Phenomenology of a semi-Dirac semi-Weyl semimetal

We extend the semiclassical study of fermionic particle-hole symmetric semi-Dirac (more appropriately, semiDirac semi-Weyl) dispersion of quasiparticles, εK = ± √ (k2 x/2m) + (vky)) = ±ε0 √ K4 x +K2 y in dimensionless units, discovered computationally in oxide heterostructures by Pardo and collaborators. This unique system is a highly anisotropic sister phase of both (symmetric) graphene and what has become known as a Weyl semimetal, having 〈v2 y〉 ≈ v independent of energy, and 〈v2 x〉 ∝ m−1/2 √ ε being very strongly dependent on energy (ε) and depending only on the effective mass m. Each of these systems is distinguished by bands crossing (sometimes referred to as touching) at a point Fermi surface, with one consequence being that for this semi-Dirac system the ratio |χorb/χsp| of orbital to spin susceptibilities diverges at low doping. We extend the study of the low-energy behavior of the semi-Dirac system, finding the plasmon frequency to be highly anisotropic while the Hall coefficient scales with carrier density in the usual manner. The Faraday rotation behavior is also reported. For Klein tunneling at normal incidence on an arbitrarily oriented barrier, the kinetic energy mixes both linear (massless) and quadratic (massive) contributions depending on orientation. Analogous to graphene, perfect transmission occurs under resonant conditions, except for the specific orientation that eliminates massless dispersion. Comparisons of the semi-Dirac system are made throughout with both other types of point Fermi surface systems.