Magnetic field induced 3D–1D crossover in type-II superconductors

Abstract

Abstract. 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 H i , applied along the i-axis, cannot grow beyond the limiting magnetic length1/2 , 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 line H C2 (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 YBa 2 Cu 4 O 8 , NdBa 2 Cu 3 O 7−δ , YBa 2 Cu 3 O 7−δ , and DyBa 2 Cu 3 O 7−δ , where 3D-xy critical behavior was already observed in zero field. Indeed, our analysis of the reversible magnetization of RbOs 2 O 6 and the specific heat of Nb 77 Zr 23 , Nb 3 Sn and NbSe 2 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 H pi (T ) superconductivity is confined to cylinders with diameter L H i (1D) and there is no continuous phase transition in the (H, T ) -plane along the H c2 (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 YBa 2 Cu 4 O 8 , NdBa 2 Cu 3 O 7−δ , YBa 2 Cu 3 O 7−δ , and DyBa 2 Cu 3 O 7−δ it turns out to be driven by 3D-xy thermal fluctuations, the specific heat data of the conventional type-II superconductors Nb 77 Zr 23 , Nb 3 Sn and NbSe 2 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.

Evidence for Kosterlitz-Thouless and three-dimensionalXYcritical behavior inBi2Sr2CaCuSchneider1, Giannini2 2009Phys. Rev. B17170View full textAdd to dashboardCite

“…Indeed, in Bi 2 Sr 2 CaCu 2 O 8+δ this peak shifts, 18 opposite to the generic behavior. 4,6 Given the Maxwell relation, vs. T for various magnetic fields reveals consistency with the anomalous shift of the specific heat peak. Indeed the dip shifts towards higher temperatures.…”

Diamagnetism, Nernst signal, and finite-size effects in superconductors above the transition temperatureTc

“…31,32 In this limit the system corresponds in D = 3 to independent superconducting cylinders of radius L Hz ∝ (Φ 0 /H z ) 1/2 and height ξ z and in D = 2 with height ξ z = d. Detailed calculations in D = 2 reveal that the crossover from the low to the high field limit occurs monotonically and according to that there is no minimum.…”

“…31 We assume that the magnetic field is applied along the z-axis. ξ x,y,z denote the correlation length along the respective axis in zero field.…”

Anisotropy of the superconducting transport properties of the LaAlO3/SrTiO3 interface

“…However, in the presence of a magnetic field this divergence is removed due to the limiting magnetic length, so that ˜͑ H Ќ , T BKT ͒ ϰ ͱ ͑⌽ 0 ͒ / ͑aH Ќ ͒ and ˜͑ H ʈ , T BKT ͒ ϰ ͑⌽ 0 ͒ / ͑aH ʈ d͒, where a Ϸ 3.12 is a universal constant. 22 The sheet conductance and the correlation length are related by ˜͑ T͒ ϰ ͱ f ͑T͒, where f is the SC fluctuation conductance related to the measured conductance by = 0 + f , 0 being the residual conductance. 21,22 T BKT was determined for the sample investigated here following the procedure described in Ref.…”

“…22 The sheet conductance and the correlation length are related by ˜͑ T͒ ϰ ͱ f ͑T͒, where f is the SC fluctuation conductance related to the measured conductance by = 0 + f , 0 being the residual conductance. 21,22 T BKT was determined for the sample investigated here following the procedure described in Ref. 2 ness of about 7 nm to be determined by taking the ratio of the high field slopes.…”