Coulomb interactions and renormalization of semi-Dirac fermions near a topological Lifshitz transition

TL;DR

This paper investigates how Coulomb interactions influence semi-Dirac fermions near a topological Lifshitz transition, revealing a flow towards Dirac cone restoration with anisotropic linear dispersion due to strong mass renormalization.

Contribution

It provides a detailed renormalization group analysis showing the emergence of Dirac cones from semi-Dirac fermions under Coulomb interactions at a Lifshitz transition, contrasting with large-N results.

Findings

Strong mass renormalization leads to Dirac cone restoration.

The system exhibits anisotropic but linear dispersion at low energy.

Berry phase remains zero due to time-reversal symmetry.

Abstract

We aim to understand how the spectrum of semi-Dirac fermions is renormalized due to long-range Coulomb electron-electron interactions at a topological Lifshitz transition, where two Dirac cones merge. At the transition, the electronic spectrum is characterized by massive quadratic dispersion in one direction, while it remains linear in the other. We have found that, to lowest order, the unconventional log squared (double logarithmic) correction to the quasiparticle mass in bare perturbation theory leads to resummation into strong mass renormalization in the exact full solution of the perturbative renormalization group equations. This behavior effectively wipes out the curvature of the dispersion and leads to Dirac cone restoration at low energy: the system flows towards Dirac dispersion which is anisotropic but linear in momentum, with interaction-depended logarithmic modulation. The Berry phase associated with the restored critical Dirac spectrum is zero - a property guaranteed by time-reversal symmetry and unchanged by renormalization. Our results are in contrast with the behavior that has been found within the large-$N$ approach.