Dirac Fermion Renormalization near Topological Lifshitz Transitions

We study Coulomb interaction effects near a Lifshitz transition, where two Dirac cones with winding numbers +1 and -1 annihilate to form a semi-Dirac dispersion, with quadratic momentum dependence in one direction and linear in the other (winding number 0). The long-range Coulomb interaction leads to an extraordinary strong spectrum renormalization at weak coupling, with unconventional log squared contributions proliferating even at first order in the interaction. We show that the renormalization group (RG) analysis, which effectively resums these logs, leads to restoration of the linear dispersion in all directions at low energies. These exotic renormalized Dirac fermions are effectively anisotropic Dirac particles with winding number 0, as required by topological arguments and confirmed by our calculations. Moreover, our weak coupling RG fixed point is charactered by long-range Coulomb vertex where screening is virtually nonexistent. Hence, the fixed point is not continuously connected to the regime of “strong-coupling”, or ‘’large-N”, where non-Fermi liquid scenarios has been previously advocated. Therefore the analysis of experimental data for various semi-Dirac materials would depend strongly on the intrinsic value of the Coulomb coupling constant.
Ref: arXiv:2008.04326