Two-dimensional fluctuations close to the zero-field transition ofBi2Sr2CaCu

Abstract

The ac-conductivity along the CuO2-layers of epitaxial films and single crystals of thicknesses 0.2µm≤ Lz ≤130µm reveals clear signatures for 2D-ordering. In particular, at Tc the screening length assumes the universal value LzΛT c /2νs predicted by the Kosterlitz-Thouless theory, which indicates that binding of long vortex strings nucleates long-range superconductivity in the present samples containing up to 10 5 CuO2-layers. Several details of the order-parameter dynamics remain unexplained.PACS numbers: 74.40.+k, 74.25.Fy, 74.72.Hs The layered structure of the high-T c oxide superconductors (HTSC) promotes the formation of topological exitations which may reduce T c to temperatures significantly below the mean-field value T c0 , where a finite Cooper-pair density n In order to provide a deeper insight into the ordering process in bulk (N ≫ 1) samples of the strongly layered HTSC Bi 2 Sr 2 CaCu 2 O 8 , where γ > ∼ 100, we present here a first study of the linear ac-conductivity σ(ω) in the highly conducting and fluctuating regime below T c0 . By scaling analyses, we determine static screening length λ 2 ± associated with superconducting and normal fluctuations above and below T c , respectively. For all temperatures above T c , λ 2 + provides quantitative evidence for 2D-ordering in the single crystals and the epitaxial film under study of thicknesses L z between 0.2µm and 130µm, and the dynamical shape of σ(ω) is described assuming 2D-fluctuations of the order parameter Ψ. At T c , the effective penetration depth 2λ 2 (T c )/L z agrees with the universal length associated with the KT transition. The high, universal value of the phase angle at T c , σ ′′ /σ ′ = 13.5 (1) 5 CuO 2 -planes, signatures of 3D-ordering appear only at temperatures below T c .Our inductive method for determining high ac conductivities from the measured linear magnetic susceptibility χ(ω) = χ ′ + iχ ′′ has been outlined before for bulk [14] and thin film [12] samples. Exact numerical relations between χ(ω) and σ(ω) = σ ′ + iσ ′′ were derived by E.H. Brandt for disks of arbitrary thickness [15], and using a complex inversion scheme, we evaluated σ(ω). We examine here a 0.2µm thick film epitaxially grown for SQUID fabrication [16] and crystalline discs of thicknesses between 13µm and 130µm, which were cleaved from the same crystal grown by L. Winkeler [17]. One of the great advantages of investigations of σ(ω) lies in the possibility of a precise determination of the onset for long-range superconductivity at the temperature where the frequency variation of the phase angle, d(σ ′′ /σ ′ )/dω, changes its sign [18].The first of such results for Bi 2 Sr 2 CaCu 2 O 8 are depicted in Fig.1 showing well defined intersections of the phase, i.e. d(σ ′′ /σ ′ )/dω = 0. Several novel features are seen. Despite the rather different T c 's of crystal and film, both attain there the same value of the phase angle, ϕ c ≡ arctan(σ ′′ /σ ′ ) Tc = 85.9 0 (8), in zero magnetic field. Since we observed the same value also on many other Bi 2 Sr 2 CaCu 2 O 8 ...

Short-wavelength cutoff effects in the ac fluctuation conductivity of superconductors

“…In the dc limit (Ω → 0), one finds that S 2 → 0, and S 1 leads to the dc result of Eq. (8). One can also verify that the ac results obtained previously by Schmidt 20 and Dorsey 22 can be recovered from our Eq.…”

“…As already discussed in the previous section, this implies that finite nonzero σ 1 (T c ) and σ 2 (T c ) can be obtained only for z = 2 (relaxational model). Since the available experimental data in anisotropic high-T c superconductors 6,7,8 show finite nonzero σ 1 (T c ) and σ 2 (T c ), we can adopt z = 2 in the remainder of this section.…”

“…At higher temperatures the conductivity σ 1 at any frequency behaves asymptotically as σ dc given by Eq. (8).…”

“…3,4,5,6,7,8,9,10,11,12,13,14 Most of them used dc resistivity measurements. 3,4,5,9,10,11,12,13,14 The reports were controversial in the conclusions about the dimensionality of the system, and the critical exponents.…”

Pinning of Vortices and Linear and Nonlinear Ac Susceptibilities in High-T c Superconductors

“…r -u l' + u (56) where E(k) and K(k) are elliptic functions with argument k = J4ul'/(r + u). Combining this with Faraday's induction law one finds the equations of motion for J in strips and disks, (strip), (57) (disk), (58) where now the unit length is a and T = /1oad/(2rrp) is a time constant which in general depends on J via p(J).…”