Effective magnetic field induced by inhomogeneous Fermi velocity in strained honeycomb structures

In addition to the known pseudomagnetic field, nonuniform strains independently induce a position-dependent Fermi velocity (PDFV) in graphene. Here we demonstrate that, due to the presence of a PDFV, the Dirac fermions on a nonuniform (strained) honeycomb lattice may experiment a sort of magnetic effect, which is linearly proportional to the momentum of the quasiparticle. As a consequence, the quasiparticles have a sublinear dispersion relation. Moreover, we analyze the general consequence of a PDFV on the Klein tunneling of electrons through pseudomagnetic barriers. In particular, we report an anomalous (Klein) tunneling for an electron passing across velocity barriers with magnetic features. Our findings about the effects induced by a PDFV on Dirac fermions in a [two-dimensional (2D)] strained honeycomb lattice could be extended to (3D) Dirac and Weyl semimetals and/or its analogous artificial systems.