Coulomb Interactions and Renormalization of semi-Dirac fermions*

We discuss Coulomb interaction effects for “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 a result of three Dirac points merger. We find that at low energy there is  a very strong, double logarithmic mass renormalization, which can be treated by renormalization group techniques. The result is a profound modification of the original dispersion in the quadratic direction, which at low energies becomes sub-linear with power 2/3.  All physical characteristics (e.g. the density of states) 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 “conventional”, type - I semi-Dirac fermions, produced by merging two Dirac points. Therefore  interpretation of experimental data at low temperatures has to take into account Coulomb interaction effects which for semi-Dirac fermions are much more pronounced compared to linear Dirac semimetals (such as graphene).