  Assuming dislocations could be meaningfully described by torsion, we propose
here a scenario based on the role of time in the low-energy regime of
two-dimensional Dirac materials, for which coupling of the fully antisymmetric
component of the torsion with the emergent spinor is not necessarily zero.
Appropriate inclusion of time is our proposal to overcome well-known
geometrical obstructions to such a program, that stopped further research of
this kind. In particular, our approach is based on the realization of an exotic
$time-loop$, that could be seen as oscillating particle-hole pairs. Although
this is a theoretical paper, we moved the first steps toward testing the
realization of these scenarios, by envisaging $Gedankenexperiments$ on the
interplay between an external electromagnetic field (to excite the pair
particle-hole and realize the time-loops), and a suitable distribution of
dislocations described as torsion (responsible for the measurable holonomy in
the time-loop, hence a current). Our general analysis here establishes that we
need to move to a nonlinear response regime. We then conclude by pointing to
recent results from the interaction laser-graphene that could be used to look
for manifestations of the torsion-induced holonomy of the time-loop, e.g., as
specific patterns of suppression/generation of higher harmonics.

High Energy Physics - Theory;Materials Science;General Relativity and Quantum Cosmology