstanding question is the nature of the microscopic mechanism responsible for superconductivity in any of these materials. The unconventional symmetry of the order parameter is evidence for a pairing caused by purely electronic interactions and not mediated by phonons. For example, the proximity to magnetic order which is found in all four families of superconductors has led to the suggestion that spin fluctuations are responsible for Cooper pairing, as is thought to be the case in superfluid 3 He. The presence of nodes in the gap function is generally associated with unconventional (non-s-wave) symmetries. These nodes are typically inferred from the observation of quasiparticle excitations at energies much lower than the gap maximum ∆ 0 , as reflected for example in the power law temperature dependence of various physical properties, such as London penetration depth and ultrasonic attenuation at T ≪ T c . Another way of detecting low-energy quasiparticles is to excite them by applying a magnetic field which introduces vortices in the material, so that the superfluid flow around each vortex Doppler shifts the quasiparticle energy. In certain limits, the quasiparticle response is the same whether induced by a thermal energy k B T or by a field energy ≃ ∆ 0 B/B c2 , where B c2 ≃ H c2 , the upper critical field [5].In this Letter, we turn our attention to another class of superconductors: the borocarbides LNi 2 B 2 C (where L = Y, Lu, Tm, Er, Ho, and Dy) [6]. It has generally been thought that these materials are described by an order parameter with s-wave symmetry and pairing which proceeds via the electron-phonon coupling [7][8][9]. However, there is recent evidence for low-energy excitations in the superconducting state, whether from the anomalous field dependence of the specific heat [10,11] and the microwave surface impedance [11,12], or from the presence of scattering below the gap in Raman measurements [13]. This has been interpreted in terms of an anisotropic s-wave gap [10,11] (see also reference [14]).Here w...

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“…Maki thus predicted an infinite slope near//c2 which, indeed, was observed experimentally for very pure niobium. 6 He also derived a relation for the anisotropy of the transport quantities. …”

Section: Thermal Conductivity Near He2mentioning

confidence: 99%

Thermal conductivity of niobium in the mixed state

Kes¹,

Veeken²,

Klerk³

1975

J Low Temp Phys

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The magnetic field dependence of the thermal conductivity of four niobium samples in the mixed state has been investigated at several temperatures and three different field orientations. The samples are of moderate purity, that is, le ~ GO" At low temperatures, just above Hc~, the phonon conductivity can be easily separated. Good agreement is obtained with qualitative predictions of Canel and Vinen for the scattering of phonons by flux lines. At high temperatures both the phonons and the electrons are scattered by the flux lines. Though it is evident that the scattering mechanism is more effective in the case that H _L VT than for H tl VT, only a qualitative discussion can be given. Near HoE the finite slopes of the 2(H) curves are in qualitative agreement with the gapless superconductivity theory of Caroli and Cyrot, but the dependence on the electron mean free path can be better understood from the theory of pure type II superconductors of Houghton and Maki. Some aspects of pure type II superconductivity are also recognized in the anisotropic behavior near Hc2.

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Ultrasonic absorption and thermal conduction in the mixed state of type-II superconductors

Cited by 55 publications

References 38 publications

Bulk Evidence for Single-Gaps-Wave Superconductivity in the Intercalated Graphite SuperconductorC6Yb

Bulk Evidence for Single-Gaps-Wave Superconductivity in the Intercalated Graphite SuperconductorC6Yb

Highly Anisotropic Gap Function in Borocarbide SuperconductorLuNi2B2C

Thermal conductivity of niobium in the mixed state

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