Flux-line entanglement as the mechanism of melting transition in high-temperature superconductors in a magnetic field

The mechanism of the flux-line-lattice melting in anisotropic high-Tc superconductors in B ‖ ĉ is clarified by Monte Carlo simulations of the 3D frustrated XY model. The percentage of entangled flux lines abruptly changes at the melting temperature Tm, while no sharp change can be found in the number of loop excitations around Tm. Therefore, the origin of this melting transition is the entanglement of flux lines. The Lindemann number is evaluated as cL ≈ 0.30 regardless of anisotropy, which confirms the validity of the Lindemann criterion for this melting transition. 74.60.Ge, 74.25.Dw, 74.20.De, 74.25.Bt Typeset using REVTEX 1 Nature of the mixed phase in type-II superconductors has been studied for many years, and much attention has been paid to this field since the discovery of high-Tc superconductors (HTSC) because of short correlation lengths and large anisotropy. In HTSC in a magnetic field along the c axis, the flux-line lattice (FLL) melts at much lower temperatures or in much weaker fields [1] than those predicted by the Abrikosov mean-field theory, where the superconducting phase transition is of second order regardless of details of models. The FLL melting in HTSC was first theoretically analyzed by Nelson and Seung [2] on the basis of the mapping to a two-dimensional Boson model, and they pointed out that the Lindemann criterion might be valid in this FLL melting because of large fluctuations in HTSC owing to large anisotropy and high transition temperatures. Similar theoretical analysis was also made by Houghton et al. [3] independently. Earlier experiments of “the FLL melting in HTSC” as reviewed in Ref. 1 were found to be explained better by the vortex-glass transition [4] rather than by the FLL melting transition. In clean systems, the “true” FLL melting was confirmed afterwards by experiments [5–10] and computer simulations [11–18], and the first-order FLL melting transition in a magnetic field has now been established in extremely type-II superconductors such as HTSC. On the other hand, the mechanism of the FLL melting has not yet been well understood. In Nelson’s theory [2,19], this transition is characterized by the entanglement of flux lines. However, this picture is challenged by some authors who claim that thermal excitations of small vortex loops [20,21], which are not included in Nelson’s theory, are important. In their picture, the FLL melting is characterized by the blowout of loop excitations. In order to resolve this controversy, the first-order phase transition should be identified by measuring thermodynamic quantities, and the behavior of flux lines induced by an external magnetic field and thermally excited vortex loops should be observed microscopically in the vicinity of the melting temperature. In this Letter, the three-dimensional anisotropic, frustrated XY model is analyzed with the Monte Carlo method from the above point of view. Our main results are as follows: First, the mechanism of the first-order FLL melting transition is exclusively the entanglement of 2 flux lines. The percentage of entangled flux lines sharply changes at the melting temperature Tm, while the number of loop excitations has a smooth temperature dependence around Tm. Second, the Lindemann number takes nearly a constant value cL ≈ 0.30 regardless of the anisotropy constant, and thus the use of the Lindemann criterion is justified for the determination of the melting line in a phase diagram. As the model of the anisotropic, extremely type-II HTSC in a magnetic field along the c axis, we consider the three-dimensional anisotropic, frustrated XY model [15,22] described by the following Hamiltonian,