Surface Green's functions and quasiparticle interference in Weyl semimetals

We use the exact analytical technique introduced by us [Phys. Rev. B 101, 115405 (2020)] to recover the surface Green's functions and the corresponding Fermi-arc surface states for various lattice models of Weyl semimetals. For these models we use the $T$-matrix formalism to calculate the quasiparticle interference patterns generated in the presence of impurity scattering. In particular, we consider the models introduced by Kourtis et al. [Phys. Rev. B 93, 041109(R) (2016)] (model A) and Lau et al. [Phys. Rev. Lett. 119, 076801 (2017)] (model B), and we find that, as opposed to observations previously obtained via joint density of states and spin-dependent scattering probability, the interarc scattering in the quasiparticle interference features is fully suppressed in model A, and is very small in model B. Our findings indicate that these models may not correctly describe materials such as ${\mathrm{MoTe}}_{2}$, since for such materials interarc scattering is clearly visible experimentally, e.g., by Deng et al. [Nat. Phys. 12, 1105 (2016)]. We also focus on the minimal models proposed by McCormick et al. [Phys. Rev. B 95, 075133 (2017)], which indeed recover significant interarc scattering features.