Magnetic field induced 3D to 1D crossover in type II superconductors

We review and analyze magnetization and specific heat investigations on type-II superconductors which uncover remarkable evidence for the magnetic field induced finite size effect and the associated 3D to 1D crossover which enhances thermal fluctuations. Indeed, the correlation length transverse to the magnetic field Hi, applied along the i-axis, cannot grow beyond the limiting magnetic length LHi = (Φ0/ (aHi)) , related to the average distance between vortex lines. Noting that 1D is incompatible with the occurrence of a continuous phase transition at finite temperatures, the mean-field transition lineHC2 (T ) is replaced by the 3D to 1D crossover line Hp (T ). Since the magnetic field induced finite size effect relies on thermal fluctuations and there enhancement originating from the 3D to 1D crossover, its observability is not be restricted to type-II superconductors with small correlation volume only, including YBa2Cu4O8, NdBa2Cu3O7−δ, YBa2Cu3O7−δ , and DyBa2Cu3O7−δ, where 3D-xy critical behavior was already observed in zero field. Indeed, our analysis of the reversible magnetization of RbOs2O6 and the specific heat of Nb77Zr23, Nb3Sn and NbSe2 reveals that even in these low Tc superconductors with comparatively large correlation volume the 3D to 1D crossover is observable in sufficiently high magnetic fields. Consequently, below Tc and above Hpi (T ) superconductivity is confined to cylinders with diameter LHi(1D) and there is no continuous phase transition in the (H, T ) plane along the Hc2 (T ) line as predicted by the mean-field treatment. Moreover we observe that the thermodynamic vortex melting transition occurs in the 3D regime. While in YBa2Cu4O8, NdBa2Cu3O7−δ, YBa2Cu3O7−δ, and DyBa2Cu3O7−δ it turns out to be driven by 3D-xy thermal fluctuations, the specific heat data of the conventional type-II superconductors Nb77Zr23, Nb3Sn and NbSe2 point to Gaussian fluctuations. Because the vortex melting and the 3D-1D crossover line occur at universal values of the scaling variable their relationship is universal. PACS numbers: 74.25.Bt, 74.25.Ha, 74.40.+k Magnetic field induced 3D to 1D crossover in type II superconductors 2 The phenomenology of superconductivity is based on the Ginzburg-Landau theory [1], which provides the starting functional for the free energy for the charged superconductor coupled to electromagnetism. The two fields determining the physics of the system are the superconducting order parameter Ψ and the vector potential A. In its simplest version the order parameter, Ψ = |Ψ| exp (iφ), is a complex scalar. The resulting mean-field phase diagram was constructed by Abrikosov in 1957 [2] and provided a rather accurate description for all conventional superconductors. This mean-field H − T phase diagram of a type-II superconductor is shown schematically in Fig. 1. It comprises a Meissner phase characterized by complete flux expulsion