The combination of Dirac physics and elasticity has been explored at length in graphene where the so--called elastic gauge fields have given rise to an entire new field of research and applications: Straintronics. The fact that these elastic fields c
ouple to fermions as the electromagnetic field, implies that many electromagnetic responses will have elastic counterparts not explored before. In this work we will first show that the presence of elastic gauge fields will be the rule rather than the exception in most of the topologically non--trivial materials in two and three dimensions. In particular we will extract the elastic gauge fields associated to the recently observed Weyl semimetals, the three dimensional graphene. As it is known, quantum electrodynamics suffers from the chiral anomaly whose consequences have been recently explored in matter systems. We will show that, associated to the physics of the anomalies, and as a counterpart of the Hall conductivity, elastic materials will have a Hall viscosity in two and three dimensions with a coefficient orders of magnitude bigger than the previously studied response. The magnitude and generality of the new effect will greatly improve the chances for the experimental observation of this topological, non dissipative response.
Here we describe how certain classes of two dimensional topological insulators, including the CdTe$/$HgTe quantum wells, display a new type of optical activity in two dimensions similar to the magneto-optical Kerr effect in the quantum Hall effect. T
his optical activity is characterized by a genuine Kerr angle and it is compatible with time reversal symmetry, being thus fundamentally different to other known types of time reversal invariant optical activity. The term responsible of such optical activity, having the form of $(mathbf{E}cdotpartialmathbf{B}/partial t-mathbf{B}cdotpartialmathbf{E}/partial t)$, can be considered a time reversal invariant counterpart of the magneto-electric term $mathbf{E}cdotmathbf{B}$. The microscopical origin of this response is a chiral non-minimal coupling between electrons and the external electromagnetic field. This optical activity constitutes a proof of principle that there is possible to find systems that are time reversal invariant displaying a genuine Kerr effect.
We show how the trigonal warping effect in doped graphene can be used to produce fully valley polarized currents. We propose a device that acts both as a beam splitter and a collimator of these electronic currents. The result is demonstrated trough a
n optical analogy using two dimensional photonic crystals.
