Interaction renormalization of generalized semi-Dirac fermions

We present a generalization of semi-Dirac fermions, and study the effects of long range Coulomb electron-electron interactions on the low energy excitations of such systems. We consider a class of two-dimensional Hamiltonians with a dispersion that is linear in one momentum direction, and an even monomial (of degree 2n) in the other. This allows us to illustrate how the degree of flatness in the non-relativistic direction affects the underlying physics. Such flat anisotropic fermionic spectra may be realized at a Lifshitz transition characterized by the merger of two lower degree generalized semi-Dirac points.



A first-order perturbative treatment of interactions produces infrared divergences in the self-energy corrections to the coupling parameters (velocity and generalized mass). We discuss the exact solutions of the perturbative renormalization group equations, within the RPA framework, which yield an extraordinarily strong spectrum renormalization at low energies whereby the flatness in the non-relativistic direction is dramatically reduced, resulting in quasi-linear behavior. Thus Coulomb interactions have a profound effect on the fermionic spectrum, and subsequently on all physical observables at low temperature.