Precision measurements of the magnetic field dependence of the penetration depth in YBCO: An experimental study of the nonlinear Meissner effect

Motivated by a well established body of theoretical work on the nonlinear Meissner state electrodynamics of type II superconductors, we have developed a high sensitivity ac susceptometer to measure the magnetic field dependence of the penetration depth λ in single crystal YBa₂Cu ₃O_7−δ. The susceptometer is capable of measuring changes in the penetration depth in typical sized crystals to within a few tenths of an Angstrom. This represents a significant increase in the resolution of such a device, and offers increased functionality over superconducting microwave resonators in its ability to measure Δλ as a function of field as well as temperature. In addition, we have developed appropriate procedures to ensure that our field dependent measurements remained free of unwanted magnetic flux penetration into the sample, and that subsequent results represented the intrinsic nonlinear Meissner response of the sample. This has allowed us to test present ideas about the nature of high temperature superconductivity through an accurate comparison of Δλ( H) measurements with theory.; In particular, the theory predicts that a d-wave superconductor will exhibit a field dependent penetration depth that is linear in field near T = 0 and crosses over to a weak quadratic field dependence with increased temperature. Furthermore, the magnitude of this effect should depend on the direction of the applied field with an anisotropy that reflects the symmetry of both the superconducting order parameter and the crystal structure.; Measurements presented in this thesis were made on three high quality single crystals of YBa₂Cu₃O_7−δ. In all cases, the field dependence of the penetration depth could not be described in full by the theory of the Nonlinear Meissner Effect. The anisotropy seen in Δλ(H) may be a result of the orthorhombic crystal structure and the strong anisotropy in the zero temperature, in-plane penetration depth λ_a,b(0), and as such may be consistent with theory. However, theory also predicts a strong suppression of Δλ(H) with increasing temperature, in stark contrast to the measurements which show a small increase.; We believe the d_x2−y2 symmetry of YBa₂Cu₃O_7−δ to be well established by other experiments, and do not think that our results represent evidence contrary to this fact. Rather, it is our contention that present theories of the Nonlinear Meissner Effect simply do not describe in full the nonlinear behaviour of the penetration depth in a d-wave superconductor. Our results are also compared with a very recent idea of a field induced gap suppression in a d-wave superconductor; this theory showed some success in its ability to correctly predict the direction in which Δλ(H) evolves with temperature. We also show that there is evidence for a possible c-axis contribution to Δλ(H). Overall, at present there appears to be no single theory that can explain the field dependence of the penetration depth measured here for YBa₂Cu₃O _7−δ.