Coulomb interactions and renormalization of topologically non-trivial semi-Dirac fermions

We discuss Coulomb interaction effects in type-II semi-Dirac fermions, relevant to TiO₂/VO₂ heterostructures, which are Chern insulators in the presence of spin-orbital coupling. Semi-Dirac fermions of this type can be viewed as arising from the merger of three Dirac points at a Lifshitz transition. We find that at low energy there is a very strong spectrum renormalization, which can be treated by renormalization group techniques in combination with a self-consistent screening RPA (Random Phase Approximation) approach. The result is a profound modification of the original energy dispersion under both the bare and screened Coulomb interaction. As a function of energy, the effective Fermi surface changes curvature from concave to convex. All physical characteristics (eg the density of states, Landau levels, etc.) are modified accordingly. Such very strong, asymptotically exact low-energy spectrum renormalization emerges as a general feature of 2D semi-Dirac systems, as it is also present for ordinary type-I semi-Dirac fermions produced by the merging two Dirac points. Therefore interpretation of experimental data for semi-Dirac systems at low temperatures must take into account Coulomb interaction effects which are much more pronounced compared to linear Dirac semimetals such as graphene.