Pii: S0038-1098(99)00092-7

By taking account of the complex relaxation times for sand d-wave order parameters in the time-dependent Ginzburg– Landau equations, our results indicate that the imaginary parts of the relaxation times can change the sign of the Hall angle for mixed sand d-wave superconductors. The effect of the concentration of the nonmagnetic impurities on the Hall angle is investigated, and it is found that the concentration of the nonmagnetic impurities can affect the parameters in the Ginzburg– Landau free energy and the relaxation times. The results of the anomalous Hall effect arising from the nonmagnetic impurities are discussed. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. High-Tc superconductors; D. Electronic transport; D. Galvanomagnetic effects The pairing symmetry of the order parameter in high-Tc superconductors (HTS) attracts attention and a number of experimental observations strongly support the d-wave pairing symmetry [1–3]. Most of the theories proposed that the superconducting state might be relevant to the heavy fermion and the high-Tc superconductors [4–6]. Based on group theory arguments, the phenomenological Ginzburg–Landau (GL) theory with many unknown parameters has been studied [4,5,7]. Ren et al. [8,9] microscopically derived the GL equations for the pure d-wave as well as mixed sand d-wave superconductors in the framework of the weak coupling theory. Recently attention has been focussed on the anomalous behavior of the Hall effect, which appears to undergo a sign change in the superconducting mixed state [10–15]. The phenomenological theories about the vortex motion have been proposed to investigate the anomalous Hall effect of superconductors [16– 20]. Dorsey [20] introduced a complex relaxation time in the time-dependent Ginzburg–Landau (TDGL) equation and then derived the equation of motion for a single vortex Vs1 × ẑ ˆ a1VL 1 a2VL × ẑ; …1† where (a 1 and a 2 are functions of the parameters that appear in the TDGL equation. The results showed that, if a 2 , 0, the Hall effect in the vortex state will change its sign, which is opposite to the sign of the normal-state Hall effect. Experimental measurements in Tl2Ba2CaCuO8 systems also showed a consistent description of the behavior of the imaginary part of the order parameter relaxation time [21]. However, the problems of the Hall effect for d-wave superconductors have not been fully understood. Following the generalized London theory, derived by Affleck et al. [22], Alvarez, Domı́nguz and Bleeder Solid State Communications 110 (1999) 425–430 0038-1098/99/$ see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-1098(99)00092-7 PERGAMON * Corresponding author. Tel.: 1886-3-5712-121 ex56081; fax: 1886-3-5725-230. E-mail address: [email protected] (T.J. Yang) studied the dynamics of vortices in d-wave superconductors. They found that an intrinsic Hall effect depended on sin…4j† with an angle j with respect to the b crystal axes [23]. Dai and Yang [19] have elucidated that both the imaginary parts of the relaxation times for the order parameters and the parameters in the GL free energy functional can affect the anomalous Hall effect for a pure d-wave superconductor. Here we will investigate the Hall effect for mixed sand d-wave superconductors from the TDGL equations. The phenomenological TDGL equations in the dimensionless form for dx22y2 superconductors can be expressed as hd…2t 1 i ~ f †d ˆ add 1 83 b2 b1 udud 1 4