Correlated second-order Dirac semimetals with Coulomb interactions

TL;DR

This paper studies how long-range Coulomb interactions affect the low-temperature behavior of second-order Dirac semimetals, revealing anisotropic effects and crossover phenomena distinct from first-order Dirac semimetals.

Contribution

It introduces a renormalization group analysis of Coulomb interactions in second-order Dirac semimetals, highlighting anisotropy and crossover scales not present in first-order counterparts.

Findings

Coulomb coupling flows to zero at low energies.

Anisotropic screening potential at short distances.

Existence of a crossover temperature scale $T_c$.

Abstract

We investigate the effects of long range Coulomb interactions on the low-temperature properties of a second-order Dirac semimetal in terms of the renormalization group. In contrast to the first-order Dirac semimetal, the full rotation symmetry is broken even in the continuum limit, and thus the low-energy physics is controlled by two dimensionless parameters: the dimensionless coupling constant and the ratio of the anisotropy parameters. We show that the former flows to zero and the latter flows to a fixed value at low energies. Thus, one may calculate physical quantities in terms of the renormalized perturbation theory. As an application, we determine the temperature dependence of the specific heat by solving the renormalization-group equations. Following from the breaking of the full rotation symmetry, there exists a crossover temperature scale $T_c$ (and a length scale $L_c$). Physical quantities approach the values for the first-order Dirac semimetal only when the temperature is much smaller than $T_c$. Similarly, the screened Coulomb potential will become anisotropic when the distance is smaller than $L_c$, while the unscreened form is recovered at its tail.