A continuum model to study the influence of dislocations on the electronic properties of condensed matter systems was described and analyzed. The model was based on a geometrical formalism that associates a density of dislocations with the torsion tensor and used the technique of quantum field theory in curved space. When applied to two-dimensional systems with Dirac points like graphene it was found that dislocations couple in the form of vector gauge fields similar to these arising from curvature or elastic strain. Ways in which to couple dislocations to normal metals with a Fermi surface were also described.

Dislocations and Torsion in Graphene and Related Systems. F.de Juan, A.Cortijo, M.A.H.Vozmediano: Nuclear Physics B, 2010, 828[3], 625-37