M.Sc Student | Abravanel Ronen |
---|---|

Subject | Intermediate Phase in a Pinned Superconducting Vortex Lattice |

Department | Department of Physics |

Supervisor | Professor Daniel Podolsky |

Full Thesis text |

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.