Distorted hexagonal lattices

When a vortex lattice forms in a Type-II superconductor, it usually forms a hexagonal lattice, although this can be distorted, for example by some sort of coupling to the underlying crystal lattice, or by the directions of any nodes in the superconducting gap.  In some cases this can give rise to a square lattice.  Here, we are going to focus on small distortions of the hexagonal latiice.  In the perfect hexagonal case, the triangles that make up the hexagon are equilateral.  The easiest distortion to consider is that these equilateral triangles become isosceles triangles.  If they become scalene triangles, as in niobium, this is a bit trickier, and we will leave that for later.

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