טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentAbravanel Ronen
SubjectIntermediate Phase in a Pinned Superconducting Vortex
Lattice
DepartmentDepartment of Physics
Supervisor Professor Daniel Podolsky
Full Thesis textFull thesis text - English Version


Abstract

We study the phase diagram of a two dimensional XY model in an orbital magnetic field, as a function of temperature. A bipartite lattice of vortex-pinning sites is present, and the magnetic field is fixed such that there is one vortex for every two pinning sites. The low temperature phase in this model breaks not only the U(1)   symmetry of the spin degree of freedom, but it also breaks a Z?2   symmetry, which describes which of the pinning sublattices is occupied by vortices. Using extensive Monte Carlo simulation, we find that this order melts in two stages as the temperature is increased. At the first phase transition the helicity modulus drops to zero and the U(1)  spin symmetry is restored. However, the system does not disorder completely at this point, as the average density of vortices on the two sublattices remains different. At a slightly higher temperature, the system undergoes a second transition, where the vortex density difference vanishes, thus restoring the Z?2  symmetry.

We provide a phenomenological picture that explains the sequence of phase transitions, and that provides a criterion for the size of the intermediate phase. In particular, the Ising transition is predicted to occur when the density of thermally-induced vortices drops beneath the distance between two adjacent magnetically-induced vortices. This is confirmed by indirect measurements of the correlation length. In addition, we argue that our model can be mapped into a fully-frustrated XY model, a system that is known to contain two similar phase transitions. The nature of the Z?2  transition in the fully-frustrated model has been disputed recently -  in our model we give numerical evidence that the Z?2   transition is in the Ising universality class.