Hierarchical structure formation in layered superconducting systems with multiscale intervortex interactionsChristopher N. Varney and Karl A. H. Sellin and QingZe Wang, and Hans Fangohr and Egor Babaev Hierarchical structure formation in layered superconducting systems with multiscale intervortex interactions, Journal of Physics: Condensed Matter 25, 415702 (2013). Chosen for IoP Select for quality and recency. PDFs are available
Overview 1 Context1.1 LennardJones potentialThe physics and emergent behaviour of interacting particles has long standing history: classical computational problems include the simulation of the behaviour of many atoms in liquids, solids, proteins etc, and common simulation techniques are Molecular Dynamics and (Metropolis) Monte Carlo methods. For both, we need to know the pairwise interaction potential between two particles (we ignore here systems that require 3 and more body interactions to be considered). For example, the well known Lennard Jones potential (shown in Figure A (left) above) for two particles such as inert atoms, has a repulsive term that for short distances R increases the energy (of the type \(1/R^{12}\), and an attractive term (of the type \(1/R^6\)). The first term originates in strong repulsion of electron orbitals that start to overlap, the second in weak attraction from induced electrical polarisation. The two terms combined result in a potential as shown in figure 1a), which has a minimum at a distance A0 (approximately 3 for the schematic sketch): each pair of particles has the lowest possible energy if they can be separated by this distance A0. 1.2 Repulsive potentialAnother area of complex system research that uses particlebased simulation techniques such as Molecular Dynamics and Monte Carlo methods is that of the the dynamics of vortex lines in (Type II) superconductors. In these systems, the vortex lines always repel each other, and a corresponding potential is shown in figure A (right): for all distances, the energy decreases if we increase the distance between the two interacting objects, separated by a distance R. In these systems, the vortex lines cannot escape the sample, so that they will arrange in a way to minimise they energy, which is  in the absence of any other disordering effects and absence of geometrical constraints of the sample  a hexagonal lattice. 2 Novelty in this workRecently, the possibility of more complicated intervortex interactions in newly discovered systems (socalled Type 1.5 superconductors) has attracted much attention: in multicomponent and multilayer superconductors the interaction potential:
Figure C demonstrates a repulsive potential with multiple length scales: for shortest length scales, the interaction energy is high (although for the discrete function on the left it doesn't matter what the particle separation is as long as the distance is with the range for which the potential is constant), and decreases as the separation increases. The figure on the right shows a physically more realistic potential with smooth rather than discrete step changes. 4 Summary
5 Bibtex fileThe bibtex entry is available here. A nearly identical version of this summary is available here. 
