Elastic Gauge Fields in Weyl Semimetals

We show that, as happens in graphene, elastic deformations couple to the electronic degrees of freedom as pseudogauge fields in Weyl semimetals. We derive the form of the elastic gauge fields in a tight-binding model hosting Weyl nodes and see that this vector electron-phonon coupling is chiral, providing an example of axial gauge fields in three dimensions. As an example of the new response functions that arise associated with these elastic gauge fields, we derive a nonzero phonon Hall viscosity for the neutral system at zero temperature. The axial nature of the fields provides a test of the chiral anomaly in high energy with three axial vector couplings.

Figure 1

Evolution of the band structure of the model given in Eq. (1) as a function of the parameter $b$. For $b_3=0$ the spectrum consists of two pairs of degenerate bands due to time reversal symmetry (a). When $0<b_3<m$ the band degeneracy breaks down and a high energy sector differentiates from a low energy sector, but the system is still gap full (b). When $b_3>m$, the low energy bands cross each other at two definite points in the Brillouin zone. At sufficiently low energies, the system consists of two pairs of Weyl fermions with opposite chirality (c).