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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 couple 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.
We study the single-particle spectrum of three-dimensional Weyl semimetals taking into account electron-phonon interactions that are the result of straining the material. We find that a well-defined fermionic excitation appears in addition to the sta
We show that 3D Lifshitz fermions arising as the critical theory at the Weyl semimetal/insulator transition naturally develop an anomalous Hall viscosity at finite temperature. We discuss how to couple the system to non-relativistic background source
Electrons in low-temperature solids are governed by the non-relativistic Schr$ddot{o}$dinger equation, since the electron velocities are much slower than the speed of light. Remarkably, the low-energy quasi-particles given by electrons in various mat
The breaking of parity and time-reversal symmetry in two-dimensional Fermi liquids gives rise to non-dissipative transport features characterized by the Hall viscosity. In magnetic fields, the Hall viscous force directly competes with the Lorentz for
Torsional strain in Weyl semimetals excites a unidirectional chiral density wave propagating in the direction of the torsional vector. This gapless excitation, named the chiral sound wave, is generated by a particular realization of the axial anomaly