Connection between in-plane upper critical field Hc2 and gap symmetry in layered d-wave superconductors

Angle-resolved upper critical field H-c2 provides an efficient tool to probe the gap symmetry of unconventional superconductors. We revisit the behavior of in-plane H-c2 in d-wave superconductors by considering both the orbital effect and Pauli paramagnetic effect. After carrying out systematic analysis, we show that the maxima of H-c2 could be along either nodal or antinodal directions of a d-wave superconducting gap, depending on the specific values of a number of tuning parameters. This behavior is in contrast to the common belief that the maxima of in-plane H-c2 are along the direction where the superconducting gap takes its maximal value. Therefore, identifying the precise d-wave gap symmetry through fitting experiments results of angle-resolved H-c2 with model calculations at a fixed temperature, as widely used in previous studies, is difficult and practically unreliable. However, our extensive analysis of angle-resolved H-c2 show that there is a critical temperature T*: in-planeH(c2) exhibits its maxima along nodal directions at T < T* and along antinodal directions at T* < T < T-c. The concrete value of T* may change as other parameters vary, but the existence of pi/4 shift of H-c2 at T * appears to be a general feature. Thus a better method to identify the precise d-wave gap symmetry is to measure H-c2 at a number of different temperatures, and examine whether there is a pi/4 shift in its angular dependence at certain T*. We further show that Landau level mixing does not change this general feature. However, in the presence of Fulde-Ferrell-Larkin-Ovchinnikov state, the angular dependence of H-c2 becomes quite complicated, which makes it more difficult to determine the gap symmetry by measuring H-c2. Our results indicate that some previous studies on the gap symmetry of CeCu2Si2 are unreliable and need to be reexamined, and also provide a candidate solution to an experimental discrepancy in the angle-resolved H-c2 in CeCoIn5.