On the renormalization of Coulomb interactions in two-dimensional tilted Dirac fermions

TL;DR

This paper studies how long-range Coulomb interactions affect two-dimensional tilted Dirac fermions, revealing that type-II Dirac semimetals are stable and exhibit distinct renormalization behaviors compared to type-I, impacting physical properties like screening and thermodynamics.

Contribution

It introduces a new RG approach with an energy cutoff for open Fermi surfaces, showing the stability of type-II Dirac fermions under Coulomb interactions and their unique renormalization effects.

Findings

Type-II Dirac fermions are stable against Coulomb interactions.

Velocities in different directions are differentially renormalized.

Type-II Dirac fermions exhibit complete impurity charge screening with long screening length.

Abstract

We investigate the effects of long-ranged Coulomb interactions in a tilted Dirac semimetal in two dimensions by using the perturbative renormalization-group method. Depending on the magnitude of the tilting parameter, the undoped system can have either Fermi points (type-I) or Fermi lines (type-II). Previous studies usually performed the renormalization-group transformations by integrating out the modes with large momenta. This is problematic when the Fermi surface is open, like type-II Dirac fermions. In this work, we study the effects of Coulomb interactions, following the spirit of Shankar\cite{Shankar}, by introducing a cutoff in the energy scale around the Fermi surface and integrating out the high-energy modes. For type-I Dirac fermions, our result is consistent with that of the previous work. On the other hand, we find that for type-II Dirac fermions, the magnitude of the tilting parameter increases monotonically with lowering energies. This implies the stability of type-II Dirac fermions in the presence of Coulomb interactions, in contrast with previous results. Furthermore, for type-II Dirac fermions, the velocities in different directions acquire different renormalization even if they have the same bare values. By taking into account the renormalization of the tilting parameter and the velocities due to the Coulomb interactions, we show that while the presence of a charged impurity leads only to charge redistribution around the impurity for type-I Dirac fermions, for type-II Dirac fermions, the impurity charge is completely screened, albeit with a very long screening length. The latter indicates that the temperature dependence of physical observables are essentially determined by the RG equations we derived. We illustrate this by calculating the temperature dependence of the compressibility and specific heat of the interacting tilted Dirac fermions.