Measurement of the Fundamental Length Scales in the Vortex State ofYBa2Cu3O6.60

Abstract

The internal field distribution in the vortex state of YBa 2 Cu 3 O 6.60 is shown to be a sensitive measure of both the magnetic penetration depth l ab and the vortex-core radius r 0 . The temperature dependence of r 0 is found to be weaker than in the conventional superconductor NbSe 2 and much weaker than theoretical predictions for an isolated vortex. The effective vortex-core radius decreases sharply with increasing H, whereas l ab ͑H͒ is found to be much stronger than in NbSe 2 . [S0031-9007 (97)04251-8] PACS numbers: 74.60.Ec, 74.72.Bk, 76.75. + iThe magnetic penetration depth l and the coherence length j are the two fundamental length scales in a superconductor. l is directly related to the superfluid density n s , whereas j is the length scale for spatial variations in the superconducting order parameter. In recent years, measurements of l have provided strong evidence for unconventional pairing in the high-T c materials in that there are line nodes in the superconducting energy gap. In particular, in both the Meissner and vortex states, l has been observed to increase linearly with temperature T [1,2] and magnetic field H [3,4] at low T in single crystals of YBa 2 Cu 3 O 6.95 .Much less is known about the behavior of j. In fact, until now there has been no measurement of j deep in the superconducting state of a high-T c superconductor. The magnitude of j near the phase boundary has been estimated from measurements of the upper critical field H c2 using Ginzburg-Landau (GL) theory. For a type-II superconductor for H near H c2 , the coherence length is related to H c2 ͑T ͒ in GL theory byReliable estimates of j in YBa 2 Cu 3 O 72d made in this way are extremely difficult because the value of H c2 at T 0 is so large (i.e., ϳ100 T). Consequently, H c2 measurements are limited to high temperatures above T ͞T c ϳ 0.85, so that the low T behavior of j͑T͒ can be determined only by extrapolation. The situation is further complicated in the high-T c compounds by strong thermal fluctuations over a sizable region near T c which result in broad transitions and poor estimates of H c2 ͑T ͒. Furthermore, Eq. (1) may not be valid for an unconventional superconductor.It is desirable to have direct measurements of the coherence length, which in the vortex state is related to the size of the vortex cores. In particular, for a conventional superconductor j ϳ r 0 , where r 0 is the vortex-core radius [5]. In principle, both scanning tunneling microscopy (STM) and muon spin rotation (mSR) can be used to characterize the size of vortex cores and thereby determine j directly deep in the superconducting state. Recent STM [6] and mSR [7] measurements on NbSe 2 show that r 0 decreases with increasing H, as a result of the increased interaction between vortices. Similar studies on high-T c materials have not yet been performed with STM. Pinning of the vortices due to surface roughness and oxygen vacancies eliminates the long-range order in the vortex lattice and results in variations in the electronic structure of the cores. Further...

Impurity Effect on Kramer-Pesch Core Shrinkage in s-Wave Vortex and Chiral p-Wave Vortex

“…On the other hand, we expect that rather weak shrinkings of vortex core observed in NbSe 2 (Refs. 26,28,29,30) and CeRu 2 (Ref. 32) may be explained partly in terms of the impurity effect, i.e., the vortex core shrinkage approximately linear in T with moderate curvature and its saturation towards a finite value in zero-temperature limit ( Fig.…”

“…Recently, µSR experiments were performed on the s-wave superconductor NbSe 2 to observe the KP effect. 26,28,29,30 The experimental data of spin precessions, which correspond to the Fourier transformation of the Redfield pattern (the magnetic field distribution) of a vortex lattice, are fitted by a theoretical formula, 31 extracting the information on the spatial profile of the supercurrent density j(r) around vortices. 26,28 While a shrinking vortex core was observed, it was weaker than the theoretical expectation of the KP effect for a clean superconductor.…”

Nanoscopic Coexistence of Magnetism and Superconductivity inYBa2Cu3OSanna1, Allodi2, Concas3 et al. 2004Phys. Rev. Lett.139151505View full textAdd to dashboardCite

“…It may well, since the coherence length [21,22] is ξ ≈ 80 − 200Å for x = 0.60 − 0.57, much larger than the characteristic length scale of the SC stripes mentioned above. Although the presence of SC below T f might be retrieved from µSR lineshape analysis, as it was attempted by modeling the complex internal field distribution in a single crystal [9], this is beyond the scope of our polycrystalline data and we reverted directly to SQUID magnetization measurements.…”

Concepts in High Temperature Superconductivity

“…However, it can be inferred indirectly [98][99][100][101][102] in various ways, and for the most part people have concluded that ξ 0 is approximately 2 or 3 lattice constants in typical optimally doped materials. This has lead many people to conclude that these materials are nearly in a "real space pairing" limit [103][104][105][106][107], in which pairs of holes form actual two particle bound states, and then Bose condense at T c .…”