Nonlocal Ginzburg-Landau Model for High-Temperature Superconductors in a Magnetic Field

Abstract

2) The Ginzburg-Landau model is particularly useful to derive such vortex structures and to discuss the behavior near the· upper critical magnetic field H C2• However, for high-temperature superconductors, the coherence lengths are very shore)-5) and the modification of the model may be required near HC2• Experimentally, the jump of the specificheat 6 ) and the resistive transition i~ a magnetic field 7 )-9) have been observed. These behaviors are different from the conventional superconductors. In this paper, we consider the generalized phenomenological Ginzburg-Landau model in a magnetic field. We particularly investigate the nonlocal interaction. In a magnetic field, the two-dimensional degree of freedom, which is perpendicular to the magnetic field direction, is quantized and the dimensional reduction occurs near Hc2 • The behavior of the specific jump in a magnetic field has been investigated 10 )-12) for the conventional GL model by the fact of this dimensional reduction. The study of the generalization to the nonlocal interaction is motivated by two following reasons. The first is that our generalized model has a remarkable similarity to the n-compo­ nent GL model. We find that a parameter of the characteristic range of the nonlocal interaction play the role of the number of the component n. This observation leads us to develop the series expansion which is similar to lin expansion without introduc­ ing a fictitious number of n for the superconductors. The second reason is that the high-temperature superconductor has very short coherence length and therefore, the interaction of point contact should be modified particularly near H c2• The distance between the vortices near HC2 becomes 2.7~ for a triangle vortex lattice and ~(o) is about loA for YBCO. 3 )-5) It may be possible that the attractive pairing interaction has the same order range of the length. We introduce a new length of the nonlocal interaction which may depend upon the microscopic mechanism of the attractive force of the paired electrons. The renormalization group analysis reveals that the non­ local interaction is generated by the renormalization procedure. 13 ) Therefore, further