Continuous Two-Dimensional Melting of Vortex-Solid in High Temperature Superconductors
- PDF / 295,055 Bytes
- 4 Pages / 420.48 x 639 pts Page_size
- 6 Downloads / 172 Views
CONTINUOUS TWO-DIMENSIONAL MELTING OF VORTEX-SOLID IN HIGH TEMPERATURE SUPERCONDUCTORS N.-C. YEH Department of Physics, California Institute of Technology Pasadena, CA 91125 ABSTRACT A model of continuous two-dimensional melting in the mixed state of high temperature superconductors is proposed. Two-dimensional melting sets in at a cross-over temperature T.(H) below the three-dimensinal phase transition TM(H) due to finite size effects, and T.(H) is a function of the sample thickness (1,), applied magnetic field (H), and x(= A/a). For a given zero-field transition temperature To 0 and material properties, (such as defect density), the onset temperature of 2D-melting (T,(H)) decreases with decreasing sample thickness and increasing magnetic field. In transport studies, thermally induced melting is further complicated by the depinning effect of high current densities. INTRODUCTION Despite intense effort in trying to understand the mixed state properties of high temperature superconducting oxides[1 -4], whether the low temperature phase is a true zero-resistance, "vortex-solid" state, or may be described by the conventional flux-creep model which asserts non-zero resistance at any finite temperature, remains an unsettled issue. Even if such a "vortex-solid" state does exist, whether the vortexsolid phase is a nearly perfect Abrikosov lattice in the weak pinning limit[l, 4], or a "glass"-like state[2], is also to be resolved. Recent controversial experimental results and interpretations[5 - 10] have added more complications to this issue. In this paper, we consider an extreme type-II superconductor (K >> 1) with high critical temperature (To0), large anisotropy, and randomly distributed defects. We assume that random defects in these superconducting oxides modifies the temperature dependence of the upper critical field. Using the elastic theory proposed by Nelson&Seung[1] and Brandt[4], we show that finite size effects result in a continuous two-dimensional melting below the "renormalized" upper critical field. THE VORTEX-SOLID PHASE Since thermal fluctuation of flux lines is amplified by the presence of disorder, we may first assume a "renormalized" upper critical field 2
HM(T) = HM(0)(1 - T/Too) e,
(1)
where To0 is the zero-field superconducting transition temperature, and v > 2/3 for a disordered 3D-XY model. We note that HM(T) is different from the mean-field upper critical field H,2 (T) = H,2(O)(1-TITo), which corresponds to v = 1/2. The shear modulus p is reduced from its mean-field value, and we may define a renormalized shear modulus as PR- The vortex-solid melting transition in the presence of disorder is defined as the temperature TM(H) at which PR rý 0[1,4]. In this context, we can introduce a vortex correlation length 4 which measures the size of fluctuation[l] and diverges near the melting temperature TM; i.e., & -r oo for T - TM(H). In an anisotropic system, the correlation length can be broken into two components: the longitudinal correlation length 4,ll (along the magnetic field) and the perpendicula
Data Loading...
