When a small magnetic field is applied to a superconductor, internal "supercurrents" are generated that completely expel the field, which is known as the Meissner effect. At higher applied fields most superconductors (called type-II) allow the field to penetrate, but the magnetic flux is quantized into tubes called vortices. When vortices are present, however, a superconductor isn't really superconducting, because the vortices move in the field and moving vortices create resistance to a current flow. In this vortex state zero resistance only occurs when the material has enough flaws to "pin" the vortices in place, forming a well defined vortex lattice as shown in the figure below. This lattice is two-dimensional in nature, and in two dimensions true long range structural order cannot exist. Hence the nature of the vortex lattice in superconductors, and the subtle role that pinning plays in the properties of superconductors, has been a topic of interest for decades. We have carried out small angle neutron scattering (SANS) measurements on the vortex lattice in the cuprate superconductor YBa2Cu3O7 (references below), as well as on the high quality prototypical elemental system of niobium that we now discuss.
As a superconductor is warmed, its critical current drops, but over a narrow range of temperatures the critical current suddenly increases and then decreases again. This "peak effect" is thought to be caused by a "softening" of the warming vortex lattice--with a Jell-O-like consistency, vortices can more easily find pinning sites (defects) in the atomic lattice, which briefly allows more supercurrent to flow. Our early data suggested that there was a melting transition to a "vortex liquid" in high temperature superconductors, but it's possible relation to the peak effect was unknown. A critical aspect was the subsequent inclusion of in-situ susceptibility measurements concurrent with the SANS measurements, which established that the peak effect was associated with a real melting transition to a "vortex liquid".
Inclined-field Structure, Morphology and Pinning of the Vortex Lattice in Microtwinned YBa2Cu3O7 Observed by Neutron Scattering, B. Keimer, I. Aksay, F. Dogan, R. W. Erwin, J. W. Lynn, and M. Sarikaya, Science 262, 83 (1993).
Reply to "Comment on Vortex Dynamics and Melting in Niobium", J. W. Lynn, N. Rosov, T. Grigereit, H. Zhang, and T. W. Clinton, Phys. Rev. Lett. 74, 1698 (1995).
Reply to `Comment on `Vortex Lattice Symmetry and Electronic Structure in YBa2Cu3O7', B. Keimer, W. Y. Shih and J. W. Lynn, Phys. Rev. Lett. 75, 1423, (1995).
Vortex Dynamics and Melting in Niobium, J. W. Lynn, N. Rosov, and T. E. Grigereit, J. Mag. Mag. Matr. 140-144, 2067 (1995).
Superheating and Supercooling of Vortex Matter in a Nb Single Crystal: Direct Evidence for a Phase Transition at the Peak Effect using Neutron Diffraction, X. S. Ling, S. R. Park, B. A. McClain, S. M. Choi, D. C. Dender, and J. W. Lynn, Phys. Rev. Lett. 86, 712 (2001).
Reply to Comment on "Direct Observation of Superheating and Supercooling of Vortex Matter using Neutron Diffraction", X. S. Ling, S. R. Park, S. M. Choi, D. C. Dender, and J. W. Lynn, Phys. Rev. Lett. 89, 259702 (2002).
Fate of the Peak Effect in a Type-II Superconductor: Multicriticality in a Bragg Glass, S. R. Park, S. M. Choi, D. C. Dender, J. W. Lynn, and X. S. Ling, Phys. Rev. Lett. 91, 167003 (2003).
Peak Effect in Polycrystalline Vortex Matter, I. K. Dimitrov, N. D. Daniilidis, C. Elbaum, J. W. Lynn, and X. S. Ling, Phys. Rev. Lett. 99, 047001 (2007).
Emergence of Quasi-Long-Range Order in a Crystallizing Vortex Lattice, N. D. Daniilidis, S. R. Park, I. K. Dimitrov, J. W. Lynn, and X. S. Ling, Phys. Rev. Lett. 99, 147007 (2007).
Neutron Investigation of the Magnetic Scattering in an Iron-based Ferromagnetic Superconductor, Jeffrey W. Lynn, Xiuquan Zhou, Christopher K. Borg, Shanta R. Saha, Johnpierre Paglione, and Efrain E. Rodriguez, Phys. Rev. B 92, 060510(R) (2015).