The substrate model

This work has been done in collaboration with Matthew Dodgson and Alex Koshelev.

We apply a mean-field approach [1] to loosly coupled pancakes in layered superconductors in the c-direction, and summarise electromagnetic inter-layer interactions of pancakes (shown as blue spheres) in a "substrate" potential (shown as green surface). This reduces the computational complexity of the problem to performing a simulation of a two-dimensional pancake system in the presence of an additional potential (the substrate potential). More details can be found in this pre-print and in Phys. Rev. B. 67, 174508, 12 pages (2003)

Melting of the substrate

Here is a sequence of 4 pictures showing the melting transition within this model. On the left hand-side we see the substrate potential representing the inter-layer pancake interactions, and on the right hand side the resulting pancake distribution. Here, the temperature is sufficiently high, and the system melts into a pancake-liquid. Accordingly, the substrate looses its hexagonal structure, and will eventually flatten out (not shown).

Animations of the freezing and melting process can be found at

[1] M. J. W. Dodgson, A. E. Koshelev, V. B. Geshkenbein, and G. Blatter, Evaporation of the Pancake-Vortex Lattice in Weakly-Coupled Layered Superconductors Phys. Rev. Lett. 84, 2698 (2000)